Electroweak Symmetry Breaking from D-branes

Joshua ErlichCollege of William & Mary

U Oregon, May 22, 2007

w/ Chris Carone, Marc Sher, Jong Anly Tan

D4

D8

D8

EWSB

SU(2)

U(1)

Outline

• QCD, Technicolor from Strings

• The D4-D8-D8 system

• Top-Down vs Bottom-Up AdS/Technicolor

The Goal

• To make predictions in strongly coupled theories like QCD or Technicolor, and compare with experiment

The Technique

• Engineer the strongly coupled field theory from a D-brane configuration

• Use string theory to make quantitative predictions of observables in certain limits of the field theory

Chiral Symmetry Breaking in QCD

The up, down quarks are light compared to the QCD scale

mu, md ~ few MeV

m ~ 770 MeV

Invariant under separate SU(2) transformations on qL, qR

Chiral Symmetry Breaking in QCD

Nonvanishing breaks chiral symmetry to diagonal subgroup (Isospin)

Technicolor

Assume a new asymptotically free gauge group factor GTC with NF techniquark flavors

Gauge a SU(2) £ U(1) subgroup of the chiral symmetry

Identify with electroweak gauge invariance

The chiral condensate breaks the electroweak symmetry to U(1)EM

The good: No fundamental scalars – no hierarchy problem

The bad: Estimates of precision electroweak observables disagree with experimentThe ugly: No fermion masses

Weinberg,Susskind

The D4-D8-D8 System

D4

D8

D8

0 1 2 3 4 5 6 7 8 9

D4 x x x x x

D8 x x x x x x x x x

Sakai,Sugimoto

Massless fluctuations of D4 branes describe non-supersymmetric SU(N) gauge theory

The D4-D8-D8 System

D4

D8

D8

0 1 2 3 4 5 6 7 8 9

D4 x x x x x

D8 x x x x x x x x x

Sakai,Sugimoto

Confinement,SB

Massless fluctuations of D4 branes describe non-supersymmetric SU(N) gauge theory

Strings stretching from D4’s to D8’s are massless chiral quarks

The D4-D8-D8 System

D4

0 1 2 3 4 5 6 7 8 9

D4 x x x x x

D8 x x x x x x x x x

Sakai,Sugimoto;Aharony,Sonnenschein,Yankielowicz

SB

D8

D8

There is a one-parameter set of D8-brane configurations that minimize the D8-brane action.

Confinement

D4 brane geometry

period:

Probe brane limit

D8-brane action

Karch,Katz

Stationary Solution:

Vector mesons on the D8-branes

SU(Nf) gauge fields live on the D8-branes

Vector mesons on the D8-branes

Solve equations of motion for modes of the vector field

Symmetric modes are identified with vector resonances

Antisymmetric modes are identified with axial vector resonances

In this setup, vector and axial vector masses alternate

VectorAxial Vector

Gauging the chiral symmetry

Decompose the gauge fields in modes

Turn on non-vanishing solution at boundaries

These solutions correspond to sources for the chiral symmetry currents

Decay constants are read off of couplings between sources and resonances

The S Parameter

Oblique corrections to electroweak observables parametrized by three quantities that can be calculated by matrix elements of products of currents: S,T,U

Peskin & Takeuchi

The S parameter in QCD-like technicolor theories is estimated to be too large to be consistent with precision electroweak measurements

The S Parameter – first few contributions

The S Parameter – sum over all modes

Factor of 10 too big

Other phenomenology

This model doesn’t satisfy electroweak constraints, but what elsecould be predicted?

Can the model be saved?

The lightest resonances contributed negatively to S.

Can we truncate the model consistently at some scale before S becomes too positive?

First thought

Raise the confinement scale with respect to chiral symmetry breaking scale:

Put the D8 branes in a box (but this isn’t string theory anymore!)

For small enough box, naively S decreases, but the electroweak sector becomes strongly coupled at the TeV scale so it is hard to calculate

Second thought

Deconstruct the extra dimension:

Replace gauge fields in extra dimension by a finite tower of massive resonances

Resulting theory is reminiscent of little Higgs models, analysis should be similar

Bottom-Up Approach

Forget about the details of the stringy construction.

Build in details of your favorite model, and calculate strong interaction observables by analogy with stringy constructions.

JE,Katz,Son,Stephanov; Da Rold,Pomarol; Brodsky,De Teramond; Hirn,Sanz

Geometry: AdS5 between z=0 and z=zm

z=0 z=zm

AdS5

SU(2) £ SU(2)

Bosonic Technicolor(Kagan, Samuel, Simmons, Carone, Georgi, Golden,..)

Gauge group: GTC £ SU(2) £ U(1)

SU(2) technifermion doublet PL=(p,m)L

SU(2) technifermion singlets pR, mR Technifermion condensate (p p + m m)=4 f 3

Scalar SU(2) doublet Higgs with vev f 0

For ETC to allow heavy fermions w/o FCNC’s the low energy theory includes technicolor + scalar Higgs (Chivukula, Cohen, Lane)

Bosonic Technicolor

Yukawa couplings:

Yukawa couplings of to technifermions produces tadpole.

This guarantees generation of SM fermion masses, even with positive Higgs mass2.

Bosonic Technicolor

Include scalar in chiral Lagrangian:

Electroweak scale:

Physical and eaten Goldstones:

Holographic Bosonic Technicolor

Results

S parameter for m=1,3,5 TeV

Carone,JE,Tan

Physical Technipion Mass

Results

Example:

m=3 TeV, h=.01

We calculate this term holographically, and infer m.

Technirho Decays

Results

m=3 TeV,h=.01

Top-Down vs Bottom-Up

Top-Down

1. Field theory described is well understood

2. Calculable models predict new states

3. Difficult to satisfy electroweak constraints

Bottom-Up

1. Not sure how well model describes 4D field theory

2. Desired properties of field theory built in

3. Easier to satisfy electroweak constraints

Final Thoughts

1. The D4-D8-D8 system provides a predictive model of EWSB.

2. Fermion masses must be included to make the model complete.

3. Related models may satisfy electroweak constraints: Can walking technicolor models be built from D-branes?

4. Chiral symmetry breaking is reflected in D8 brane configuration with two boundaries. How does this paradigm affect the bottom-up approach (usually w/ one boundary)?

5. AdS/CFT correspondence can be used to calculate current correlators, agrees with effective theory on D8-branes: derivation of AdS/CFT?