1. Electroweak Symmetry Breaking from D-branes Joshua Erlich College of William & Mary Title U Oregon, May 22, 2007 w/ Chris Carone, Marc Sher, Jong Anly Tan D4 D8 EWSB SU(2) 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 m u, m d ~ few MeV m  ~ 770 MeV Invariant under separate SU(2) transformations on q L, q R

6. Chiral Symmetry Breaking in QCD Nonvanishing breaks chiral symmetry to diagonal subgroup (Isospin)

7. Technicolor Assume a new asymptotically free gauge group factor G TC with N F 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 Weinberg,Susskind

8. The D4-D8-D8 System 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 Sakai,Sugimoto Massless fluctuations of D4 branes describe non-supersymmetric SU(N) gauge theory

9. The D4-D8-D8 System 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 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

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

11. D4 brane geometry  period:

12. Probe brane limit D8-brane action Karch,Katz Stationary Solution:

13. Vector mesons on the D8-branes SU(N f ) gauge fields live on the D8-branes

14. 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 Vector Axial Vector

15. 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

16. 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

17. The S Parameter – first few contributions

18. The S Parameter – sum over all modes Factor of 10 too big

19. Other phenomenology This model doesn’t satisfy electroweak constraints, but what else could be predicted?

20. 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?

21. 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

22. 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 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: AdS 5 between z=0 and z=z m z=0 z=z m AdS 5 SU(2) £ SU(2)

24. Bosonic Technicolor (Kagan, Samuel, Simmons, Carone, Georgi, Golden,..) Gauge group: G TC £ SU(2) £ U(1) SU(2) technifermion doublet P L =(p,m) L SU(2) technifermion singlets p R, m R 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)

25. Bosonic Technicolor Yukawa couplings: Yukawa couplings of  to technifermions produces  tadpole. This guarantees generation of SM fermion masses, even with positive Higgs mass 2.

26. Bosonic Technicolor Include scalar in chiral Lagrangian: Electroweak scale: Physical and eaten Goldstones:

27. Holographic Bosonic Technicolor Results S parameter for m  =1,3,5 TeV Carone,JE,Tan

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

29. Technirho Decays Results m  =3 TeV, h=.01

30. 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

31. 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?