Electroweak Symmetry Breaking from Dbranes

1
Title
Electroweak Symmetry Breaking from D-branes
Joshua Erlich
College of William Mary
w/ Chris Carone, Marc Sher, Jong Anly Tan
SU(2)
D8
D4
EWSB
D8
U Oregon, May 22, 2007
U(1)
2
Outline

• QCD, Technicolor from Strings
• The D4-D8-D8 system
• Top-Down vs Bottom-Up AdS/Technicolor

3
The Goal

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

4
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

5
Chiral Symmetry Breaking in QCD

• The up, down quarks are light compared to the QCD
  scale
• mu, md few MeV
• m? 770 MeV

6
Chiral Symmetry Breaking in QCD
Nonvanishing breaks chiral
symmetry to diagonal subgroup (Isospin)
7
Technicolor
Weinberg,Susskind

• 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 experiment
The ugly No fermion masses
8
The D4-D8-D8 System
Sakai,Sugimoto
D8
D4
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
9
The D4-D8-D8 System
Sakai,Sugimoto
D8
D4
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
Massless fluctuations of D4 branes describe
non-supersymmetric SU(N) gauge theory
Strings stretching from D4s to D8s are massless
chiral quarks
10
The D4-D8-D8 System
Sakai,Sugimoto Aharony,Sonnenschein,Yankielowicz
D8
D4
D8
Confinement
?SB
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
There is a one-parameter set of D8-brane
configurations that minimize the D8-brane action.
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D4 brane geometry
? period
12
Probe brane limit
Karch,Katz
D8-brane action
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Vector mesons on the D8-branes

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

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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
Axial Vector
Vector
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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
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The S Parameter
Peskin Takeuchi
Oblique corrections to electroweak observables
parametrized by three quantities that can be
calculated by matrix elements of products of
currents S,T,U
The S parameter in QCD-like technicolor theories
is estimated to be too large to be consistent
with precision electroweak measurements
17
The S Parameter first few contributions
18
The S Parameter sum over all modes
Factor of 10 too big
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Other phenomenology
This model doesnt satisfy electroweak
constraints, but what else could be predicted?
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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?
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First thought
Raise the confinement scale with respect to
chiral symmetry breaking scale Put the D8
branes in a box (but this isnt string theory
anymore!)
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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
23
Bottom-Up Approach
JE,Katz,Son,Stephanov Da Rold,Pomarol
Brodsky,De Teramond Hirn,Sanz
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.
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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 FCNCs the
• low energy theory includes technicolor scalar
  Higgs
• (Chivukula, Cohen, Lane)

25
Bosonic Technicolor

• Yukawa couplings

Yukawa couplings of ? to technifermions produces
? tadpole. This guarantees generation of SM
fermion masses, even with positive Higgs mass2.
26
Bosonic Technicolor

• Include scalar in chiral Lagrangian
• Electroweak scale
• Physical and eaten Goldstones

27
Results
Holographic Bosonic Technicolor
Carone,JE,Tan
S parameter for m?1,3,5 TeV
28
Results
Physical Technipion Mass
We calculate this term holographically, and infer
m?.
Example m?3 TeV, h.01
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Results
Technirho Decays
m?3 TeV, h.01
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Top-Down vs Bottom-Up

• Top-Down
• Field theory described is well understood
• Calculable models predict new states
• Difficult to satisfy electroweak constraints

• Bottom-Up
• Not sure how well model describes 4D field theory
• Desired properties of field theory built in
• Easier to satisfy electroweak constraints

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Final Thoughts

• 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?