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
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
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
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:
Physical Technipion Mass
Results
Example:
m=3 TeV, h=.01
We calculate this term holographically, and infer m.
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?