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Correlation functions in massive Landau-Ginzburg orbifolds and tests of dualities. (English) Zbl 1457.81111
Summary: In this paper we discuss correlation function computations in massive topological Landau-Ginzburg orbifolds, extending old results of C. Vafa [Mod. Phys. Lett. A 6, No. 4, 337–346 (1991; Zbl 1020.81886)]. We then apply these computations to provide further tests of the nonabelian mirrors proposal and two-dimensional Hori-Seiberg dualities with \((S)O_\pm\) gauge groups and their mirrors.

MSC:
81T45 Topological field theories in quantum mechanics
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
62P35 Applications of statistics to physics
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References:
[1] Vafa, C., Topological Landau-Ginzburg models, Mod. Phys. Lett. A, 6, 337 (1991) · Zbl 1020.81886
[2] Witten, E., Phases of N = 2 theories in two-dimensions, AMS/IP Stud. Adv. Math., 1, 143 (1996) · Zbl 0910.14019
[3] Greene, BR; Vafa, C.; Warner, NP, Calabi-Yau manifolds and renormalization group flows, Nucl. Phys. B, 324, 371 (1989) · Zbl 0744.53044
[4] Morrison, DR; Plesser, M., Towards mirror symmetry as duality for two-dimensional Abelian gauge theories, Nucl. Phys. B Proc. Suppl., 46, 177 (1996) · Zbl 0957.81656
[5] T. Maxfield, D.R. Morrison and M.R. Plesser, Mirror symmetry and partition functions, arXiv:1902.05552 [INSPIRE].
[6] K. Hori and C. Vafa, Mirror symmetry, hep-th/0002222 [INSPIRE]. · Zbl 1044.14018
[7] K. Hori, A. Iqbal and C. Vafa, D-branes and mirror symmetry, hep-th/0005247 [INSPIRE].
[8] E. Witten, The Verlinde algebra and the cohomology of the Grassmannian, hep-th/9312104 [INSPIRE]. · Zbl 0863.53054
[9] Hori, K.; Tong, D., Aspects of non-Abelian gauge dynamics in two-dimensional N = (2, 2) theories, JHEP, 05, 079 (2007)
[10] Caldararu, A.; Distler, J.; Hellerman, S.; Pantev, T.; Sharpe, E., Non-birational twisted derived equivalences in Abelian GLSMs, Commun. Math. Phys., 294, 605 (2010) · Zbl 1231.14035
[11] Hori, K., Duality in two-dimensional (2, 2) supersymmetric non-Abelian gauge theories, JHEP, 10, 121 (2013) · Zbl 1342.81635
[12] Seiberg, N., Electric-magnetic duality in supersymmetric non-Abelian gauge theories, Nucl. Phys. B, 435, 129 (1995) · Zbl 1020.81912
[13] Benini, F.; Cremonesi, S., Partition functions of N = (2, 2) gauge theories on S^2and vortices, Commun. Math. Phys., 334, 1483 (2015) · Zbl 1308.81131
[14] Doroud, N.; Gomis, J.; Le Floch, B.; Lee, S., Exact results in D = 2 supersymmetric gauge theories, JHEP, 05, 093 (2013) · Zbl 1342.81573
[15] Benini, F.; Zaffaroni, A., A topologically twisted index for three-dimensional supersymmetric theories, JHEP, 07, 127 (2015) · Zbl 1388.81400
[16] Closset, C.; Cremonesi, S.; Park, DS, The equivariant A-twist and gauged linear σ-models on the two-sphere, JHEP, 06, 076 (2015) · Zbl 1388.81713
[17] Pestun, V., Localization techniques in quantum field theories, J. Phys. A, 50 (2017) · Zbl 1378.00123
[18] Park, DS, Recent developments in 2d N = (2, 2) supersymmetric gauge theories, Int. J. Mod. Phys. A, 31 (2016) · Zbl 1348.81005
[19] Halverson, J.; Kumar, V.; Morrison, DR, New methods for characterizing phases of 2D supersymmetric gauge theories, JHEP, 09, 143 (2013)
[20] Benini, F.; Eager, R.; Hori, K.; Tachikawa, Y., Elliptic genera of two-dimensional N = 2 gauge theories with rank-one gauge groups, Lett. Math. Phys., 104, 465 (2014) · Zbl 1312.58008
[21] 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
[22] Gadde, A.; Gukov, S., 2d index and surface operators, JHEP, 03, 080 (2014) · Zbl 1333.81399
[23] W. Gu, Gauged linear sigma model and mirror symmetry, Ph.D. thesis, Virginia Tech, Blacksburg, VA, U.S.A. (2019) [INSPIRE].
[24] W. Gu and E. Sharpe, A proposal for non-Abelian mirrors, arXiv:1806.04678 [INSPIRE]. · Zbl 1383.81295
[25] Chen, Z.; Gu, W.; Parsian, H.; Sharpe, E., Two-dimensional supersymmetric gauge theories with exceptional gauge groups, Adv. Theor. Math. Phys., 24, 67 (2020)
[26] Gu, W.; Parsian, H.; Sharpe, E., More non-Abelian mirrors and some two-dimensional dualities, Int. J. Mod. Phys. A, 34 (2019)
[27] Morrison, DR; Plesser, M., Summing the instantons: quantum cohomology and mirror symmetry in toric varieties, Nucl. Phys. B, 440, 279 (1995) · Zbl 0908.14014
[28] I.V. Melnikov and M. Plesser, A-model correlators from the Coulomb branch, hep-th/0507187 [INSPIRE].
[29] Donagi, R.; Sharpe, E., GLSM’s for partial flag manifolds, J. Geom. Phys., 58, 1662 (2008) · Zbl 1218.81091
[30] Melnikov, IV; Plesser, M., A (0, 2) mirror map, JHEP, 02, 001 (2011) · Zbl 1294.81223
[31] Jockers, H.; Kumar, V.; Lapan, JM; Morrison, DR; Romo, M., Non-Abelian 2D gauge theories for determinantal Calabi-Yau varieties, JHEP, 11, 166 (2012) · Zbl 1397.81378
[32] Jockers, H.; Kumar, V.; Lapan, JM; Morrison, DR; Romo, M., Two-sphere partition functions and Gromov-Witten invariants, Commun. Math. Phys., 325, 1139 (2014) · Zbl 1301.81253
[33] Gomis, J.; Lee, S., Exact Kähler potential from gauge theory and mirror symmetry, JHEP, 04, 019 (2013) · Zbl 1342.81586
[34] Closset, C.; Cremonesi, S., Comments on N = (2, 2) supersymmetry on two-manifolds, JHEP, 07, 075 (2014) · Zbl 1333.81164
[35] Gomis, J.; Hsin, P-S; Komargodski, Z.; Schwimmer, A.; Seiberg, N.; Theisen, S., Anomalies, conformal manifolds, and spheres, JHEP, 03, 022 (2016) · Zbl 1388.81820
[36] Closset, C.; Gu, W.; Jia, B.; Sharpe, E., Localization of twisted N = (0, 2) gauged linear σ-models in two dimensions, JHEP, 03, 070 (2016) · Zbl 1388.81714
[37] K. Hori and J. Knapp, A pair of Calabi-Yau manifolds from a two parameter non-Abelian gauged linear σ-model, arXiv:1612.06214 [INSPIRE].
[38] Aharony, O.; Razamat, SS; Seiberg, N.; Willett, B., The long flow to freedom, JHEP, 02, 056 (2017) · Zbl 1377.81193
[39] Gu, W.; Sharpe, E., A proposal for (0, 2) mirrors of toric varieties, JHEP, 11, 112 (2017) · Zbl 1383.81295
[40] Cabo Bizet, N.; Martínez-Merino, A.; Pando Zayas, LA; Santos-Silva, R., Non Abelian T-duality in gauged linear σ-models, JHEP, 04, 054 (2018) · Zbl 1390.81488
[41] Knapp, J.; Sharpe, E., GLSMs, joins, and nonperturbatively-realized geometries, JHEP, 12, 096 (2019) · Zbl 1431.81104
[42] W. Gu, J. Guo and E. Sharpe, A proposal for non-Abelian (0, 2) mirrors, arXiv:1908.06036 [INSPIRE].
[43] Closset, C.; Mekareeya, N.; Park, DS, A-twisted correlators and Hori dualities, JHEP, 08, 101 (2017) · Zbl 1381.81134
[44] Sharpe, E., Notes on certain other (0, 2) correlation functions, Adv. Theor. Math. Phys., 13, 33 (2009) · Zbl 1171.81420
[45] Vafa, C., Modular invariance and discrete torsion on orbifolds, Nucl. Phys. B, 273, 592 (1986) · Zbl 0992.81515
[46] Sharpe, ER, Discrete torsion, Phys. Rev. D, 68, 126003 (2003)
[47] Dixon, LJ; Harvey, JA; Vafa, C.; Witten, E., Strings on orbifolds, Nucl. Phys. B, 261, 678 (1985)
[48] Dixon, LJ; Harvey, JA; Vafa, C.; Witten, E., Strings on orbifolds. 2, Nucl. Phys. B, 274, 285 (1986)
[49] Hatcher, A., Algebraic topology (2002), Cambridge, U.K.: Cambridge University Press, Cambridge, U.K. · Zbl 1044.55001
[50] Nekrasov, NA; Shatashvili, SL, Bethe/gauge correspondence on curved spaces, JHEP, 01, 100 (2015) · Zbl 1388.81735
[51] Hori, K.; Kapustin, A., Duality of the fermionic 2D black hole and N = 2 Liouville theory as mirror symmetry, JHEP, 08, 045 (2001)
[52] Witten, E., Topological σ-models, Commun. Math. Phys., 118, 411 (1988) · Zbl 0674.58047
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