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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, …
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
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
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?