1. Electroweak Symmetry Breaking from the D4-D8-D8 System Joshua Erlich College of William & Mary Budapest, June 25, 2007 w/ Chris Carone, Marc Sher, Jong Anly Tan D4 D8 EWSB

2. Outline Quick Technicolor Review The D4-D8-D8 system as a Technicolor model Precision Electroweak Constraints Top-Down vs Bottom-Up AdS/QCD/Technicolor

3. Your favorite strongly coupled theory (at least for the next 25 minutes) SU(N) gauge theory with N f light Dirac fermions (QCD for short) Asymptotic Freedom Confinement Chiral Symmetry Breaking Electroweak Symmetry Breaking (when fermions are coupled to SU(2) W £ U(1) Y as in the SM) A prototypical gauge theory featuring:

4. 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

5. Chiral Symmetry Breaking in QCD Nonvanishing breaks chiral symmetry to diagonal subgroup (Isospin) JJ J Goldstones

6. 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. q L q R +q R q L charged under SU(2) W £ U(1) Y, Invariant under U(1) EM Even in the absence of any other source of EWSB, nonvanishing h q L q R +q R q L i breaks EW to EM, gives small mass to W, Z bosons. But we need more EWSB -- lot’s more!

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 ( £ 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 better The ugly: No fermion masses ! Extended Technicolor Weinberg,Susskind

8. A Minimal Technicolor Model 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 (No Standard Model fermion masses yet, doesn’t satisfy electroweak constraints…) Breaks Electroweak Symmetry

9. 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

10. 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

11. 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 fermions break SUSY U 

12. Adding massless chiral quarks D4 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 

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

14. QCD bound state masses and interactions 1)Probe brane limit: Assume N f ¿ 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, …

15. D4 brane geometry  period: The U-tube

16. Probe brane limit D8-brane action Stationary Solution:

17. Probe brane limit Induced metric on D8-brane:

18. Vector mesons on the D8-branes SU(N f ) gauge fields live on the D8-branes – identify 4D modes with vector mesons

19. 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

20. Holographic Technicolor Hirn,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

21. 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

22. Precision Electroweak Constraints Particle Data Group

23. 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

24. Constraints on S,T PDG

25. The SS S Parameter – first few contributions

26. The S Parameter – sum over all modes Factor of 10 too big g 2 N=4 , N=4

27. Other phenomenology This model doesn’t satisfy electroweak constraints, but what else could be predicted in the model? Can also predict meson couplings, form factors. Technibaryons appear as skyrmions.

28. 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?

29. 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

30. 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.

31. 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)

32. 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 scalar Higgs (Chivukula, Cohen, Lane)

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

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

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

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

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

38. 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

39. 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?

40. 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?

41. 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?

42. 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?

43. 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?