Electroweak Symmetry Breaking from the D4-D8-D8 System

Joshua ErlichCollege of William & Mary

Budapest, June 25, 2007

w/ Chris Carone, Marc Sher, Jong Anly Tan

D4

D8

D8

EWSB

Outline

• Quick Technicolor Review

• The D4-D8-D8 system as a Technicolor model

• Precision Electroweak Constraints

• Top-Down vs Bottom-Up AdS/QCD/Technicolor

Your favorite strongly coupled theory(at least for the next 25 minutes)

SU(N) gauge theory with Nf light Dirac fermions

(QCD for short)

Asymptotic FreedomConfinementChiral Symmetry BreakingElectroweak Symmetry Breaking (when fermions are coupled to SU(2)W £ U(1)Y as in the SM)

A prototypical gauge theory featuring:

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)

J J

Goldstones

QCD and Electroweak Symmetry Breaking

Quarks are charged under electroweak symmetry, which in the

quark sector is a gauged subgroup of the chiral symmetry £ U(1)B-L.

qLqR+qRqL charged under SU(2)W £ U(1)Y ,

Invariant under U(1)EM

Even in the absence of any other source of EWSB, nonvanishing

hqLqR+qRqLi breaks EW to EM, gives small mass to W, Z bosons.

But we need more EWSB -- lot’s more!

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 (£U(1)B-L)

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 experiment ! walking TC may be betterThe ugly: No fermion masses ! Extended Technicolor

Weinberg,Susskind

A Minimal Technicolor Model

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

(No Standard Model fermion masses yet, doesn’t satisfy electroweak constraints…)

Breaks ElectroweakSymmetry

The Basic Goals of AdS/QCD/Technicolor

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

• To cure problems in 4D models by modifying the strongly coupled theories in a controlled way

The Technique

• Engineer your favorite strongly coupled field theory (or a similar one) from a D-brane configuration

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

Top-Down AdS/QCD

QCD from strings

D4

0 1 2 3 5 6 7 8 U

D4 x x x x x

Witten; Csaki,Ooguri,Oz,Terning; …

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

Antiperiodic BC’s on fermionsbreak SUSY

U

Adding massless chiral quarks

D4

D8

D8

0 1 2 3 5 6 7 8 U

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

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

The U-tube

Confinement,SB U

The D4-D8-D8 System

D4

0 1 2 3 5 6 7 8 U

D4 x x x x x

D8 x x x x x x x x x

Sakai,Sugimoto; Antonyan,Harvey,Jensen,Kutasov;Aharony,Sonnenschein,Yankielowicz

SB

D8

D8

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

Confinement

QCD bound state masses and interactions

1) Probe brane limit: Assume Nf ¿ N (Karch,Katz)

2) Determine shape of D8-brane by minimizing D8-brane action in D4-brane background

3) Fluctuations of the D8-brane describe bound states of quarks; D8-brane action determines their masses, decay constants, form factors, couplings, …

D4 brane geometry

period:

The U-tube

Probe brane limit

D8-brane action

Stationary Solution:

Probe brane limit

Induced metric on D8-brane:

Vector mesons on the D8-branes

SU(Nf) gauge fields live on the D8-branes – identify 4D modes with vector mesons

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

Holographic TechnicolorHirn,Sanz; Piai; Agashe,Csaki,Grojean,Reece; Hong,Yee,…

Technicolor is like QCD.AdS/QCD makes nonperturbative predictions in theories like QCD.

Simple idea:

Use AdS/QCD to define and make predictions in Technicolor-like Models of EWSB

Gauging the EW symmetry on the D8 branes

Decompose the D8-brane gauge fields in modes

Turn on non-vanishing solution at boundaries (zero modes)

These solutions correspond to sources for the electroweak currents

Decay constants are read off of couplings between sources and resonances

Precision Electroweak Constraints

Particle Data Group

Oblique Parameters

Oblique corrections describe influence of new physics on vacuum polarization corrections to electroweak observables

-- Parametrized by three quantities that can be calculated from matrix elements of products of electroweak 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

Constraints on S,T

PDG

The SS S Parameter – first few contributions

The S Parameter – sum over all modes

Factor of 10 too big

g2N=4, N=4

Other phenomenology

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

Can also predict meson couplings, form factors.

Technibaryons appear as skyrmions.

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 the 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)

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. Standard Model fermions, masses must be included to make the model complete.

3. Related models may satisfy electroweak and FCNC constraints: walking technicolor models from D-branes?

4. How does the 2 UV boundary paradigm affect 5D models of EWSB?

5. The AdS/CFT correspondence can be used with metric on D8-brane to calculate current correlators, agrees with effective theory on D8-branes: is this a hint as to why AdS/CFT works?

Final Thoughts

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

2. Standard Model fermions, masses must be included to make the model complete.

3. Related models may satisfy electroweak and FCNC constraints: walking technicolor models from D-branes?

4. How does the 2 UV boundary paradigm affect 5D models of EWSB?

5. The AdS/CFT correspondence can be used with metric on D8-brane to calculate current correlators, agrees with effective theory on D8-branes: is this a hint as to why AdS/CFT works?

Final Thoughts

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

2. Standard Model fermions, masses must be included to make the model complete.

3. Related models may satisfy electroweak and FCNC constraints: walking technicolor models from D-branes?

4. How does the 2 UV boundary paradigm affect 5D models of EWSB?

5. The AdS/CFT correspondence can be used with metric on D8-brane to calculate current correlators, agrees with effective theory on D8-branes: is this a hint as to why AdS/CFT works?

Final Thoughts

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

2. Standard Model fermions, masses must be included to make the model complete.

3. Related models may satisfy electroweak and FCNC constraints: walking technicolor models from D-branes?

4. How does the 2 UV boundary paradigm affect 5D models of EWSB?

5. The AdS/CFT correspondence can be used with metric on D8-brane to calculate current correlators, agrees with effective theory on D8-branes: is this a hint as to why AdS/CFT works?

Final Thoughts

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

2. Standard Model fermions, masses must be included to make the model complete.

3. Related models may satisfy electroweak and FCNC constraints: walking technicolor models from D-branes?

4. How does the 2 UV boundary paradigm affect 5D models of EWSB?

5. The AdS/CFT correspondence can be used with metric on D8-brane to calculate current correlators, agrees with effective theory on D8-branes: is this a hint as to why AdS/CFT works?