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\( \mathcal{N} \) =1 geometries via M-theory

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Abstract

We provide an M-theory geometric set-up to describe four-dimensional \( \mathcal{N} \) = 1 gauge theories. This is realized by a generalization of Hitchin’s equation. This framework encompasses a rich class of theories including superconformal and confining ones. We show how the spectral data of the generalized Hitchin’s system encode the infrared properties of the gauge theory in terms of \( \mathcal{N} \) = 1 curves. For \( \mathcal{N} \) = 1 deformations of \( \mathcal{N} \) = 2 theories in class \( \mathcal{S} \), we show how the superpotential is encoded in an appropriate choice of boundary conditions at the marked points in different S-duality frames. We elucidate our approach in a number of cases — including Argyres-Douglas points, confining phases and gaugings of T N theories — and display new results for linear and generalized quivers.

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References

  1. E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  2. D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. K. Hori, H. Ooguri and Y. Oz, Strong coupling dynamics of four-dimensional N = 1 gauge theories from M-theory five-brane, Adv. Theor. Math. Phys. 1 (1998) 1 [hep-th/9706082] [INSPIRE].

    MathSciNet  Google Scholar 

  4. E. Witten, Branes and the dynamics of QCD, Nucl. Phys. B 507 (1997) 658 [hep-th/9706109] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. A. Brandhuber, N. Itzhaki, V. Kaplunovsky, J. Sonnenschein and S. Yankielowicz, Comments on the M-theory approach to N = 1 SQCD and brane dynamics, Phys. Lett. B 410 (1997) 27 [hep-th/9706127] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. J. de Boer and Y. Oz, Monopole condensation and confining phase of N = 1 gauge theories via M-theory five-brane, Nucl. Phys. B 511 (1998) 155 [hep-th/9708044] [INSPIRE].

    Article  ADS  Google Scholar 

  7. F. Benini, Y. Tachikawa and B. Wecht, Sicilian gauge theories and N = 1 dualities, JHEP 01 (2010) 088 [arXiv:0909.1327] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. I. Bah, C. Beem, N. Bobev and B. Wecht, Four-dimensional SCFTs from M 5-branes, JHEP 06 (2012) 005 [arXiv:1203.0303] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. K. Maruyoshi, M. Taki, S. Terashima and F. Yagi, New Seiberg dualities from N = 2 dualities, JHEP 09 (2009) 086 [arXiv:0907.2625] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. I. Bah and B. Wecht, New N = 1 superconformal field theories in four dimensions, JHEP 07 (2013) 107 [arXiv:1111.3402] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  11. C. Beem and A. Gadde, The superconformal index of N = 1 class S fixed points, arXiv:1212.1467 [INSPIRE].

  12. A. Gadde, K. Maruyoshi, Y. Tachikawa and W. Yan, New N = 1 dualities, JHEP 06 (2013) 056 [arXiv:1303.0836] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  13. F. Cachazo, M.R. Douglas, N. Seiberg and E. Witten, Chiral rings and anomalies in supersymmetric gauge theory, JHEP 12 (2002) 071 [hep-th/0211170] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  14. R. Dijkgraaf and C. Vafa, A perturbative window into nonperturbative physics, hep-th/0208048 [INSPIRE].

  15. Y. Tachikawa and K. Yonekura, N = 1 curves for trifundamentals, JHEP 07 (2011) 025 [arXiv:1105.3215] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. K. Maruyoshi, Y. Tachikawa, W. Yan and K. Yonekura, N = 1 dynamics with T N theory, JHEP 10 (2013) 010 [arXiv:1305.5250] [INSPIRE].

    Article  ADS  Google Scholar 

  17. 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 

  18. S. Elitzur, A. Forge, A. Giveon, K.A. Intriligator and E. Rabinovici, Massless monopoles via confining phase superpotentials, Phys. Lett. B 379 (1996) 121 [hep-th/9603051] [INSPIRE].

    Article  ADS  Google Scholar 

  19. F. Cachazo, K.A. Intriligator and C. Vafa, A large-N duality via a geometric transition, Nucl. Phys. B 603 (2001) 3 [hep-th/0103067] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. S. Elitzur, A. Giveon and D. Kutasov, Branes and N = 1 duality in string theory, Phys. Lett. B 400 (1997) 269 [hep-th/9702014] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. S. Elitzur, A. Giveon, D. Kutasov, E. Rabinovici and A. Schwimmer, Brane dynamics and N =1 supersymmetric gauge theory, Nucl. Phys. B 505 (1997) 202 [hep-th/9704104] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. A. Giveon and D. Kutasov, Brane dynamics and gauge theory, Rev. Mod. Phys. 71 (1999) 983 [hep-th/9802067] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. P.C. Argyres, M.R. Plesser and N. Seiberg, The moduli space of vacua of N = 2 SUSY QCD and duality in N = 1 SUSY QCD, Nucl. Phys. B 471 (1996) 159 [hep-th/9603042] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. 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].

    Article  MathSciNet  ADS  Google Scholar 

  25. 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 

  26. P.C. Argyres, M.R. Plesser and A.D. Shapere, The Coulomb phase of N = 2 supersymmetric QCD, Phys. Rev. Lett. 75 (1995) 1699 [hep-th/9505100] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. A. Hanany and Y. Oz, On the quantum moduli space of vacua of N = 2 supersymmetric SU(N c ) gauge theories, Nucl. Phys. B 452 (1995) 283 [hep-th/9505075] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. R.G. Leigh and M.J. Strassler, Exactly marginal operators and duality in four-dimensional N =1 supersymmetric gauge theory, Nucl. Phys. B 447 (1995) 95 [hep-th/9503121] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. K.A. Intriligator and N. Seiberg, Phases of N = 1 supersymmetric gauge theories in four-dimensions, Nucl. Phys. B 431 (1994) 551 [hep-th/9408155] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. P.C. Argyres and M.R. Douglas, New phenomena in SU(3) supersymmetric gauge theory, Nucl. Phys. B 448 (1995) 93 [hep-th/9505062] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. T. Eguchi, K. Hori, K. Ito and S.-K. Yang, Study of N = 2 superconformal field theories in four-dimensions, Nucl. Phys. B 471 (1996) 430 [hep-th/9603002] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  32. S. Cecotti and C. Vafa, Classification of complete N = 2 supersymmetric theories in 4 dimensions, Surveys in differential geometry volume 18, International Press, U.S.A. (2013), arXiv:1103.5832 [INSPIRE].

  33. G. Bonelli, K. Maruyoshi and A. Tanzini, Wild quiver gauge theories, JHEP 02 (2012) 031 [arXiv:1112.1691] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. O. Chacaltana and J. Distler, Tinkertoys for Gaiotto duality, JHEP 11 (2010) 099 [arXiv:1008.5203] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  35. J. de Boer and S. de Haro, The off-shell M 5-brane and nonperturbative gauge theory, Nucl. Phys. B 696 (2004) 174 [hep-th/0403035] [INSPIRE].

    Article  ADS  Google Scholar 

  36. F. Cachazo, N. Seiberg and E. Witten, Chiral rings and phases of supersymmetric gauge theories, JHEP 04 (2003) 018 [hep-th/0303207] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. N. Seiberg, Adding fundamental matter to ‘Chiral rings and anomalies in supersymmetric gauge theory’, JHEP 01 (2003) 061 [hep-th/0212225] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. L. Di Pietro and S. Giacomelli, Confining vacua in SQCD, the Konishi anomaly and the Dijkgraaf-Vafa superpotential, JHEP 02 (2012) 087 [arXiv:1108.6049] [INSPIRE].

    Article  Google Scholar 

  39. S.G. Naculich, H.J. Schnitzer and N. Wyllard, Cubic curves from matrix models and generalized Konishi anomalies, JHEP 08 (2003) 021 [hep-th/0303268] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. R. Casero and E. Trincherini, Quivers via anomaly chains, JHEP 09 (2003) 041 [hep-th/0304123] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. R. Casero and E. Trincherini, Phases and geometry of the N = 1 A 2 quiver gauge theory and matrix models, JHEP 09 (2003) 063 [hep-th/0307054] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. R. Dijkgraaf and C. Vafa, On geometry and matrix models, Nucl. Phys. B 644 (2002) 21 [hep-th/0207106] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  43. N.A. Nekrasov and S.L. Shatashvili, Quantization of integrable systems and four dimensional gauge theories, arXiv:0908.4052 [INSPIRE].

  44. G. Bonelli and A. Tanzini, Hitchin systems, N = 2 gauge theories and W-gravity, Phys. Lett. B 691 (2010) 111 [arXiv:0909.4031] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  45. A. Mironov and A. Morozov, Nekrasov functions and exact Bohr-Zommerfeld integrals, JHEP 04 (2010) 040 [arXiv:0910.5670] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  46. K. Maruyoshi and M. Taki, Deformed prepotential, quantum integrable system and Liouville field theory, Nucl. Phys. B 841 (2010) 388 [arXiv:1006.4505] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  47. N. Nekrasov, A. Rosly and S. Shatashvili, Darboux coordinates, Yang-Yang functional and gauge theory, Nucl. Phys. Proc. Suppl. 216 (2011) 69 [arXiv:1103.3919] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  48. G. Bonelli, K. Maruyoshi and A. Tanzini, Quantum Hitchin systems via beta-deformed matrix models, arXiv:1104.4016 [INSPIRE].

  49. M.-C. Tan, M-theoretic derivations of 4D-2D dualities: from a geometric Langlands duality for surfaces, to the AGT correspondence, to integrable systems, JHEP 07 (2013) 171 [arXiv:1301.1977] [INSPIRE].

    Article  ADS  Google Scholar 

  50. G. Vartanov and J. Teschner, Supersymmetric gauge theories, quantization of moduli spaces of flat connections and conformal field theory, arXiv:1302.3778 [INSPIRE].

  51. F. Fucito, J.F. Morales, R. Poghossian and A. Tanzini, N = 1 superpotentials from multi-instanton calculus, JHEP 01 (2006) 031 [hep-th/0510173] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  52. L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville correlation functions from four-dimensional gauge theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  53. N. Dorey, T.J. Hollowood and S.P. Kumar, An exact elliptic superpotential for N = 1* deformations of finite N = 2 gauge theories, Nucl. Phys. B 624 (2002) 95 [hep-th/0108221] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  54. D. Gaiotto, S. Gukov and N. Seiberg, Surface defects and resolvents, JHEP 09 (2013) 070 [arXiv:1307.2578] [INSPIRE].

    Article  Google Scholar 

  55. S. Franco, Bipartite field theories: from D-brane probes to scattering amplitudes, JHEP 11 (2012) 141 [arXiv:1207.0807] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  56. J.J. Heckman, C. Vafa, D. Xie and M. Yamazaki, String theory origin of bipartite SCFTs, JHEP 05 (2013) 148 [arXiv:1211.4587] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  57. D. Xie and M. Yamazaki, Network and Seiberg duality, JHEP 09 (2012) 036 [arXiv:1207.0811] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  58. D. Xie, M 5 brane and four dimensional N = 1 theories I, arXiv:1307.5877 [INSPIRE].

  59. A. Giveon and O. Pelc, M theory, type IIA string and 4D N = 1 SUSY SU(N (L)) × SU(N (R)) gauge theory, Nucl. Phys. B 512 (1998) 103 [hep-th/9708168] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. International School of Advanced Studies (SISSA) and INFN, Sezione di Trieste, via Bonomea 265, 34136, Trieste, Italy

    Giulio Bonelli & Alessandro Tanzini

  2. ICTP, Strada Costiera 11, 34014, Trieste, Italy

    Giulio Bonelli

  3. Scuola Normale Superiore, Piazza dei Cavalieri 7, Pisa, Italy

    Simone Giacomelli

  4. California Institute of Technology, Pasadena, CA, 91125, U.S.A.

    Kazunobu Maruyoshi

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  1. Giulio Bonelli
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  2. Simone Giacomelli
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  3. Kazunobu Maruyoshi
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  4. Alessandro Tanzini
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Correspondence to Simone Giacomelli.

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ArXiv ePrint: 1307.7703

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Bonelli, G., Giacomelli, S., Maruyoshi, K. et al. \( \mathcal{N} \) =1 geometries via M-theory. J. High Energ. Phys. 2013, 227 (2013). https://doi.org/10.1007/JHEP10(2013)227

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