1. Construction of the models of the dynamical Electroweak symmetry breaking using the ideas that come from the effective field model of Helium - 3 superfluid. 1. Nambu sum rule 2. Lorentz group as a source of DESB.

2. The Nambu sum rule and the relation between the masses of composite Higgs bosons G.E.Volovik (Aalto U& ITP, Moscow) M.A.Zubkov (ITEP, Moscow) ArXiv:1302.2360, to appear in JETP lett. arXiv:1209.0204

3. abstract It may appear that the recently found resonance at 125 GeV is not the only Higgs boson. The masses of the Higgses may be related to the mass of t — quark as (The sum is within a group of the scalar excitations.) This rule is the analogue of the sum rule in He3-B (for the excitations of the same total momentum J). It was originally proposed by Nambu for He3-B. We call it the Nambu sum rule.

4. Plan 1. Introduction: experimental situation; accidents; the essence of the Nambu sum rule. 2. Review of bosonic excitations in He3-B,A and thin films He3-a,b. 3. Consideration of the toy model for the top — quark condensation 4. Review of bosonic excitations in dense QCD 5. Conclusions

6. Nambu Sum rule QCD He3-B

7. Accidents Excess of events at the Tevatron and CMS in 2011 at 325 GeV "A 325 GeV scalar resonance seen at CDF?", Krzysztof A. Meissner, Hermann Nicolai, arXiv:1208.5653 "Probing Minimal Supersymmetry at the LHC with the Higgs Boson Masses", L. Maiani, A. D. Polosa, V. Riquer, arXiv:1202.5998 Excess of events at ATLAS in 2011 at 245 GeV

8. He-3

9. Bosons

11. He3-B

12. derivation

14. He3-b thin film

15. He3-a thin film Triply degenerated

16. He3-A Goldstones: hidden symmetry: there are three terms that depend on with definite these terms are transformed to each other by New massless modes:

17. He3-A Bosonic modes (triply degenerated): and six massless models

18. Relativistic models of top quark condensation

19. Particular case

20. bosons C is diagonal

21. T-anti t and q — anti q channels

22. Channels with different quarks

24. Nambu Sum Rule If one of the quarks dominates

25. Veltman identity vs Nambu Sum Rule The number of colors is important

27. Hadronic phase diquarks: Color superconductivity, CFL phase

28. Conclusions 1. The notion of the Nambu Sum rule is introduced. It works in: - Helium superfluid 3-B, 3-A, in thin films 3-b,3-a - QCD at finite chemical potential (normal phase, small T, small mu), - color superconductor (CFL phase) - the considered models of top — quark condensation 2. Lessons for the TeV — scale physics: - The 125 GeV Higgs cannot be the Nambu partner of the neutral Goldstone boson - If there are two twice degenerated Higgs bosons, then the Namby partner of the 125 GeV Higgs should have mass 210 GeV -If there are only two states, then the second Higgs should have mass 325 GeV -If there are two Higgs bosons of equal masses, these masses are around 245 GeV

29. M. Zubkov ITEP Moscow 2010-2013 1. 1. M.A.Zubkov, arXiv:1301.6971 2. G.E. Volovik, M.A. Zubkov, arXiv:1302.2360, To appear in JETP lett. 3. M.A.Zubkov, Mod. Phys. Lett. A, Vol. 25, No. 34 (2010) pp. 2885-2898 Lorentz Group as the source of dynamical electroweak symmetry breaking

30. 30Abstract 1. Dynamics of torsion degrees of freedom in Poincare gravity can be considered as the gauge theory of Lorentz group. 2. Suppose this theory is coupled in a nonminimal way to spinors. The effective four - fermion interactions appear that may lead to the condensation of fermions. 2. Suppose this theory is coupled in a nonminimal way to spinors. The effective four - fermion interactions appear that may lead to the condensation of fermions. 3. The given construction may provide the dynamical Electroweak symmetry breaking. 3. The given construction may provide the dynamical Electroweak symmetry breaking.

31. 31 Plan 1. From Superconductivity to Technicolor 2. Fermions in Riemann – Cartan space. 3. 4 – fermion interactions. 4. Condensation of fermions. 5. Fermion masses.

32. Ginzburg _ Landau Model Superconductivity BCS Model

33. Weinberg – Salam Model (Higgs sector) N J L model

34. Technicolor Effective N J L model Nonlinear Sigma - Model

35. SM fermions and Technifermions from the same multiplet of ETC gauge group SM mass

36. Idea Poincare gravity = Gauge theory of Lorentz group + group of translations Variables: Translational connection = Tetrad field Lorentz group connection

37. Massless fermions (S.Alexandrov, Class.Quant.Grav.25:145012,2008)

38. Massless fermions

39. Action for the torsion (I.L.Shapiro, Phys.Rep. 357, 113 (2002) PARTICULAR CASE

40. Flat metric, CP invariance

41. SO(3,1) gauge field action (S.Holst, Phys.Rev.D. 53, 5966 (1996) (E.Elizalde,S.D.Odintsov, Phys.Atom.Nucl.56:409-411,1993)

42. ( S.Mercuri, Phys. Rev. D 73 (2006) 084016 ) ( S.Alexandrov, Class.Quant.Grav.25:145012,2008)

43. ( S.Mercuri, Phys. Rev. D 73 (2006) 084016 ) ( S.Alexandrov, Class.Quant.Grav.25:145012,2008)

44. Attractive force between fermions => condensate J.Bijnens, C.Bruno, E. de Rafael, Nucl.Phys. B390 (1993) 501-541

45. SM fields + technifermions J.Bijnens, C.Bruno, E. de Rafael, Nucl.Phys. B390 (1993) 501-541

46. Corrections to the effective action are taken into account

47. Lattice discretization

48. Gauge field action

49. 49 Conclusions 1.The dynamical SO(3,1) gauge theory with the scale >1000 TeV and the torsion mass ~ this scale is coupled in a nonminimal way to fermions. 2.Due to the effecitve 4 – fermion interactions fermions are condensed and provide the DEWSB. 3.In zero order approximation all fermions acquire equal masses. 4.When the corrections due to the other gauge fields are taken into account, the hierarchy of fermion masses appears. 5.The given gauge theory is unusual since it should provide chiral symmetry breaking but cannot be confining.

50. Summary of two talks: 1. Nambu sum rules in the NJL models: from Helium-3 to top quark condensation. G.E. Volovik, M.A. Zubkov, ArXiv:1302.2360, to appear in JETP lett.; arXiv:1209.0204. 2. Numerical investigation of the effective field model of graphene monolayer using lattice field theory technique. M.V.Ulybyshev, M.A. Zubkov, Solid State Comm. http://dx.doi.org/10.1016/j.ssc.2012.12.030 3. Calculation of Euler — Heisenberg effective lagrangian for the effective field model of multilayer graphene. M.I. Katsnelson, G.E. Volovik, M.A. Zubkov, Annals Phys. 331 (2013) 160 4. Momentum space topology in 4D relativistic quantum field theory. M.A. Zubkov, G.E. Volovik, Nucl.Phys. B860 (2012) 295-309, M.A. Zubkov, Phys.Rev. D86 (2012) 034505 5. Numerical investigation of Weinberg — Salam model in lattice regularization. M.A. Zubkov, Phys.Rev. D85 (2012) 073001. 6. Gauge theory of Lorentz group as a source of the dynamical Electroweak symmetry breaking. M.A. Zubkov. arXiv:1301.6971