Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July...
Transcript of Phases of Gauge Theories - Laboratori Nazionali di Frascati€¦ · Phases of Gauge Theories July...
Phases of Gauge Theories
July 2010 @ Quark Matter - Roma
Francesco Sannino
Cosmology
Atoms4%
Dark Matter22%
Dark Energy74%
Cosmology
Low Energy Effective TheoryStandard Model
Low Energy Effective Theory
SM
Standard Model
WW Scattering
WW Scattering
S-wave amplitude:
WW Scattering
S-wave amplitude:
WW Scattering
S-wave amplitude:
WW Scattering
S-wave amplitude:
Unitarity:
WW Scattering
Theorem:
Unitarity requires the existence of a weakly coupled Higgs particle or New Physics around the Terascale!
Origin of mass
The Higgs
Custodial symmetries
Custodial symmetries
Custodial symmetries
Custodial symmetries
SUL(2)× UY (1)
SUL(2)× UY (1)
m2 < 0
|H|
m2 < 0
�σ2� ≡ v2 = |m2|λ
|H|
m2 < 0
�σ2� ≡ v2 = |m2|λ
σ = v + h
Gauge Boson-Masses
Gauge Boson-Masses
Gauge Boson-Masses
Gauge Boson-Masses
−λd QL · HdR
Gauge Boson-Masses
Quark-Masses
−λd QL · HdR
Gauge Boson-Masses
Quark-Masses
−λd QL · HdR
Gauge Boson-Masses
Quark-Masses
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
Higgs mechanism in Nature
Superconductivity
Macroscopic-ScreeningNon-Relativistic
SM-ScreeningRelativistic
Superconductivity
Macroscopic-ScreeningNon-Relativistic
SM-ScreeningRelativistic
Superconductivity
Macroscopic-ScreeningNon-Relativistic
SM-ScreeningRelativistic
Superconductivity
|H|2 =v2
2
Macroscopic-ScreeningNon-Relativistic
SM-ScreeningRelativistic
Superconductivity
Meissner-MassStatic Vector Potential
Weak-GB-Mass
Meissner-MassStatic Vector Potential
Weak-GB-Mass
Meissner-MassStatic Vector Potential
Weak-GB-Mass
Meissner-MassStatic Vector Potential
Weak-GB-Mass
Meissner-MassStatic Vector Potential
Weak-GB-Mass
Meissner-MassStatic Vector Potential
Weak-GB-Mass
Hidden structure
Meissner-MassStatic Vector Potential
Weak-GB-Mass
Hidden structure ????
Instability of the Fermi Scale
M2H
= 2λ v2
Quantum corrections
Quantum corrections
A mass appears even if ab initio is set to zero!
Quantum corrections
No custodial symmetry protecting a scalar mass.
A mass appears even if ab initio is set to zero!
Quantum corrections
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
Definition of Natural
Small parameters stay small under radiative corrections.
Definition of Natural
Electron mass
If set to zero the U(1)L× U(1)R forbids its regeneration
Electron mass
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
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
Low Energy Effective TheoryMany Models
(?)MSSMXLMS D
AdS/?Unparticle
Branes......
Technicolor
Low Energy Effective TheoryMany Models
(?)MSSMXLMS D
AdS/?Unparticle
Branes......
Technicolor
$
Theory landscape
Gauge Group
Theory landscape
Gauge Group
Matter
Theory landscape
Gauge Group
SUSY
Matter
Theory landscape
Gauge Group
SUSY
Matter
N=1
N=2
N=4
Theory landscape
Gauge Group
SUSY Non SUSY
Matter
N=1
N=2
N=4
Theory landscape
Gauge Group
SUSY Non SUSY
Matter
N=1
N=2
N=4
Fermions
Fermions + Bosons
Bosons
Theory landscape
Gauge Group
SUSY Non SUSY
Matter
N=1
N=2
N=4
Fermions
Fermions + Bosons
Bosons
Vector
Theory landscape
Gauge Group
SUSY Non SUSY
Matter
N=1
N=2
N=4
Fermions
Fermions + Bosons
Bosons
Vector Chiral
Theory landscape
Gauge Group
SUSY Non SUSY
Matter
N=1
N=2
N=4
Fermions
Fermions + Bosons
Bosons
Vector Chiral
Theory landscape
Gauge Group
SUSY Non SUSY
Matter
N=1
N=2
N=4
Fermions
Fermions + Bosons
Bosons
Vector Chiral
Theory landscape
Gauge Group
SUSY Non SUSY
Matter
N=1
N=2
N=4
Fermions
Fermions + Bosons
Bosons
Vector Chiral
Theory landscape
Phases
α(r)→ 1log(r)
UVUVIR IR
β =d g
d lnµα =g2
4π
V (r) ∝ 1r log(r)
Free Electric
UVUV IRIR
IR Conformal Phase
IR conformal behavior
V (r) ∝ 1r
Coulomb
UV
UV
IR
IR
V ∝ σ r
QCD - Like
Knobs
Gauge Group, i.e. SU, SO, SP
Knobs
Gauge Group, i.e. SU, SO, SP
Matter Representation
Knobs
Gauge Group, i.e. SU, SO, SP
Matter Representation
# of Flavors per Representation
Knobs
Gauge Group, i.e. SU, SO, SP
Matter Representation
# of Flavors per Representation
Knobs
Nf
Gauge Group, i.e. SU, SO, SP
Matter Representation
# of Flavors per Representation
Knobs
NfQCD
Gauge Group, i.e. SU, SO, SP
Matter Representation
# of Flavors per Representation
Knobs
NfQCD IR Conformal
Gauge Group, i.e. SU, SO, SP
Matter Representation
# of Flavors per Representation
Knobs
NfQCD IR Conformal NA-QED
Gauge Group, i.e. SU, SO, SP
Matter Representation
# of Flavors per Representation
Knobs
NfQCD IR Conformal NA-QED
SU(N)
Adjoint Dirac Matter
Nf
Matter Density (i.e. Chemical Potential(s)) =0
Temperature = 0
Example
SU(N)
Adjoint Dirac Matter
Nf
Matter Density (i.e. Chemical Potential(s)) =0
Temperature = 0
Example
SU(N)
Adjoint Dirac Matter
Nf
Matter Density (i.e. Chemical Potential(s)) =0
Temperature = 0
Example
SU(N)
Adjoint Dirac Matter
Nf
Matter Density (i.e. Chemical Potential(s)) =0
Temperature = 0
Example
SU(N)
Adjoint Dirac Matter
Nf
Matter Density (i.e. Chemical Potential(s)) =0
Temperature = 0
Example
β(g) = −β0
(4π)2g3−
β1
(4π)4g5 +O(g7)
β0 = 0
β(g) = −β0
(4π)2g3−
β1
(4π)4g5 +O(g7)
β0 = 0
β = 0
β(g) = −β0
(4π)2g3−
β1
(4π)4g5 +O(g7)
β0 = 0
β = 0
Weakly Coupled
β(g) = −β0
(4π)2g3−
β1
(4π)4g5 +O(g7)
β0 = 0
β = 0
Weakly Coupled
Strongly Coupled
β(g) = −β0
(4π)2g3−
β1
(4π)4g5 +O(g7)
β0 = 0
β = 0
Weakly Coupled
Strongly Coupled
Analytic Tools
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
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
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
The full nonperturbative fermion propagator reads:
Schwinger - Dyson
The Euclidianized gap equation in Landau gauge is:
αc =π
3C2(r)
In practice
β(g) = − β0
(4π)2g3 − β1
(4π)4g5
β = 0
β(g) = − β0
(4π)2g3 − β1
(4π)4g5
β = 0
β(g) = − β0
(4π)2g3 − β1
(4π)4g5
β = 0α∗
4π= −β0
β1
β(g) = − β0
(4π)2g3 − β1
(4π)4g5
β = 0α∗
4π= −β0
β1
αc =π
3C2(r)
β(g) = − β0
(4π)2g3 − β1
(4π)4g5
β = 0α∗
4π= −β0
β1
αc =π
3C2(r)
β(g) = − β0
(4π)2g3 − β1
(4π)4g5
β = 0α∗
4π= −β0
β1
αc =π
3C2(r)γ(2− γ) = 1
β(g) = − β0
(4π)2g3 − β1
(4π)4g5
β = 0α∗
4π= −β0
β1
αc =π
3C2(r)γ(2− γ) = 1
β(g) = − β0
(4π)2g3 − β1
(4π)4g5
α∗ ≤ αc
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”
SU(N) Adjoint Dirac Matter
Back to the example
SU(N) Adjoint Dirac Matter
C2(r) = C2(G) = T (G) = N
Back to the example
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
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
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
SU(N) Adjoint Dirac Matter
NAsympf = 2.75
N cf Ladder
= 2.075
F.S. - Tuominen 04
Back to the example
Another Example
SU(N) 2-index Symmetric Rep
Diagram for Symm. Rep.
Diagram for Symm. Rep.
Dietrich and F.S. 06
Fund
2A
2S
Adj
Ladder approximation
SD - Phase Diagram
SUSY
SUSY β function
NSVZ
SUSY β function
NSVZ
SUSY β function
NSVZ
SUSY β function
NSVZ
SUSY β function
Ryttov and F.S. 07
Fund
2A
2SAdj
NSVZ, SeibergIntriligator-Seiberg
SUSY Phase Diagram
Ryttov and F.S. 07
β - function
β function conjecture
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
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
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
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
SU(N) Nf =12
Adjoint Matter
Recovering SYM
Ryttov and F.S. 07
SU(N) Nf =12
Adjoint Matter
Recovering SYM
Ryttov and F.S. 07
SU(N) Nf =12
Adjoint Matter
Recovering SYM
Ryttov and F.S. 07
SU(N) Nf =12
Adjoint Matter
Recovering SYM
Ryttov and F.S. 07
SU(N) Nf =12
Adjoint Matter
Recovering SYM
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
Ryttov and F.S. 07
β = 0
Unitarity of the Conformal Operators demands:
γ ≤ 2
Bounding the window
Back to the Example
SU(N) Adjoint Dirac Matter
γ ≤ 2 , =⇒ N cf ≥
118
Confronting with YM
Back to the Example
SU(N) Adjoint Dirac Matter
γ ≤ 2 , =⇒ N cf ≥
118
γ = 1 , =⇒ N cf =
116
= 1.83
Confronting with YM
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
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
SU(N) Adjoint Dirac Matter
NAsympf = 2.75
γ ≤ 2→ N cf ≥
118
Back to the example
Universal Picture
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
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
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
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
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
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
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
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 ?
Be imaginative!
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
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
Chiral Gauge Theories
What does chiral mean?
Cannot give a mass term in the Lagrangian
What does chiral mean?
Cannot give a mass term in the Lagrangian
Why study them?
What does chiral mean?
Cannot give a mass term in the Lagrangian
The Standard Model is chiral
Why study them?
What does chiral mean?
Cannot give a mass term in the Lagrangian
Grand Unifications
The Standard Model is chiral
Why study them?
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
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
Bars - Yankielowicz (BY)
Bars - Yankielowicz (BY)
Generalized Georgi-Glashow (GGG)
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
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
Duals
T1
UV
T2T1
T1
IR
UV
T2T1
T1
IR
UV
T2
Electric
T1
Magnetic
T1 Weak
Electric
Strong
Magnetic
T1 Weak
Electric
Strong
Magnetic
e g = 2 π n
QCD Dual F.S. 09
QCD Dual F.S. 09
Within the Conformal Window
QCD Dual
‘t Hooft Anomaly Conditions Respected
F.S. 09
Within the Conformal Window
QCD Dual
‘t Hooft Anomaly Conditions Respected
F.S. 09
Within the Conformal Window
Operator Matching
QCD Dual
‘t Hooft Anomaly Conditions Respected
F.S. 09
Within the Conformal Window
Operator Matching
Flavor Decoupling
QCD Dual
‘t Hooft Anomaly Conditions Respected
F.S. 09
Within the Conformal Window
Operator Matching
Flavor Decoupling
RS beta function
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
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
T1
T1
T2
‘t Hooft Anomaly Matching
UV (1)
SUL(Nf )
SUL(Nf )
SUL(Nf )
SUL(Nf )
SUL(Nf )
Operator Matching
Baryonic bound states
Magnetic Electric
Baryons
M ∼ QQ
A, S, ....
M
�c1....cX qc1 · · · qcX
A QCD Dual F.S. 09
Dual Theory
LDual = LKin
�q, q, A,BA, DA, A
�+ LM
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
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 ]
Nf
N
Electric
Strong
Weak
Nf
N
Magnetic
Electric
Weak
StrongStrong
Weak
Magnetic Asymp. Freedom
β0 =113
(2Nf − 5N)− 23Nf ≥ 0
Magnetic Asymp. Freedom
β0 =113
(2Nf − 5N)− 23Nf ≥ 0
Nf ≥114
N
Magnetic Asymp. Freedom
β0 =113
(2Nf − 5N)− 23Nf ≥ 0
Nf ≥114
N NBFf |γ=2 ≥
114
N
Magnetic Asymp. Freedom
ElectricChiral Sym. Restored
• Duality can be tested on the Lattice
• Reduces the number of theories
• Use to compute nonperturbative quantities like the VV-AA correlator.
Duality summary
Low Energy Effective TheoryMany Models
(?)MSSM XLMS D
AdS/?Unparticle
Branes......
Technicolor
Low Energy Effective Theory Unifying in Model Space
(?)MSSM
XLMS D
AdS/?
Unparticle
Branes
Technicolor?
Low Energy Effective TheoryMinimal Superconformal TC
MSSM
Strings
AdS/CFT
Unparticle
Branes
Technicolor
MSCT
Conclusions
๏ DEWSB can naturally occur at the LHC
Conclusions
๏ DEWSB can naturally occur at the LHC
๏ Phase Diagram of strongly interacting theories
Conclusions
๏ DEWSB can naturally occur at the LHC
๏ Phase Diagram of strongly interacting theories
๏ Unification in theory space
Conclusions
๏ DEWSB can naturally occur at the LHC
๏ Phase Diagram of strongly interacting theories
๏ Unification in theory space
๏ DEWSB cosmology is exciting.. another time
Conclusions