Skip to main content
SpringerLink
Log in

Massive \( \mathcal{N} \) = 2 gauge theories at large N

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

Using exact results obtained from localization on S 4, we explore the large N limit of \( \mathcal{N} \) = 2 super Yang-Mills theories with massive matter multiplets. We focus on three cases: \( \mathcal{N} \) = 2* theory, describing a massive hypermultiplet in the adjoint representation, SU(N) super-Yang-Mills with 2N massive hypermultiplets in the fundamental, and super QCD with massive quarks. When the radius of the four-sphere is sent to infinity the theories at hand are described by solvable matrix models, which exhibit a number of interesting phenomena including quantum phase transitions at finite ’t Hooft coupling.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  3. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].

  4. S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  6. N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [Erratum ibid. B 430 (1994) 485-486] [hep-th/9407087] [INSPIRE].

  7. N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. M.R. Douglas and S.H. Shenker, Dynamics of SU(N) supersymmetric gauge theory, Nucl. Phys. B 447 (1995) 271 [hep-th/9503163] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. F. Ferrari, The large-N limit of N = 2 super Yang-Mills, fractional instantons and infrared divergences, Nucl. Phys. B 612 (2001) 151 [hep-th/0106192] [INSPIRE].

    Article  ADS  Google Scholar 

  10. S.-J. Rey and T. Suyama, Exact Results and Holography of Wilson Loops in N = 2 Superconformal (Quiver) Gauge Theories, JHEP 01 (2011) 136 [arXiv:1001.0016] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. F. Passerini and K. Zarembo, Wilson Loops in N = 2 super-Yang-Mills from Matrix Model, JHEP 09 (2011) 102 [Erratum ibid. 1110 (2011) 065] [arXiv:1106.5763] [INSPIRE].

  12. J.-E. Bourgine, A Note on the integral equation for the Wilson loop in N = 2 D = 4 superconformal Yang-Mills theory, J. Phys. A 45 (2012) 125403 [arXiv:1111.0384] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  13. B. Fraser and S.P. Kumar, Large rank Wilson loops in N = 2 superconformal QCD at strong coupling, JHEP 03 (2012) 077 [arXiv:1112.5182] [INSPIRE].

    Article  ADS  Google Scholar 

  14. J.G. Russo, A note on perturbation series in supersymmetric gauge theories, JHEP 06 (2012) 038 [arXiv:1203.5061] [INSPIRE].

    Article  ADS  Google Scholar 

  15. J. Russo and K. Zarembo, Large-N Limit of N = 2 SU(N) Gauge Theories from Localization, JHEP 10 (2012) 082 [arXiv:1207.3806] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. A. Buchel, J.G. Russo and K. Zarembo, Rigorous Test of Non-conformal Holography: Wilson Loops in N = 2* Theory, JHEP 03 (2013) 062 [arXiv:1301.1597] [INSPIRE].

    Article  ADS  Google Scholar 

  17. J.G. Russo and K. Zarembo, Evidence for Large-N Phase Transitions in N = 2* Theory, JHEP 04 (2013) 065 [arXiv:1302.6968] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. 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].

    Article  ADS  Google Scholar 

  19. G. Veneziano, Some Aspects of a Unified Approach to Gauge, Dual and Gribov Theories, Nucl. Phys. B 117 (1976) 519 [INSPIRE].

    Article  ADS  Google Scholar 

  20. G. Festuccia and N. Seiberg, Rigid Supersymmetric Theories in Curved Superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2004) 831 [hep-th/0206161] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  22. N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, hep-th/0306238 [INSPIRE].

  23. K. Pilch and N.P. Warner, N = 2 supersymmetric RG flows and the IIB dilaton, Nucl. Phys. B 594 (2001) 209 [hep-th/0004063] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. A. Buchel, A.W. Peet and J. Polchinski, Gauge dual and noncommutative extension of an N =2 supergravity solution, Phys. Rev. D 63 (2001) 044009[hep-th/0008076] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  25. J.E. Carlisle and C.V. Johnson, Holographic RG flows and universal structures on the Coulomb branch of N = 2 supersymmetric large-N gauge theory, JHEP 07 (2003) 039 [hep-th/0306168] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. A. Buchel, Compactifications of the N = 2* flow, Phys. Lett. B 570 (2003) 89 [hep-th/0302107] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. A. Buchel, Localization and holography in N = 2 gauge theories, arXiv:1304.5652 [INSPIRE].

  28. J. Erickson, G. Semenoff and K. Zarembo, Wilson loops in N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 582 (2000) 155 [hep-th/0003055] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. 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].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. E. Brézin, C. Itzykson, G. Parisi and J. Zuber, Planar Diagrams, Commun. Math. Phys. 59 (1978) 35 [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  32. J. Minahan and K. Zarembo, The Bethe ansatz for N = 4 super Yang-Mills, JHEP 03 (2003) 013 [hep-th/0212208] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. N. Beisert, C. Kristjansen and M. Staudacher, The dilatation operator of conformal N = 4 super Yang-Mills theory, Nucl. Phys. B 664 (2003) 131 [hep-th/0303060] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. N. Beisert and M. Staudacher, The N = 4 SYM integrable super spin chain, Nucl. Phys. B 670 (2003) 439 [hep-th/0307042] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. N. Beisert, V. Dippel and M. Staudacher, A novel long range spin chain and planar N = 4 super Yang-Mills, JHEP 07 (2004) 075 [hep-th/0405001] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. N. Beisert, The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 945 [hep-th/0511082] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  37. A.W. Peet and J. Polchinski, UV/IR relations in AdS dynamics, Phys. Rev. D 59 (1999) 065011 [hep-th/9809022] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  38. M. Bianchi, D.Z. Freedman and K. Skenderis, How to go with an RG flow, JHEP 08 (2001) 041 [hep-th/0105276] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. F. Bigazzi, A. Cotrone and A. Zaffaroni, N = 2 gauge theories from wrapped five-branes, Phys. Lett. B 519 (2001) 269 [hep-th/0106160] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. J. Hoppe, unpublished.

  41. V.A. Kazakov, I.K. Kostov and N.A. Nekrasov, D particles, matrix integrals and KP hierarchy, Nucl. Phys. B 557 (1999) 413 [hep-th/9810035] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. I. Kostov, O(n) Vector Model on a Planar Random Lattice: Spectrum of Anomalous Dimensions, Mod. Phys. Lett. A 4 (1989) 217 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  43. M. Gaudin and I. Kostov, O(n) Model On A Fluctuating Planar Lattice: Some Exact Results, Phys. Lett. B 220 (1989) 200 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  44. I.K. Kostov and M. Staudacher, Multicritical phases of the O(n) model on a random lattice, Nucl. Phys. B 384 (1992) 459 [hep-th/9203030] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  45. B. Eynard and J. Zinn-Justin, The O(n) model on a random surface: Critical points and large order behavior, Nucl. Phys. B 386 (1992) 558 [hep-th/9204082] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  46. B. Eynard and C. Kristjansen, Exact solution of the O(n) model on a random lattice, Nucl. Phys. B 455 (1995) 577 [hep-th/9506193] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  47. B. Eynard and C. Kristjansen, More on the exact solution of the O(n) model on a random lattice and an investigation of the case |n| > 2, Nucl. Phys. B 466 (1996) 463 [hep-th/9512052] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  48. L. Chekhov and C. Kristjansen, Hermitian matrix model with plaquette interaction, Nucl. Phys. B 479 (1996) 683 [hep-th/9605013] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  49. T. Azeyanagi, M. Hanada, M. Honda, Y. Matsuo and S. Shiba, A new look at instantons and large-N limit, arXiv:1307.0809 [INSPIRE].

  50. V. Kazakov, A Simple Solvable Model of Quantum Field Theory of Open Strings, Phys. Lett. B 237 (1990) 212 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  51. N. Hama and K. Hosomichi, Seiberg-Witten Theories on Ellipsoids, JHEP 09 (2012) 033 [Addendum ibid. 1210 (2012) 051] [arXiv:1206.6359] [INSPIRE].

  52. F. Fucito, J.F. Morales, R. Poghossian and D.R. Pacifici, Exact results in \( \mathcal{N} \) = 2 gauge theories, JHEP 10 (2013) 178 [arXiv:1307.6612] [INSPIRE].

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institució Catalana de Recerca i Estudis Avançats (ICREA), Pg. Lluis Companys, 23, 08010, Barcelona, Spain

    J. G. Russo

  2. Department ECM, Institut de Ciències del Cosmos, Universitat de Barcelona, MartíFranquès, 1, 08028, Barcelona, Spain

    J. G. Russo

  3. Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91, Stockholm, Sweden

    K. Zarembo

  4. Department of Physics and Astronomy, Uppsala University, SE-751 08, Uppsala, Sweden

    K. Zarembo

  5. ITEP, Moscow, Russia

    K. Zarembo

Authors
  1. J. G. Russo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Zarembo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. Zarembo.

Additional information

ArXiv ePrint: 1309.1004

Rights and permissions

Reprints and permissions

About this article

Cite this article

Russo, J.G., Zarembo, K. Massive \( \mathcal{N} \) = 2 gauge theories at large N . J. High Energ. Phys. 2013, 130 (2013). https://doi.org/10.1007/JHEP11(2013)130

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP11(2013)130

Keywords

Search

Navigation