Advertisement

Spontaneous symmetry breaking in tensor theories

  • P. DiazEmail author
  • J. A. Rosabal
Open Access
Regular Article - Theoretical Physics
  • 31 Downloads

Abstract

In this work we study spontaneous symmetry breaking patterns in tensor models. We focus on the patterns which lead to effective matrix theories transforming in the adjoint of U(N). We find the explicit form of the Goldstone bosons which are organized as matrix multiplets in the effective theory. The choice of these symmetry breaking patterns is motivated by the fact that, in some contexts, matrix theories are dual to gravity theories. Based on this, we aim to build a bridge between tensor theories, quantum gravity and holography.

Keywords

M(atrix) Theories Spontaneous Symmetry Breaking Effective Field Theories 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    R. Gurau, Colored Group Field Theory, Commun. Math. Phys. 304 (2011) 69 [arXiv:0907.2582] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    R. Gurau, The 1/N expansion of colored tensor models, Annales Henri Poincaré 12 (2011) 829 [arXiv:1011.2726] [INSPIRE].
  3. [3]
    R. Gurau and V. Rivasseau, The 1/N expansion of colored tensor models in arbitrary dimension, EPL 95 (2011) 50004 [arXiv:1101.4182] [INSPIRE].
  4. [4]
    R. Gurau, The complete 1/N expansion of colored tensor models in arbitrary dimension, Annales Henri Poincaré 13 (2012) 399 [arXiv:1102.5759] [INSPIRE].
  5. [5]
    R. Gurau and J.P. Ryan, Colored Tensor Models — a review, SIGMA 8 (2012) 020 [arXiv:1109.4812] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  6. [6]
    I.R. Klebanov and G. Tarnopolsky, On Large N Limit of Symmetric Traceless Tensor Models, JHEP 10 (2017) 037 [arXiv:1706.00839] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    S. Giombi, I.R. Klebanov and G. Tarnopolsky, Bosonic tensor models at large N and small ϵ, Phys. Rev. D 96 (2017) 106014 [arXiv:1707.03866] [INSPIRE].
  8. [8]
    K. Bulycheva, I.R. Klebanov, A. Milekhin and G. Tarnopolsky, Spectra of Operators in Large N Tensor Models, Phys. Rev. D 97 (2018) 026016 [arXiv:1707.09347] [INSPIRE].
  9. [9]
    S. Giombi, I.R. Klebanov, F. Popov, S. Prakash and G. Tarnopolsky, Prismatic Large N Models for Bosonic Tensors, Phys. Rev. D 98 (2018) 105005 [arXiv:1808.04344] [INSPIRE].
  10. [10]
    I.R. Klebanov, F. Popov and G. Tarnopolsky, TASI Lectures on Large N Tensor Models, PoS(TASI2017)004 (2018) [arXiv:1808.09434] [INSPIRE].
  11. [11]
    F. Ferrari, V. Rivasseau and G. Valette, A New Large N Expansion for General Matrix-Tensor Models, arXiv:1709.07366 [INSPIRE].
  12. [12]
    J. Ben Geloun and S. Ramgoolam, Counting Tensor Model Observables and Branched Covers of the 2-Sphere, arXiv:1307.6490 [INSPIRE].
  13. [13]
    J. Ben Geloun and S. Ramgoolam, Tensor Models, Kronecker coefficients and Permutation Centralizer Algebras, JHEP 11 (2017) 092 [arXiv:1708.03524] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    H. Itoyama, A. Mironov and A. Morozov, Rainbow tensor model with enhanced symmetry and extreme melonic dominance, Phys. Lett. B 771 (2017) 180 [arXiv:1703.04983] [INSPIRE].
  15. [15]
    A. Mironov and A. Morozov, Correlators in tensor models from character calculus, Phys. Lett. B 774 (2017) 210 [arXiv:1706.03667] [INSPIRE].
  16. [16]
    H. Itoyama, A. Mironov and A. Morozov, Cut and join operator ring in tensor models, Nucl. Phys. B 932 (2018) 52 [arXiv:1710.10027] [INSPIRE].
  17. [17]
    H. Itoyama, A. Mironov and A. Morozov, From Kronecker to tableau pseudo-characters in tensor models, Phys. Lett. B 788 (2019) 76 [arXiv:1808.07783] [INSPIRE].
  18. [18]
    P. Diaz and S.-J. Rey, Orthogonal Bases of Invariants in Tensor Models, JHEP 02 (2018) 089 [arXiv:1706.02667] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    P. Diaz and S.-J. Rey, Invariant Operators, Orthogonal Bases and Correlators in General Tensor Models, Nucl. Phys. B 932 (2018) 254 [arXiv:1801.10506] [INSPIRE].
  20. [20]
    P. Diaz, Tensor and Matrix models: a one-night stand or a lifetime romance?, JHEP 06 (2018) 140 [arXiv:1803.04471] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    E. Witten, An SYK-Like Model Without Disorder, arXiv:1610.09758 [INSPIRE].
  22. [22]
    T. Azeyanagi, F. Ferrari and F.I. Schaposnik Massolo, Phase Diagram of Planar Matrix Quantum Mechanics, Tensor and Sachdev-Ye-Kitaev Models, Phys. Rev. Lett. 120 (2018) 061602 [arXiv:1707.03431] [INSPIRE].
  23. [23]
    J. Yoon, Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation, JHEP 10 (2017) 172 [arXiv:1706.05914] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    J. Yoon, SYK Models and SYK-like Tensor Models with Global Symmetry, JHEP 10 (2017) 183 [arXiv:1707.01740] [INSPIRE].
  25. [25]
    P. Narayan and J. Yoon, Supersymmetric SYK Model with Global Symmetry, JHEP 08 (2018) 159 [arXiv:1712.02647] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    T. Nosaka, D. Rosa and J. Yoon, The Thouless time for mass-deformed SYK, JHEP 09 (2018) 041 [arXiv:1804.09934] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  27. [27]
    A. Jevicki, K. Suzuki and J. Yoon, Bi-Local Holography in the SYK Model, JHEP 07 (2016) 007 [arXiv:1603.06246] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    A. Jevicki and K. Suzuki, Bi-Local Holography in the SYK Model: Perturbations, JHEP 11 (2016) 046 [arXiv:1608.07567] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    S.R. Das, A. Jevicki and K. Suzuki, Three Dimensional View of the SYK/AdS Duality, JHEP 09 (2017) 017 [arXiv:1704.07208] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    S.R. Das, A. Ghosh, A. Jevicki and K. Suzuki, Space-Time in the SYK Model, JHEP 07 (2018) 184 [arXiv:1712.02725] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    T. Banks, W. Fischler, S.H. Shenker and L. Susskind, M theory as a matrix model: A Conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].
  32. [32]
    P. Di Francesco, P.H. Ginsparg and J. Zinn-Justin, 2-D Gravity and random matrices, Phys. Rept. 254 (1995) 1 [hep-th/9306153] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    D. Berenstein, A Toy model for the AdS/CFT correspondence, JHEP 07 (2004) 018 [hep-th/0403110] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    R. de Mello Koch, J. Smolic and M. Smolic, Giant Gravitons - with Strings Attached (I), JHEP 06 (2007) 074 [hep-th/0701066] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  35. [35]
    S.R. Coleman and E. Witten, Chiral Symmetry Breakdown in Large N Chromodynamics, Phys. Rev. Lett. 45 (1980) 100 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  36. [36]
    H. Matsumoto, N.J. Papastamatiou and H. Umezawa, The formulation of spontaneous breakdown in the path-integral method, Nucl. Phys. B 68 (1974) 236 [INSPIRE].
  37. [37]
    H. Matsumoto, H. Umezawa, G. Vitiello and J.K. Wyly, Spontaneous breakdown of a nonAbelian symmetry, Phys. Rev. D 9 (1974) 2806 [INSPIRE].
  38. [38]
    R. de Mello Koch, R. Mello Koch, D. Gossman and L. Tribelhorn, Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models, JHEP 09 (2017) 011 [arXiv:1707.01455] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    S. Weinberg, The quantum theory of fields. Vol. 2: Modern applications, Cambridge University Press (1995) [INSPIRE].
  40. [40]
    J. Polchinski, String Theory. Vol. 1: An Introduction to the Bosonic String, Cambridge University Press, Cambridge (1998) [INSPIRE].
  41. [41]
    S. Choudhury, A. Dey, I. Halder, L. Janagal, S. Minwalla and R. Poojary, Notes on melonic O(N)q−1 tensor models, JHEP 06 (2018) 094 [arXiv:1707.09352] [INSPIRE].
  42. [42]
    I.R. Klebanov and G. Tarnopolsky, Uncolored random tensors, melon diagrams and the Sachdev-Ye-Kitaev models, Phys. Rev. D 95 (2017) 046004 [arXiv:1611.08915] [INSPIRE].
  43. [43]
    W. Fulton and J. Harris, Representation Theory, Springer-Verlag New York (2004).Google Scholar
  44. [44]
    S. Weinberg, Effective Gauge Theories, Phys. Lett. B 91 (1980) 51 [INSPIRE].
  45. [45]
    E. D’Hoker and S. Weinberg, General effective actions, Phys. Rev. D 50 (1994) R6050 [hep-ph/9409402] [INSPIRE].
  46. [46]
    S. Weinberg, Effective field theories in the large N limit, Phys. Rev. D 56 (1997) 2303 [hep-th/9706042] [INSPIRE].
  47. [47]
    Y. Bai and B.A. Dobrescu, Minimal SU(3) × SU(3) Symmetry Breaking Patterns, Phys. Rev. D 97 (2018) 055024 [arXiv:1710.01456] [INSPIRE].
  48. [48]
    V. Bonzom and F. Combes, Tensor models from the viewpoint of matrix models: the case of loop models on random surfaces, Ann. Inst. H. Poincaré Comb. Phys. Interact. 2 (2015) 1 [arXiv:1304.4152] [INSPIRE].
  49. [49]
    F. Ferrari, The Large D Limit of Planar Diagrams, arXiv:1701.01171 [INSPIRE].
  50. [50]
    C. Krishnan, S. Sanyal and P.N. Bala Subramanian, Quantum Chaos and Holographic Tensor Models, JHEP 03 (2017) 056 [arXiv:1612.06330] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  51. [51]
    C. Krishnan, K.V.P. Kumar and S. Sanyal, Random Matrices and Holographic Tensor Models, JHEP 06 (2017) 036 [arXiv:1703.08155] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  52. [52]
    H. Itoyama, A. Mironov and A. Morozov, Ward identities and combinatorics of rainbow tensor models, JHEP 06 (2017) 115 [arXiv:1704.08648] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  53. [53]
    A. Eichhorn, T. Koslowski, J. Lumma and A.D. Pereira, Towards background independent quantum gravity with tensor models, arXiv:1811.00814 [INSPIRE].
  54. [54]
    A. Eichhorn, T. Koslowski and A.D. Pereira, Status of background-independent coarse-graining in tensor models for quantum gravity, arXiv:1811.12909 [INSPIRE].
  55. [55]
    M. Blasone, P. Jizba and G. Vitiello, Quantum Field Theory and Its Macroscopic Manifestations, Imperial College Press (2011).Google Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Fields, Gravity & Strings @ CTPU, Institute for Basic ScienceDaejeonKorea

Personalised recommendations