Advertisement

Large N phase transition in \( T\overline{T} \) -deformed 2d Yang-Mills theory on the sphere

  • Leonardo Santilli
  • Miguel Tierz
Open Access
Regular Article - Theoretical Physics
  • 6 Downloads

Abstract

We study the partition function of a \( T\overline{T} \) -deformed version of Yang-Mills theory on the two-sphere. We show that the Douglas-Kazakov phase transition persists for a range of values of the deformation parameter, and that the critical area is lowered. The transition is of third order and also induced by instantons, whose contributions we characterize.

Keywords

Field Theories in Lower Dimensions Matrix Models Nonperturbative Effects 

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]
    A.B. Zamolodchikov, Expectation value of composite field \( T\overline{T} \) in two-dimensional quantum field theory, hep-th/0401146 [INSPIRE].
  2. [2]
    F.A. Smirnov and A.B. Zamolodchikov, On space of integrable quantum field theories, Nucl. Phys. B 915 (2017) 363 [arXiv:1608.05499] [INSPIRE].
  3. [3]
    A. Cavaglià, S. Negro, I.M. Szécsényi and R. Tateo, \( T\overline{T} \) -deformed 2D quantum field theories, JHEP 10 (2016) 112 [arXiv:1608.05534] [INSPIRE].
  4. [4]
    S. Dubovsky, V. Gorbenko and M. Mirbabayi, Asymptotic fragility, near AdS 2 holography and \( T\overline{T} \), JHEP 09 (2017) 136 [arXiv:1706.06604] [INSPIRE].
  5. [5]
    S. Dubovsky, V. Gorbenko and G. Hernández-Chifflet, \( T\overline{T} \) partition function from topological gravity, JHEP 09 (2018) 158 [arXiv:1805.07386] [INSPIRE].
  6. [6]
    A. Giveon, N. Itzhaki and D. Kutasov, \( T\overline{T} \) and LST, JHEP 07 (2017) 122 [arXiv:1701.05576] [INSPIRE].
  7. [7]
    A. Giveon, N. Itzhaki and D. Kutasov, A solvable irrelevant deformation of AdS 3 /CFT 2, JHEP 12 (2017) 155 [arXiv:1707.05800] [INSPIRE].
  8. [8]
    S. Datta and Y. Jiang, \( T\overline{T} \) deformed partition functions, JHEP 08 (2018) 106 [arXiv:1806.07426] [INSPIRE].
  9. [9]
    O. Aharony, S. Datta, A. Giveon, Y. Jiang and D. Kutasov, Modular invariance and uniqueness of \( T\overline{T} \) deformed CFT, arXiv:1808.02492 [INSPIRE].
  10. [10]
    J. Cardy, The \( T\overline{T} \) deformation of quantum field theory as random geometry, JHEP 10 (2018) 186 [arXiv:1801.06895] [INSPIRE].
  11. [11]
    R. Conti, S. Negro and R. Tateo, The \( T\overline{T} \) perturbation and its geometric interpretation, arXiv:1809.09593 [INSPIRE].
  12. [12]
    J. Cardy, \( T\overline{T} \) deformations of non-Lorentz invariant field theories, arXiv:1809.07849 [INSPIRE].
  13. [13]
    R. Conti, L. Iannella, S. Negro and R. Tateo, Generalised Born-Infeld models, Lax operators and the \( T\overline{T} \) perturbation, JHEP 11 (2018) 007 [arXiv:1806.11515] [INSPIRE].
  14. [14]
    S. Cordes, G.W. Moore and S. Ramgoolam, Lectures on 2D Yang-Mills theory, equivariant cohomology and topological field theories, Nucl. Phys. Proc. Suppl. 41 (1995) 184 [hep-th/9411210] [INSPIRE].
  15. [15]
    M.R. Douglas and V.A. Kazakov, Large N phase transition in continuum QCD in two-dimensions, Phys. Lett. B 319 (1993) 219 [hep-th/9305047] [INSPIRE].
  16. [16]
    D.J. Gross and A. Matytsin, Instanton induced large N phase transitions in two-dimensional and four-dimensional QCD, Nucl. Phys. B 429 (1994) 50 [hep-th/9404004] [INSPIRE].
  17. [17]
    A.A. Migdal, Recursion equations in gauge theories, Sov. Phys. JETP 42 (1975) 413 [Zh. Eksp. Teor. Fiz. 69 (1975) 810] [INSPIRE].
  18. [18]
    P. Menotti and E. Onofri, The action of SU(N) lattice gauge theory in terms of the heat kernel on the group manifold, Nucl. Phys. B 190 (1981) 288 [INSPIRE].
  19. [19]
    B.E. Rusakov, Loop averages and partition functions in U(N) gauge theory on two-dimensional manifolds, Mod. Phys. Lett. A 5 (1990) 693 [INSPIRE].
  20. [20]
    M.R. Douglas, Conformal field theory techniques in large N Yang-Mills theory, in NATO Advanced Research Workshop on New Developments in String Theory, Conformal Models and Topological Field Theory, Cargese, France, 12-21 May 1993 [hep-th/9311130] [INSPIRE].
  21. [21]
    J.A. Minahan and A.P. Polychronakos, Classical solutions for two-dimensional QCD on the sphere, Nucl. Phys. B 422 (1994) 172 [hep-th/9309119] [INSPIRE].
  22. [22]
    D.J. Gross and E. Witten, Possible third order phase transition in the large N lattice gauge theory, Phys. Rev. D 21 (1980) 446 [INSPIRE].
  23. [23]
    S.R. Wadia, N = ∞ phase transition in a class of exactly soluble model lattice gauge theories, Phys. Lett. B 93 (1980) 403 [INSPIRE].
  24. [24]
    S.R. Wadia, A study of U(N) lattice gauge theory in 2-dimensions, arXiv:1212.2906 [INSPIRE].
  25. [25]
    M. Caselle, A. D’Adda, L. Magnea and S. Panzeri, Two-dimensional QCD on the sphere and on the cylinder, in Proceedings, Summer School in High-energy physics and cosmology, Trieste, Italy, 15 June-31 July 1992, pg. 0245 [hep-th/9309107] [INSPIRE].
  26. [26]
    D.J. Gross, Two-dimensional QCD as a string theory, Nucl. Phys. B 400 (1993) 161 [hep-th/9212149] [INSPIRE].
  27. [27]
    D.J. Gross and W. Taylor, Two-dimensional QCD is a string theory, Nucl. Phys. B 400 (1993) 181 [hep-th/9301068] [INSPIRE].
  28. [28]
    W. Donnelly and G. Wong, Entanglement branes in a two-dimensional string theory, JHEP 09 (2017) 097 [arXiv:1610.01719] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    A.C. Pipkin, A course on integral equations, Texts Appl. Math. 9, Springer, New York, U.S.A. (1991).Google Scholar
  30. [30]
    N.I. Muskhelishvili, Singular integral equations, Noordhoff, The Netherlands (1977).Google Scholar
  31. [31]
    D. Jafferis and J. Marsano, A DK phase transition in q-deformed Yang-Mills on S 2 and topological strings, hep-th/0509004 [INSPIRE].
  32. [32]
    R.J. Szabo and M. Tierz, q-deformations of two-dimensional Yang-Mills theory: classification, categorification and refinement, Nucl. Phys. B 876 (2013) 234 [arXiv:1305.1580] [INSPIRE].
  33. [33]
    E. Witten, On quantum gauge theories in two-dimensions, Commun. Math. Phys. 141 (1991) 153 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  34. [34]
    E. Witten, Two-dimensional gauge theories revisited, J. Geom. Phys. 9 (1992) 303 [hep-th/9204083] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    M. Blau and G. Thompson, Derivation of the Verlinde formula from Chern-Simons theory and the G/G model, Nucl. Phys. B 408 (1993) 345 [hep-th/9305010] [INSPIRE].
  36. [36]
    M. Blau and G. Thompson, Lectures on 2D gauge theories: topological aspects and path integral techniques, in Proceedings, Summer School in High-energy physics and cosmology, Trieste, Italy, 14 June-30 July 1993, pg. 0175 [hep-th/9310144] [INSPIRE].
  37. [37]
    N. Caporaso, M. Cirafici, L. Griguolo, S. Pasquetti, D. Seminara and R.J. Szabo, Topological strings and large N phase transitions. I. Nonchiral expansion of q-deformed Yang-Mills theory, JHEP 01 (2006) 035 [hep-th/0509041] [INSPIRE].
  38. [38]
    S. Giombi and V. Pestun, Correlators of local operators and 1/8 BPS Wilson loops on S 2 from 2d YM and matrix models, JHEP 10 (2010) 033 [arXiv:0906.1572] [INSPIRE].
  39. [39]
    S. Giombi and V. Pestun, The 1/2 BPS ’t Hooft loops in N = 4 SYM as instantons in 2d Yang-Mills, J. Phys. A 46 (2013) 095402 [arXiv:0909.4272] [INSPIRE].
  40. [40]
    A. Bassetto and L. Griguolo, Two-dimensional QCD, instanton contributions and the perturbative Wu-Mandelstam-Leibbrandt prescription, Phys. Lett. B 443 (1998) 325 [hep-th/9806037] [INSPIRE].
  41. [41]
    N. Drukker and D.J. Gross, An exact prediction of N = 4 SUSYM theory for string theory, J. Math. Phys. 42 (2001) 2896 [hep-th/0010274] [INSPIRE].
  42. [42]
    B. Durhuus and P. Olesen, The spectral density for two-dimensional continuum QCD, Nucl. Phys. B 184 (1981) 461 [INSPIRE].
  43. [43]
    J.-P. Blaizot and M.A. Nowak, Large N c confinement and turbulence, Phys. Rev. Lett. 101 (2008) 102001 [arXiv:0801.1859] [INSPIRE].
  44. [44]
    H. Neuberger, Complex Burgers’ equation in 2D SU(N) YM, Phys. Lett. B 670 (2008) 235 [arXiv:0809.1238] [INSPIRE].
  45. [45]
    M.J. Crescimanno and W. Taylor, Large N phases of chiral QCD in two-dimensions, Nucl. Phys. B 437 (1995) 3 [hep-th/9408115] [INSPIRE].
  46. [46]
    M.R. Douglas, K. Li and M. Staudacher, Generalized two-dimensional QCD, Nucl. Phys. B 420 (1994) 118 [hep-th/9401062] [INSPIRE].
  47. [47]
    O. Ganor, J. Sonnenschein and S. Yankielowicz, The string theory approach to generalized 2D Yang-Mills theory, Nucl. Phys. B 434 (1995) 139 [hep-th/9407114] [INSPIRE].
  48. [48]
    A. Gadde, L. Rastelli, S.S. Razamat and W. Yan, The 4d superconformal index from q-deformed 2d Yang-Mills, Phys. Rev. Lett. 106 (2011) 241602 [arXiv:1104.3850] [INSPIRE].
  49. [49]
    M. Aganagic, H. Ooguri, N. Saulina and C. Vafa, Black holes, q-deformed 2d Yang-Mills and non-perturbative topological strings, Nucl. Phys. B 715 (2005) 304 [hep-th/0411280] [INSPIRE].
  50. [50]
    C. Beasley and E. Witten, Non-Abelian localization for Chern-Simons theory, J. Diff. Geom. 70 (2005) 183 [hep-th/0503126] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  51. [51]
    J. Kallen, Cohomological localization of Chern-Simons theory, JHEP 08 (2011) 008 [arXiv:1104.5353] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  52. [52]
    X. Arsiwalla, R. Boels, M. Mariño and A. Sinkovics, Phase transitions in q-deformed 2D Yang-Mills theory and topological strings, Phys. Rev. D 73 (2006) 026005 [hep-th/0509002] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Departamento de Matemática, Grupo de Física MatemáticaFaculdade de Ciências, Universidade de LisboaLisboaPortugal

Personalised recommendations