Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July...

218
Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino

Transcript of Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July...

Page 1: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

Phases of Gauge Theories

July 2010 @ Quark Matter - Roma

Francesco Sannino

Page 2: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%
Page 3: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%
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Cosmology

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Atoms4%

Dark Matter22%

Dark Energy74%

Cosmology

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Low Energy Effective TheoryStandard Model

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Low Energy Effective Theory

SM

Standard Model

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WW Scattering

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WW Scattering

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S-wave amplitude:

WW Scattering

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S-wave amplitude:

WW Scattering

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S-wave amplitude:

WW Scattering

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S-wave amplitude:

Unitarity:

WW Scattering

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Theorem:

Unitarity requires the existence of a weakly coupled Higgs particle or New Physics around the Terascale!

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Origin of mass

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The Higgs

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Custodial symmetries

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Custodial symmetries

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Custodial symmetries

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Custodial symmetries

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SUL(2)× UY (1)

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SUL(2)× UY (1)

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m2 < 0

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|H|

m2 < 0

�σ2� ≡ v2 = |m2|λ

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|H|

m2 < 0

�σ2� ≡ v2 = |m2|λ

σ = v + h

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Gauge Boson-Masses

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Gauge Boson-Masses

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Gauge Boson-Masses

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Gauge Boson-Masses

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−λd QL · HdR

Gauge Boson-Masses

Quark-Masses

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−λd QL · HdR

Gauge Boson-Masses

Quark-Masses

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−λd QL · HdR

Gauge Boson-Masses

Quark-Masses

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SM Higgs: Current Status:

0

1

2

3

4

5

6

10030 300

mH [GeV]

!"2

Excluded Preliminary

!#had =!#(5)

0.02758±0.000350.02749±0.00012incl. low Q2 data

Theory uncertaintymLimit = 144 GeV

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Higgs mechanism in Nature

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Superconductivity

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Macroscopic-ScreeningNon-Relativistic

SM-ScreeningRelativistic

Superconductivity

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Macroscopic-ScreeningNon-Relativistic

SM-ScreeningRelativistic

Superconductivity

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Macroscopic-ScreeningNon-Relativistic

SM-ScreeningRelativistic

Superconductivity

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|H|2 =v2

2

Macroscopic-ScreeningNon-Relativistic

SM-ScreeningRelativistic

Superconductivity

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Meissner-MassStatic Vector Potential

Weak-GB-Mass

Page 46: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

Meissner-MassStatic Vector Potential

Weak-GB-Mass

Page 47: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

Meissner-MassStatic Vector Potential

Weak-GB-Mass

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Meissner-MassStatic Vector Potential

Weak-GB-Mass

Page 49: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

Meissner-MassStatic Vector Potential

Weak-GB-Mass

Page 50: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

Meissner-MassStatic Vector Potential

Weak-GB-Mass

Hidden structure

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Meissner-MassStatic Vector Potential

Weak-GB-Mass

Hidden structure ????

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Instability of the Fermi Scale

Page 53: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%
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M2H

= 2λ v2

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Quantum corrections

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Quantum corrections

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A mass appears even if ab initio is set to zero!

Quantum corrections

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No custodial symmetry protecting a scalar mass.

A mass appears even if ab initio is set to zero!

Quantum corrections

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Hierarchy between the EW scale and the Planck Scale.

No custodial symmetry protecting a scalar mass.

A mass appears even if ab initio is set to zero!

Quantum corrections

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Definition of Natural

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Small parameters stay small under radiative corrections.

Definition of Natural

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Electron mass

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If set to zero the U(1)L× U(1)R forbids its regeneration

Electron mass

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If set to zero the U(1)L× U(1)R forbids its regeneration

Naturalness begs an explanation of the origin of mass.

Electron mass

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If set to zero the U(1)L× U(1)R forbids its regeneration

Naturalness begs an explanation of the origin of mass.

No conflict with any small value of the electron mass

Electron mass

Page 66: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%
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Low Energy Effective TheoryMany Models

(?)MSSMXLMS D

AdS/?Unparticle

Branes......

Technicolor

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Low Energy Effective TheoryMany Models

(?)MSSMXLMS D

AdS/?Unparticle

Branes......

Technicolor

$

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Theory landscape

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Gauge Group

Theory landscape

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Gauge Group

Matter

Theory landscape

Page 74: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

Gauge Group

SUSY

Matter

Theory landscape

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Gauge Group

SUSY

Matter

N=1

N=2

N=4

Theory landscape

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Gauge Group

SUSY Non SUSY

Matter

N=1

N=2

N=4

Theory landscape

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Gauge Group

SUSY Non SUSY

Matter

N=1

N=2

N=4

Fermions

Fermions + Bosons

Bosons

Theory landscape

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Gauge Group

SUSY Non SUSY

Matter

N=1

N=2

N=4

Fermions

Fermions + Bosons

Bosons

Vector

Theory landscape

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Gauge Group

SUSY Non SUSY

Matter

N=1

N=2

N=4

Fermions

Fermions + Bosons

Bosons

Vector Chiral

Theory landscape

Page 80: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

Gauge Group

SUSY Non SUSY

Matter

N=1

N=2

N=4

Fermions

Fermions + Bosons

Bosons

Vector Chiral

Theory landscape

Page 81: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

Gauge Group

SUSY Non SUSY

Matter

N=1

N=2

N=4

Fermions

Fermions + Bosons

Bosons

Vector Chiral

Theory landscape

Page 82: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

Gauge Group

SUSY Non SUSY

Matter

N=1

N=2

N=4

Fermions

Fermions + Bosons

Bosons

Vector Chiral

Theory landscape

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Phases

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α(r)→ 1log(r)

UVUVIR IR

β =d g

d lnµα =g2

V (r) ∝ 1r log(r)

Free Electric

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UVUV IRIR

IR Conformal Phase

IR conformal behavior

V (r) ∝ 1r

Coulomb

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UV

UV

IR

IR

V ∝ σ r

QCD - Like

Page 87: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

Knobs

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Gauge Group, i.e. SU, SO, SP

Knobs

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Gauge Group, i.e. SU, SO, SP

Matter Representation

Knobs

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Gauge Group, i.e. SU, SO, SP

Matter Representation

# of Flavors per Representation

Knobs

Page 91: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

Gauge Group, i.e. SU, SO, SP

Matter Representation

# of Flavors per Representation

Knobs

Nf

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Gauge Group, i.e. SU, SO, SP

Matter Representation

# of Flavors per Representation

Knobs

NfQCD

Page 93: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

Gauge Group, i.e. SU, SO, SP

Matter Representation

# of Flavors per Representation

Knobs

NfQCD IR Conformal

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Gauge Group, i.e. SU, SO, SP

Matter Representation

# of Flavors per Representation

Knobs

NfQCD IR Conformal NA-QED

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Gauge Group, i.e. SU, SO, SP

Matter Representation

# of Flavors per Representation

Knobs

NfQCD IR Conformal NA-QED

Page 96: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

SU(N)

Adjoint Dirac Matter

Nf

Matter Density (i.e. Chemical Potential(s)) =0

Temperature = 0

Example

Page 97: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

SU(N)

Adjoint Dirac Matter

Nf

Matter Density (i.e. Chemical Potential(s)) =0

Temperature = 0

Example

Page 98: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

SU(N)

Adjoint Dirac Matter

Nf

Matter Density (i.e. Chemical Potential(s)) =0

Temperature = 0

Example

Page 99: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

SU(N)

Adjoint Dirac Matter

Nf

Matter Density (i.e. Chemical Potential(s)) =0

Temperature = 0

Example

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SU(N)

Adjoint Dirac Matter

Nf

Matter Density (i.e. Chemical Potential(s)) =0

Temperature = 0

Example

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β(g) = −β0

(4π)2g3−

β1

(4π)4g5 +O(g7)

β0 = 0

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β(g) = −β0

(4π)2g3−

β1

(4π)4g5 +O(g7)

β0 = 0

β = 0

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β(g) = −β0

(4π)2g3−

β1

(4π)4g5 +O(g7)

β0 = 0

β = 0

Weakly Coupled

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β(g) = −β0

(4π)2g3−

β1

(4π)4g5 +O(g7)

β0 = 0

β = 0

Weakly Coupled

Strongly Coupled

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β(g) = −β0

(4π)2g3−

β1

(4π)4g5 +O(g7)

β0 = 0

β = 0

Weakly Coupled

Strongly Coupled

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Analytic Tools

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The all orders beta function of NSVZ

Unitarity Bounds for Conformal Theories

Non-Renormalization of Superpotentials

‘t Hoofts Anomaly Matching Conditions

a-Maximization

Instanton Calculus

....

Seiberg, Intriligator, Novikov, Shifman, Vainshtein, Zakharov.

SUSY

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Different approaches

Schwinger - Dyson

Instanton Inspired Calculus

Thermal degrees of freedom count

Exact Renormalization Methods

Certain Topological excitations

Appelquist, Bowick, Chivukula, Cohen, Eichten, Gies, Hill, Holdom, Karabali, Jaeckel, Fisher, Lane, Litim, Mahanta, Miransky, Pawlowski, Percacci, Poppitz, Shrock, Simmons, Terning, Unsal, Wijewardhana, Yamawaki

Non SUSY

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Also:

The all orders beta function conjecture* (RS)

Chiral Gauge Theories beta function (F.S.)

Unitarity of the Operators for Conformal Theories

Gauge Dualities (F.S.)

First Principle Lattice Computations

RS - Ryttov, F.S. 07F.S. 09AT - Antipin, Tuominen 09

*Variations on the beta function (AT)

..continued

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The full nonperturbative fermion propagator reads:

Schwinger - Dyson

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The Euclidianized gap equation in Landau gauge is:

αc =π

3C2(r)

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In practice

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β(g) = − β0

(4π)2g3 − β1

(4π)4g5

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β = 0

β(g) = − β0

(4π)2g3 − β1

(4π)4g5

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β = 0

β(g) = − β0

(4π)2g3 − β1

(4π)4g5

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β = 0α∗

4π= −β0

β1

β(g) = − β0

(4π)2g3 − β1

(4π)4g5

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β = 0α∗

4π= −β0

β1

αc =π

3C2(r)

β(g) = − β0

(4π)2g3 − β1

(4π)4g5

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β = 0α∗

4π= −β0

β1

αc =π

3C2(r)

β(g) = − β0

(4π)2g3 − β1

(4π)4g5

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β = 0α∗

4π= −β0

β1

αc =π

3C2(r)γ(2− γ) = 1

β(g) = − β0

(4π)2g3 − β1

(4π)4g5

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β = 0α∗

4π= −β0

β1

αc =π

3C2(r)γ(2− γ) = 1

β(g) = − β0

(4π)2g3 − β1

(4π)4g5

α∗ ≤ αc

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N cf Ladder

=17C2(G) + 66C2(r)10C2(G) + 30C2(r)

C2(G)T (r)

C2(G) = C2(Adj) = N

SU(N) Dirac Fermions in representation “r”

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SU(N) Adjoint Dirac Matter

Back to the example

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SU(N) Adjoint Dirac Matter

C2(r) = C2(G) = T (G) = N

Back to the example

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SU(N) Adjoint Dirac Matter

C2(r) = C2(G) = T (G) = N

β0 =113

N − 43NNf = 0 , → NAsymp

f =114

= 2.75

Back to the example

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SU(N) Adjoint Dirac Matter

C2(r) = C2(G) = T (G) = N

N cf Ladder

=17 + 6610 + 30

= 2.075

β0 =113

N − 43NNf = 0 , → NAsymp

f =114

= 2.75

Back to the example

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SU(N) Adjoint Dirac Matter

C2(r) = C2(G) = T (G) = N

N cf Ladder

=17 + 6610 + 30

= 2.075

β0 =113

N − 43NNf = 0 , → NAsymp

f =114

= 2.75

F.S. - Tuominen 04

Back to the example

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SU(N) Adjoint Dirac Matter

NAsympf = 2.75

N cf Ladder

= 2.075

F.S. - Tuominen 04

Back to the example

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Another Example

SU(N) 2-index Symmetric Rep

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Diagram for Symm. Rep.

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Diagram for Symm. Rep.

Page 133: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

Dietrich and F.S. 06

Fund

2A

2S

Adj

Ladder approximation

SD - Phase Diagram

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SUSY

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SUSY β function

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NSVZ

SUSY β function

Page 137: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

NSVZ

SUSY β function

Page 138: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

NSVZ

SUSY β function

Page 139: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

NSVZ

SUSY β function

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Ryttov and F.S. 07

Fund

2A

2SAdj

NSVZ, SeibergIntriligator-Seiberg

SUSY Phase Diagram

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Ryttov and F.S. 07

β - function

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β function conjecture

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Ryttov and F.S. 07

β(g) = − g3

(4π)2β0 − 2

3T (r)Nfγ(g2)

1− g2

8π2 C2(G)(1 + 2β�0

β0)

β function conjecture

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Ryttov and F.S. 07

γ = −d lnm/d lnµ

β(g) = − g3

(4π)2β0 − 2

3T (r)Nfγ(g2)

1− g2

8π2 C2(G)(1 + 2β�0

β0)

β function conjecture

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Ryttov and F.S. 07

γ(g2) =32C2(r)

g2

4π2+ O(g4)γ = −d lnm/d lnµ

β(g) = − g3

(4π)2β0 − 2

3T (r)Nfγ(g2)

1− g2

8π2 C2(G)(1 + 2β�0

β0)

β function conjecture

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Ryttov and F.S. 07

γ(g2) =32C2(r)

g2

4π2+ O(g4)γ = −d lnm/d lnµ

β0 =113

C2(G)− 43T (r)Nf

β�0 = C2(G)− T (r)Nf

β(g) = − g3

(4π)2β0 − 2

3T (r)Nfγ(g2)

1− g2

8π2 C2(G)(1 + 2β�0

β0)

β function conjecture

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SU(N) Nf =12

Adjoint Matter

Recovering SYM

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Ryttov and F.S. 07

SU(N) Nf =12

Adjoint Matter

Recovering SYM

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Ryttov and F.S. 07

SU(N) Nf =12

Adjoint Matter

Recovering SYM

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Ryttov and F.S. 07

SU(N) Nf =12

Adjoint Matter

Recovering SYM

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Ryttov and F.S. 07

SU(N) Nf =12

Adjoint Matter

Recovering SYM

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1.00.5 2.00.2 5.0 10.0

4

6

8

10

!!Gev"

g2N

All Orders2-loops1-loop

SU(2)SU(3)SU(4)

Luscher, Sommer, Wolff, Weisz, 92Luscher, Sommer, Weisz, Wolff 94Lucini and Moraitis 07

SU(2)

SU(3)SU(4)

Confronting with YM

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Ryttov and F.S. 07

β = 0

Unitarity of the Conformal Operators demands:

γ ≤ 2

Bounding the window

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Back to the Example

SU(N) Adjoint Dirac Matter

γ ≤ 2 , =⇒ N cf ≥

118

Confronting with YM

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Back to the Example

SU(N) Adjoint Dirac Matter

γ ≤ 2 , =⇒ N cf ≥

118

γ = 1 , =⇒ N cf =

116

= 1.83

Confronting with YM

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Back to the Example

SU(N) Adjoint Dirac Matter

γ ≤ 2 , =⇒ N cf ≥

118

N cf Ladder

= 2.075

γ = 1 , =⇒ N cf =

116

= 1.83

Confronting with YM

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Back to the Example

SU(N) Adjoint Dirac Matter

γ ≤ 2 , =⇒ N cf ≥

118

N cf Ladder

= 2.075

γ = 1 , =⇒ N cf =

116

= 1.83

Conformal in the IR

Confronting with YM

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SU(N) Adjoint Dirac Matter

NAsympf = 2.75

γ ≤ 2→ N cf ≥

118

Back to the example

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Universal Picture

Page 160: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

Fund

2A

2S

Adj

Ladder

Ryttov & Sannino 07

All Orders Beta Function

SU(N) Phase Diagram

Dietrich & Sannino 07

Sannino & Tuominen 04

Ryttov & Sannino 07

γm = 1 γm = 2

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Fund

2A

2S

Adj

Ladder

Ryttov & Sannino 07

All Orders Beta Function

SU(N) Phase Diagram

Dietrich & Sannino 07

Sannino & Tuominen 04

Ryttov & Sannino 07

γm = 1 γm = 2

Page 162: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

Fund

2A

2S

Adj

Ladder

Ryttov & Sannino 07

All Orders Beta Function

SU(N) Phase Diagram

Dietrich & Sannino 07

Sannino & Tuominen 04

Ryttov & Sannino 07

γm = 1 γm = 2

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Fund

2A

2S

Adj

Ladder

Ryttov & Sannino 07

All Orders Beta Function

SU(N) Phase Diagram

Dietrich & Sannino 07

Sannino & Tuominen 04

Ryttov & Sannino 07

γm = 1 γm = 2

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3

2

1

Sannino Tuominen

Adjoint - SU(2)Minimal Walking Technicolor

Catterall, Sannino 07Catterall, Gidet, Sannino, Schneible 08Del Debbio, Patella, Pica 08Del Debbio et al.. 09Hietanen, Rummukainen, Tuominen 09Catterall, Giedt, Sannino Schneible 09Bursa, Del Debbio, Keegan, Pica, Pickup

Υ=2 Ryttov Sannino

Conformal Chiral Symmetry Breaks ?

SD

Dual Sannino

Ryttov Sannino

Υ=1

Page 165: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

NDualf ≥ 8.25

4

3

2

1

Dual - Fund

Dual - 2-index

Sannino Tuominen

Sannino

Sannino

Sym - SU(3)

Shamir, Svetitsky, DeGrand 08 DeGrand 09

Ryttov SanninoΥ=1

Υ=2 Ryttov Sannino

Conformal Chiral Symmetry Breaks ?

SD

Page 166: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

11

10

9

8

7

6

5

4

3

2

SU(2) Fundamental

RS = Ryttov-Sannino 2007

RSΥ=1

Υ=2 RS

ATW = Appelquist-Terning-Wijewardhana 97

ATW

ACS = Appelquist-Cohen-Schmaltz 99

ACS

Muraya, Nakamura, Nonaka 03Skullerud et al. 04Iwasaki et al. 04

Iwasaki et al. 04

Conformal Chiral Symmetry Breaks ?

99

F.S. 09

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SU(3) Fundamental17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

RS = Ryttov-Sannino 2007

RSΥ=1

Υ=2 RS

Dual S = Sannino 2009

FSDual

FSDual

ATW = Appelquist-Terning-Wijewardhana 97

ATW

ACS = Appelquist-Cohen-Schmaltz 99

ACS

Sui 01Hasenfratz 09Fodor et al. 09

Yamada et al. 09

Heller 98Hasenfratz 09Fodor et al. 09

Hasenfratz 09Fodor et al. 09Appelquist, Fleming, Neil 07Deuzeman, Lombardo, Pallante 09Jin, Mawhinney 09

Iwasaki et al. 04

Appelquist, Fleming, Neil 07Deuzeman, Lombardo, Pallante 09Fodor et al. 09Jin, Mawhinney 09

Fodor et al. 09

Conformal Chiral Symmetry Breaks ?

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Be imaginative!

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5 6 7 8 9 100

5

10

15

20

N

Nf

A.F.B.F. & γ= 2 SD

SO(N)

F.S. 09All Orders Beta Function

SO(N) Phase Diagram

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F.S. 09All Orders Beta Function2 3 4 5 60

5

10

15

20

25

30

35

N

N Wf

A.F. B.F. & γ= 2 SD

SP(2N)

Sp(N) Phase Diagram

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Chiral Gauge Theories

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What does chiral mean?

Cannot give a mass term in the Lagrangian

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What does chiral mean?

Cannot give a mass term in the Lagrangian

Why study them?

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What does chiral mean?

Cannot give a mass term in the Lagrangian

The Standard Model is chiral

Why study them?

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What does chiral mean?

Cannot give a mass term in the Lagrangian

Grand Unifications

The Standard Model is chiral

Why study them?

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What does chiral mean?

Cannot give a mass term in the Lagrangian

Grand Unifications

The Standard Model is chiral

Why study them?

Extended technicolor models

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What does chiral mean?

Cannot give a mass term in the Lagrangian

Grand Unifications

The Standard Model is chiral

Why study them?

Extended technicolor models

First principle lattice computations are impossible

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Bars - Yankielowicz (BY)

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Bars - Yankielowicz (BY)

Generalized Georgi-Glashow (GGG)

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F.S. 09

Chiral beta function conjecture

vector-like pairsp(ri)

γi

β0

mass anomalous dimension

one-loop coefficient

β�χ Fixed to agree with the 2-loop coefficient

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Chiral Gauge Theories Phase Diagram

F.S. 09Chiral Beta Function

2 4 6 8 10

5

10

15

20

N

p

2 4 6 8 10

5

10

15

20

Np

BY GGG

ϒ=2ϒ=2

ϒ=1ϒ=1

ACS

ACS

Thermal: Appelquist, Cohen, Schmaltz, Shrock 99 Appelquist, Duan, F.S., 2000

Poppitz & Unsal have similar results with a different method

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Duals

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T1

UV

T2T1

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T1

IR

UV

T2T1

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T1

IR

UV

T2

Electric

T1

Magnetic

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T1 Weak

Electric

Strong

Magnetic

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T1 Weak

Electric

Strong

Magnetic

e g = 2 π n

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QCD Dual F.S. 09

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QCD Dual F.S. 09

Within the Conformal Window

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QCD Dual

‘t Hooft Anomaly Conditions Respected

F.S. 09

Within the Conformal Window

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QCD Dual

‘t Hooft Anomaly Conditions Respected

F.S. 09

Within the Conformal Window

Operator Matching

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QCD Dual

‘t Hooft Anomaly Conditions Respected

F.S. 09

Within the Conformal Window

Operator Matching

Flavor Decoupling

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QCD Dual

‘t Hooft Anomaly Conditions Respected

F.S. 09

Within the Conformal Window

Operator Matching

Flavor Decoupling

RS beta function

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QCD Dual

‘t Hooft Anomaly Conditions Respected

F.S. 09

Within the Conformal Window

Operator Matching

Flavor Decoupling

RS beta function

Super QCD Seiberg 96

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QCD Dual

‘t Hooft Anomaly Conditions Respected

F.S. 09

Within the Conformal Window

Operator Matching

Flavor Decoupling

RS beta function

Super QCD Seiberg 96

Previous attempt Terning 98

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T1

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T1

T2

Page 198: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

‘t Hooft Anomaly Matching

UV (1)

SUL(Nf )

SUL(Nf )

SUL(Nf )

SUL(Nf )

SUL(Nf )

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Operator Matching

Baryonic bound states

Magnetic Electric

Baryons

M ∼ QQ

A, S, ....

M

�c1....cX qc1 · · · qcX

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A QCD Dual F.S. 09

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Dual Theory

LDual = LKin

�q, q, A,BA, DA, A

�+ LM

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Dual Theory

LM = Yqeq q M �q + YABA A MBA + YCBA C MBA + YCBS C MBS + YSBS S MBS ++ YBADA BA M DA + YBADS BA M DS + YBSDA BS M DA + YBSDS BS M DS + h.c.

LDual = LKin

�q, q, A,BA, DA, A

�+ LM

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Dual Theory

LM = Yqeq q M �q + YABA A MBA + YCBA C MBA + YCBS C MBS + YSBS S MBS ++ YBADA BA M DA + YBADS BA M DS + YBSDA BS M DA + YBSDS BS M DS + h.c.

LDual = LKin

�q, q, A,BA, DA, A

�+ LM

B[�c1....cX qc1 · · · qcX ] = 3 (2Nf − 5) = #×B[�c1....c3Qc1 · · · Qc3 ]

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Nf

N

Electric

Strong

Weak

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Nf

N

Magnetic

Electric

Weak

StrongStrong

Weak

Page 206: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

Magnetic Asymp. Freedom

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β0 =113

(2Nf − 5N)− 23Nf ≥ 0

Magnetic Asymp. Freedom

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β0 =113

(2Nf − 5N)− 23Nf ≥ 0

Nf ≥114

N

Magnetic Asymp. Freedom

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β0 =113

(2Nf − 5N)− 23Nf ≥ 0

Nf ≥114

N NBFf |γ=2 ≥

114

N

Magnetic Asymp. Freedom

ElectricChiral Sym. Restored

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• Duality can be tested on the Lattice

• Reduces the number of theories

• Use to compute nonperturbative quantities like the VV-AA correlator.

Duality summary

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Low Energy Effective TheoryMany Models

(?)MSSM XLMS D

AdS/?Unparticle

Branes......

Technicolor

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Low Energy Effective Theory Unifying in Model Space

(?)MSSM

XLMS D

AdS/?

Unparticle

Branes

Technicolor?

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Low Energy Effective TheoryMinimal Superconformal TC

MSSM

Strings

AdS/CFT

Unparticle

Branes

Technicolor

MSCT

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Conclusions

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๏ DEWSB can naturally occur at the LHC

Conclusions

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๏ DEWSB can naturally occur at the LHC

๏ Phase Diagram of strongly interacting theories

Conclusions

Page 217: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

๏ DEWSB can naturally occur at the LHC

๏ Phase Diagram of strongly interacting theories

๏ Unification in theory space

Conclusions

Page 218: Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July 2010 @ Quark Matter - Roma Francesco Sannino. Cosmology. Atoms 4% Dark Matter 22%

๏ DEWSB can naturally occur at the LHC

๏ Phase Diagram of strongly interacting theories

๏ Unification in theory space

๏ DEWSB cosmology is exciting.. another time

Conclusions