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Chiral algebras from \({\Omega}\)-deformation. (English) Zbl 1421.81086

Summary: In the presence of an \({\Omega}\)-deformation, local operators generate a chiral algebra in the topological-holomorphic twist of a four-dimensional \(\mathcal{N} = 2\) supersymmetric field theory. We show that for a unitary \(\mathcal{N} = 2\) superconformal field theory, the chiral algebra thus defined is isomorphic to the one introduced by C. Beem et al. [Commun. Math. Phys. 336, No. 3, 1359–1433 (2015; Zbl 1320.81076)]. Our definition of the chiral algebra covers nonconformal theories with insertions of suitable surface defects.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T60 Supersymmetric field theories in quantum mechanics
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations

Citations:

Zbl 1320.81076
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References:

[1] C. Beem, M. Lemos, P. Liendo, W. Peelaers, L. Rastelli and B.C. van Rees, Infinite chiral symmetry in four dimensions, Commun. Math. Phys.336 (2015) 1359 [arXiv:1312.5344] [INSPIRE]. · Zbl 1320.81076
[2] P. Liendo, I. Ramírez and J. Seo, Stress-tensor OPE in \(\mathcal{N} = 2\) superconformal theories, JHEP02 (2016) 019 [arXiv:1509.00033] [INSPIRE]. · Zbl 1388.81682
[3] M. Lemos and P. Liendo, \( \mathcal{N} = 2\) central charge bounds from 2d chiral algebras, JHEP04 (2016) 004 [arXiv:1511.07449] [INSPIRE]. · Zbl 1388.81057
[4] A. Kapustin, Holomorphic reduction of \(\mathcal{N} = 2\) gauge theories, Wilson-’t Hooft operators and S-duality, hep-th/0612119 [INSPIRE].
[5] Witten, E., Topological quantum field theory, Commun. Math. Phys., 117, 353 (1988) · Zbl 0656.53078 · doi:10.1007/BF01223371
[6] Witten, E., Topological σ-models, Commun. Math. Phys., 118, 411 (1988) · Zbl 0674.58047 · doi:10.1007/BF01466725
[7] Costello, K.; Gaiotto, D., Vertex Operator Algebras and 3d \(\mathcal{N} = 4\) gauge theories, JHEP, 05, 018 (2019) · Zbl 1416.81185 · doi:10.1007/JHEP05(2019)018
[8] Nekrasov, NA, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys., 7, 831 (2003) · Zbl 1056.81068 · doi:10.4310/ATMP.2003.v7.n5.a4
[9] N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, Prog. Math.244 (2006) 525 [hep-th/0306238] [INSPIRE]. · Zbl 1233.14029
[10] D. Butson, Omega backgrounds and boundary theories in twisted supersymmetric gauge theories, in preparation.
[11] Rozansky, L.; Witten, E., HyperKähler geometry and invariants of three manifolds, Selecta Math., 3, 401 (1997) · Zbl 0908.53027 · doi:10.1007/s000290050016
[12] Beem, C.; Peelaers, W.; Rastelli, L., Deformation quantization and superconformal symmetry in three dimensions, Commun. Math. Phys., 354, 345 (2017) · Zbl 1375.81227 · doi:10.1007/s00220-017-2845-6
[13] Dedushenko, M.; Pufu, SS; Yacoby, R., A one-dimensional theory for Higgs branch operators, JHEP, 03, 138 (2018) · Zbl 1388.81803 · doi:10.1007/JHEP03(2018)138
[14] Vafa, C., Topological Landau-Ginzburg models, Mod. Phys. Lett., A 6, 337 (1991) · Zbl 1020.81886 · doi:10.1142/S0217732391000324
[15] E. Witten, Mirror manifolds and topological field theory, hep-th/9112056 [INSPIRE]. · Zbl 0834.58013
[16] J. Yagi, Ω-deformation and quantization, JHEP08 (2014) 112 [arXiv:1405.6714] [INSPIRE]. · Zbl 1333.81277
[17] Luo, Y.; Tan, M-C; Yagi, J.; Zhao, Q., Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence, JHEP, 02, 047 (2015) · Zbl 1388.81421 · doi:10.1007/JHEP02(2015)047
[18] N. Nekrasov, Tying up instantons with anti-instantons, arXiv:1802.04202, [INSPIRE]. · Zbl 1397.81078
[19] K. Costello and J. Yagi, Unification of integrability in supersymmetric gauge theories, arXiv:1810.01970 [INSPIRE]. · Zbl 1527.81103
[20] C. Cordova, D. Gaiotto and S.-H. Shao, Surface defects and chiral algebras, JHEP05 (2017) 140 [arXiv:1704.01955] [INSPIRE]. · Zbl 1380.81393
[21] Pan, Y.; Peelaers, W., Chiral algebras, localization and surface defects, JHEP, 02, 138 (2018) · Zbl 1387.81356 · doi:10.1007/JHEP02(2018)138
[22] Friedan, D.; Martinec, EJ; Shenker, SH, Conformal invariance, supersymmetry and string theory, Nucl. Phys., B 271, 93 (1986) · doi:10.1016/S0550-3213(86)80006-2
[23] Pan, Y.; Peelaers, W., Schur correlation functions on S^3 × S^1, JHEP, 07, 013 (2019) · Zbl 1418.81078 · doi:10.1007/JHEP07(2019)013
[24] M. Dedushenko and M. Fluder, Chiral algebra, localization, modularity, surface defects, and all that, arXiv:1904.02704 [INSPIRE]. · Zbl 1456.81368
[25] Witten, E., Two-dimensional models with (0, 2) supersymmetry: perturbative aspects, Adv. Theor. Math. Phys., 11, 1 (2007) · Zbl 1200.17014 · doi:10.4310/ATMP.2007.v11.n1.a1
[26] Tan, M-C, Two-dimensional twisted σ-models and the theory of chiral differential operators, Adv. Theor. Math. Phys., 10, 759 (2006) · Zbl 1132.81045 · doi:10.4310/ATMP.2006.v10.n6.a1
[27] Tan, M-C; Yagi, J., Chiral algebras of (0, 2) σ-models: beyond perturbation theory, Lett. Math. Phys., 84, 257 (2008) · Zbl 1165.81038 · doi:10.1007/s11005-008-0249-4
[28] Tan, M-C; Yagi, J., Chiral algebras of (0, 2) σ-models: beyond perturbation theory, Lett. Math. Phys., 84, 257 (2008) · Zbl 1165.81038 · doi:10.1007/s11005-008-0249-4
[29] Yagi, J., Chiral algebras of (0, 2) models, Adv. Theor. Math. Phys., 16, 1 (2012) · Zbl 1272.81132 · doi:10.4310/ATMP.2012.v16.n1.a1
[30] M. Del Zotto and G. Lockhart, Universal features of BPS strings in six-dimensional SCFTs, JHEP08 (2018) 173 [arXiv:1804.09694] [INSPIRE]. · Zbl 1396.81173
[31] Callan, CG; Harvey, JA, Anomalies and fermion zero modes on strings and domain walls, Nucl. Phys., B 250, 427 (1985) · doi:10.1016/0550-3213(85)90489-4
[32] A. Kapustin and K. Vyas, A-models in three and four dimensions, arXiv:1002.4241 [INSPIRE].
[33] Bullimore, M.; Dimofte, T.; Gaiotto, D., The Coulomb branch of 3d \(\mathcal{N} = 4\) theories, Commun. Math. Phys., 354, 671 (2017) · Zbl 1379.81072 · doi:10.1007/s00220-017-2903-0
[34] Bullimore, M.; Dimofte, T.; Gaiotto, D.; Hilburn, J., Boundaries, mirror symmetry and symplectic duality in 3d \(\mathcal{N} = 4\) gauge theory, JHEP, 10, 108 (2016) · Zbl 1390.81309 · doi:10.1007/JHEP10(2016)108
[35] Bullimore, M.; Dimofte, T.; Gaiotto, D.; Hilburn, J.; Kim, H-C, Vortices and Vermas, Adv. Theor. Math. Phys., 22, 803 (2018) · Zbl 07430942 · doi:10.4310/ATMP.2018.v22.n4.a1
[36] K. Costello, M-theory in the Ω-background and 5-dimensional non-commutative gauge theory, arXiv:1610.04144 [INSPIRE].
[37] K. Costello, Holography and Koszul duality: the example of the M 2 brane, arXiv:1705.02500 [INSPIRE].
[38] M. Dedushenko, Y. Fan, S.S. Pufu and R. Yacoby, Coulomb branch operators and mirror symmetry in three dimensions, JHEP04 (2018) 037 [arXiv:1712.09384] [INSPIRE]. · Zbl 1390.81502
[39] C. Beem, D. Ben-Zvi, M. Bullimore, T. Dimofte and A. Neitzke, Secondary products in supersymmetric field theory, arXiv:1809.00009 [INSPIRE]. · Zbl 1443.81052
[40] M. Dedushenko, Y. Fan, S.S. Pufu and R. Yacoby, Coulomb branch quantization and abelianized monopole bubbling, arXiv:1812.08788 [INSPIRE]. · Zbl 1427.81165
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