On the quantization of Seiberg-Witten geometry. (English) Zbl 1459.81063
Summary: We propose a double quantization of four-dimensional \(\mathcal{N} = 2\) Seiberg-Witten geometry, for all classical gauge groups and a wide variety of matter content. This can be understood as a set of certain non-perturbative Schwinger-Dyson identities, following the program initiated by N. Nekrasov [J. High Energy Phys. 2016, No. 3, Paper No. 181, 70 p. (2016; Zbl 1388.81872)]. The construction relies on the computation of the instanton partition function of the gauge theory on the so-called \(\Omega\)-background on \(\mathbb{R}^4\), in the presence of half-BPS codimension 4 defects. The two quantization parameters are identified as the two parameters of this background. The Seiberg-Witten curve of each theory is recovered in the flat space limit. Whenever possible, we motivate our construction from type IIA string theory.
MSC:
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 81T16 | Nonperturbative methods of renormalization applied to problems in quantum field theory |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 83E30 | String and superstring theories in gravitational theory |
Keywords:
nonperturbative effects; supersymmetric gauge theory; Wilson; ’t Hooft and Polyakov loops; quantum groupsCitations:
Zbl 1388.81872References:
| [1] | Nekrasov, N., BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters, JHEP, 03, 181 (2016) · Zbl 1388.81872 |
| [2] | N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B426 (1994) 19 [Erratum ibid.430 (1994) 485] [hep-th/9407087] [INSPIRE]. · Zbl 0996.81511 |
| [3] | Nekrasov, NA, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys., 7, 831 (2003) · Zbl 1056.81068 |
| [4] | Nekrasov, N.; Okounkov, A., Seiberg-Witten theory and random partitions, Prog. Math., 244, 525 (2006) · Zbl 1233.14029 |
| [5] | N. Nekrasov and V. Pestun, Seiberg-Witten geometry of four dimensional N = 2 quiver gauge theories, arXiv:1211.2240 [INSPIRE]. |
| [6] | Nekrasov, N.; Pestun, V.; Shatashvili, S., Quantum geometry and quiver gauge theories, Commun. Math. Phys., 357, 519 (2018) · Zbl 1393.81033 |
| [7] | Bullimore, M.; Kim, H-C; Koroteev, P., Defects and quantum Seiberg-Witten geometry, JHEP, 05, 095 (2015) · Zbl 1388.81788 |
| [8] | E. Frenkel and N. Reshetikhin, The q-characters of representations of quantum affine algebras and deformations of W -algebras, Contemp. Math.248 (2000) [math.QA/9810055]. · Zbl 0973.17015 |
| [9] | J. Shiraishi, H. Kubo, H. Awata and S. Odake, A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions, Lett. Math. Phys.38 (1996) 33 [q-alg/9507034] [INSPIRE]. · Zbl 0867.17010 |
| [10] | H. Awata, H. Kubo, S. Odake and J. Shiraishi, Quantum W_Nalgebras and Macdonald polynomials, Commun. Math. Phys.179 (1996) 401 [q-alg/9508011] [INSPIRE]. · Zbl 0873.17016 |
| [11] | E. Frenkel and N. Reshetikhin, Deformations of W -algebras associated to simple Lie algebras, Commun. Math. Phys.197 (1998) 1 [q-alg/9708006]. · Zbl 0939.17011 |
| [12] | Kimura, T.; Pestun, V., Fractional quiver W -algebras, Lett. Math. Phys., 108, 2425 (2018) · Zbl 1402.81245 |
| [13] | N. Haouzi and C. Kozçaz, Supersymmetric Wilson loops, instantons, and deformed W -algebras, arXiv:1907.03838 [INSPIRE]. |
| [14] | Ennes, IP; Lozano, C.; Naculich, SG; Schnitzer, HJ, Elliptic models and M-theory, Nucl. Phys. B, 576, 313 (2000) · Zbl 0976.81060 |
| [15] | Gomis, J.; Passerini, F., Holographic Wilson loops, JHEP, 08, 074 (2006) |
| [16] | Atiyah, MF; Hitchin, NJ; Drinfeld, VG; Manin, YI, Construction of instantons, Phys. Lett. A, 65, 185 (1978) · Zbl 0424.14004 |
| [17] | Gaiotto, D.; Kim, H-C, Duality walls and defects in 5d N = 1 theories, JHEP, 01, 019 (2017) · Zbl 1373.81351 |
| [18] | Jeffrey, L.; Kirwan, F., Localization for non-Abelian group actions, Topology, 34, 291 (1995) · Zbl 0833.55009 |
| [19] | Benini, F.; Eager, R.; Hori, K.; Tachikawa, Y., Elliptic genera of 2d N = 2 gauge theories, Commun. Math. Phys., 333, 1241 (2015) · Zbl 1321.81059 |
| [20] | C. Hwang, J. Kim, S. Kim and J. Park, General instanton counting and 5d SCFT, JHEP07 (2015) 063 [Addendum ibid.04 (2016) 094] [arXiv:1406.6793] [INSPIRE]. · Zbl 1388.81331 |
| [21] | C. Cordova and S.-H. Shao, An index formula for supersymmetric quantum mechanics, arXiv:1406.7853 [INSPIRE]. · Zbl 1346.81120 |
| [22] | Hori, K.; Kim, H.; Yi, P., Witten index and wall crossing, JHEP, 01, 124 (2015) · Zbl 1388.81832 |
| [23] | Kimura, T.; Pestun, V., Quiver W -algebras, Lett. Math. Phys., 108, 1351 (2018) · Zbl 1388.81850 |
| [24] | I.V. Cherednik, Factorizing particles on a half line and root systems, Theor. Math. Phys.61 (1984) 977 [Teor. Mat. Fiz.61 (1984) 35] [INSPIRE]. · Zbl 0575.22021 |
| [25] | Sklyanin, EK, Boundary conditions for integrable quantum systems, J. Phys. A, 21, 2375 (1988) · Zbl 0685.58058 |
| [26] | D. Tong and K. Wong, Instantons, Wilson lines, and D-branes, Phys. Rev. D91 (2015) 026007 [arXiv:1410.8523] [INSPIRE]. |
| [27] | Kim, H-C, Line defects and 5d instanton partition functions, JHEP, 03, 199 (2016) |
| [28] | Assel, B.; Sciarappa, A., Wilson loops in 5d N = 1 theories and S-duality, JHEP, 10, 082 (2018) · Zbl 1402.81207 |
| [29] | Agarwal, P.; Kim, J.; Kim, S.; Sciarappa, A., Wilson surfaces in M5-branes, JHEP, 08, 119 (2018) · Zbl 1396.83038 |
| [30] | Tong, D., The holographic dual of AdS_3 × S^3 × S^3 × S^1, JHEP, 04, 193 (2014) |
| [31] | Nekrasov, N.; Prabhakar, NS, Spiked instantons from intersecting D-branes, Nucl. Phys. B, 914, 257 (2017) · Zbl 1353.81094 |
| [32] | Mironov, A.; Morozov, A.; Zenkevich, Y., Ding-Iohara-Miki symmetry of network matrix models, Phys. Lett. B, 762, 196 (2016) · Zbl 1390.81216 |
| [33] | Maldacena, JM, Wilson loops in large N field theories, Phys. Rev. Lett., 80, 4859 (1998) · Zbl 0947.81128 |
| [34] | Rey, S-J; Yee, J-T, Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. C, 22, 379 (2001) · Zbl 1072.81555 |
| [35] | Drukker, N.; Fiol, B., All-genus calculation of Wilson loops using D-branes, JHEP, 02, 010 (2005) |
| [36] | Yamaguchi, S., Wilson loops of anti-symmetric representation and D5-branes, JHEP, 05, 037 (2006) |
| [37] | Banks, T.; Seiberg, N.; Silverstein, E., Zero and one-dimensional probes with N = 8 supersymmetry, Phys. Lett. B, 401, 30 (1997) |
| [38] | Assel, B.; Sciarappa, A., On monopole bubbling contributions to ’t Hooft loops, JHEP, 05, 180 (2019) · Zbl 1416.81178 |
| [39] | D’Hoker, E.; Phong, DH, Calogero-Moser systems in SU(N ) Seiberg-Witten theory, Nucl. Phys. B, 513, 405 (1998) · Zbl 1052.81624 |
| [40] | Shadchin, S., Saddle point equations in Seiberg-Witten theory, JHEP, 10, 033 (2004) |
| [41] | Ennes, IP; Naculich, SG; Rhedin, H.; Schnitzer, HJ, One instanton predictions for nonhyperelliptic curves derived from M-theory, Nucl. Phys. B, 536, 245 (1998) · Zbl 0948.81638 |
| [42] | Ennes, IP; Naculich, SG; Rhedin, H.; Schnitzer, HJ, One instanton predictions of a Seiberg-Witten curve from M-theory: the symmetric representation of SU(N ), Int. J. Mod. Phys. A, 14, 301 (1999) · Zbl 0924.53053 |
| [43] | Shadchin, S., Cubic curves from instanton counting, JHEP, 03, 046 (2006) · Zbl 1226.81273 |
| [44] | Naculich, SG; Rhedin, H.; Schnitzer, HJ, One instanton test of a Seiberg-Witten curve from M-theory: the antisymmetric representation of SU(N ), Nucl. Phys. B, 533, 275 (1998) · Zbl 1078.81567 |
| [45] | Nekrasov, N.; Shadchin, S., ABCD of instantons, Commun. Math. Phys., 252, 359 (2004) · Zbl 1108.81038 |
| [46] | Mariño, M.; Wyllard, N., A note on instanton counting for N = 2 gauge theories with classical gauge groups, JHEP, 05, 021 (2004) |
| [47] | D’Hoker, E.; Krichever, IM; Phong, DH, The effective prepotential of N = 2 supersymmetric SO(N_c) and Sp(N_c) gauge theories, Nucl. Phys. B, 489, 211 (1997) · Zbl 0925.81381 |
| [48] | Argyres, PC; Shapere, AD, The vacuum structure of N = 2 super-QCD with classical gauge groups, Nucl. Phys. B, 461, 437 (1996) · Zbl 0925.81354 |
| [49] | Hyakutake, Y.; Imamura, Y.; Sugimoto, S., Orientifold planes, type-I Wilson lines and non-BPS D-branes, JHEP, 08, 043 (2000) · Zbl 0989.81576 |
| [50] | Danielsson, UH; Sundborg, B., The moduli space and monodromies of N = 2 supersymmetric SO(2r + 1) Yang-Mills theory, Phys. Lett. B, 358, 273 (1995) |
| [51] | Chang, C-M; Ganor, O.; Oh, J., An index for ray operators in 5d E_nSCFTs, JHEP, 02, 018 (2017) · Zbl 1377.83110 |
| [52] | Seiberg, N., Five-dimensional SUSY field theories, nontrivial fixed points and string dynamics, Phys. Lett. B, 388, 753 (1996) |
| [53] | Haouzi, N., Quantum geometry and θ-angle in five-dimensional super Yang-Mills, JHEP, 09, 035 (2020) · Zbl 1454.81228 |
| [54] | Kim, H-C; Kim, S-S; Lee, K., 5-dim superconformal index with enhanced E_nglobal symmetry, JHEP, 10, 142 (2012) · Zbl 1397.81382 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
