Abstract
The Hori-Tong and Hori dualities are infrared dualities between two-dimensional gauge theories with \( \mathcal{N} \) = (2, 2) supersymmetry, which are reminiscent of four-dimensional Seiberg dualities. We provide additional evidence for those dualities with U(N c ), USp(2N c ), SO(N ) and O(N ) gauge groups, by matching correlation functions of Coulomb branch operators on a Riemann surface Σ g , in the presence of the topological A-twist. The O(N ) theories studied, denoted by O+(N ) and O_(N ), can be understood as \( {\mathbb{Z}}_2 \) orbifolds of an SO(N ) theory. The correlators of these theories on Σ g with g > 0 are obtained by computing correlators with \( {\mathbb{Z}}_2 \)-twisted boundary conditions and summing them up with weights determined by the orbifold projection.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K. Hori and D. Tong, Aspects of Non-Abelian Gauge Dynamics in Two-Dimensional N =(2,2) Theories, JHEP 05 (2007) 079 [hep-th/0609032] [INSPIRE].
K. Hori, Duality In Two-Dimensional (2, 2) Supersymmetric Non-Abelian Gauge Theories, JHEP 10 (2013) 121 [arXiv:1104.2853] [INSPIRE].
F. Benini and S. Cremonesi, Partition Functions of \( \mathcal{N} \) = (2, 2) Gauge Theories on S 2 and Vortices, Commun. Math. Phys. 334 (2015) 1483 [arXiv:1206.2356] [INSPIRE].
N. Seiberg, Electric-magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B 435 (1995) 129 [hep-th/9411149] [INSPIRE].
N. Doroud, J. Gomis, B. Le Floch and S. Lee, Exact Results in D = 2 Supersymmetric Gauge Theories, JHEP 05 (2013) 093 [arXiv:1206.2606] [INSPIRE].
F. Benini, R. Eager, K. Hori and Y. Tachikawa, Elliptic genera of two-dimensional N = 2 gauge theories with rank-one gauge groups, Lett. Math. Phys. 104 (2014) 465 [arXiv:1305.0533] [INSPIRE].
F. Benini, R. Eager, K. Hori and Y. Tachikawa, Elliptic Genera of 2d \( \mathcal{N} \) = 2 Gauge Theories, Commun. Math. Phys. 333 (2015) 1241 [arXiv:1308.4896] [INSPIRE].
F. Benini and B. Le Floch, Supersymmetric localization in two dimensions, arXiv:1608.02955 [INSPIRE].
D.S. Park, Recent developments in 2d \( \mathcal{N} \) = (2, 2) supersymmetric gauge theories, Int. J. Mod. Phys. A 31 (2016) 1630045 [arXiv:1608.03607] [INSPIRE].
F. Benini and A. Zaffaroni, A topologically twisted index for three-dimensional supersymmetric theories, JHEP 07 (2015) 127 [arXiv:1504.03698] [INSPIRE].
C. Closset, S. Cremonesi and D.S. Park, The equivariant A-twist and gauged linear σ-models on the two-sphere, JHEP 06 (2015) 076 [arXiv:1504.06308] [INSPIRE].
C. Closset, W. Gu, B. Jia and E. Sharpe, Localization of twisted \( \mathcal{N} \) = (0, 2) gauged linear σ-models in two dimensions, JHEP 03 (2016) 070 [arXiv:1512.08058] [INSPIRE].
E. Witten, Phases of N = 2 theories in two-dimensions, Nucl. Phys. B 403 (1993) 159 [hep-th/9301042] [INSPIRE].
E. Witten, The Verlinde algebra and the cohomology of the Grassmannian, hep-th/9312104 [INSPIRE].
D.R. Morrison and M.R. Plesser, Summing the instantons: Quantum cohomology and mirror symmetry in toric varieties, Nucl. Phys. B 440 (1995) 279 [hep-th/9412236] [INSPIRE].
I.V. Melnikov and M.R. Plesser, The Coulomb branch in gauged linear σ-models, JHEP 06 (2005) 013 [hep-th/0501238] [INSPIRE].
I.V. Melnikov and M.R. Plesser, A-model correlators from the Coulomb branch, hep-th/0507187 [INSPIRE].
D. Orlando and S. Reffert, Relating Gauge Theories via Gauge/ Bethe Correspondence, JHEP 10 (2010) 071 [arXiv:1005.4445] [INSPIRE].
B. Jia, E. Sharpe and R. Wu, Notes on nonabelian (0,2) theories and dualities, JHEP 08 (2014) 017 [arXiv:1401.1511] [INSPIRE].
F. Benini, D.S. Park and P. Zhao, Cluster Algebras from Dualities of 2d \( \mathcal{N} \) = (2, 2) Quiver Gauge Theories, Commun. Math. Phys. 340 (2015) 47 [arXiv:1406.2699] [INSPIRE].
J. Gomis and B. Le Floch, M2-brane surface operators and gauge theory dualities in Toda, JHEP 04 (2016) 183 [arXiv:1407.1852] [INSPIRE].
M. Yamazaki and W. Yan, Integrability from 2d \( \mathcal{N} \) = (2, 2) dualities, J. Phys. A 48 (2015) 394001 [arXiv:1504.05540] [INSPIRE].
J. Gomis, P.-S. Hsin, Z. Komargodski, A. Schwimmer, N. Seiberg and S. Theisen, Anomalies, Conformal Manifolds and Spheres, JHEP 03 (2016) 022 [arXiv:1509.08511] [INSPIRE].
J. Bae, C. Imbimbo, S.-J. Rey and D. Rosa, New Supersymmetric Localizations from Topological Gravity, JHEP 03 (2016) 169 [arXiv:1510.00006] [INSPIRE].
J. Guo, Z. Lu and E. Sharpe, Quantum sheaf cohomology on Grassmannians, Commun. Math. Phys. 352 (2017) 135 [arXiv:1512.08586] [INSPIRE].
K. Ueda and Y. Yoshida, Equivariant A-twisted GLSM and Gromov-Witten invariants of CY 3-folds in Grassmannians, arXiv:1602.02487 [INSPIRE].
A. Gerhardus and H. Jockers, Quantum periods of Calabi-Yau fourfolds, Nucl. Phys. B 913 (2016) 425 [arXiv:1604.05325] [INSPIRE].
K. Cho, H. Kim and J. Park, 2D Seiberg-like dualities with an adjoint matter, arXiv:1702.00235 [INSPIRE].
E. Witten, Topological σ-models, Commun. Math. Phys. 118 (1988) 411 [INSPIRE].
C. Closset and S. Cremonesi, Comments on \( \mathcal{N} \) = (2, 2) supersymmetry on two-manifolds, JHEP 07 (2014) 075 [arXiv:1404.2636] [INSPIRE].
N.A. Nekrasov and S.L. Shatashvili, Bethe/Gauge correspondence on curved spaces, JHEP 01 (2015) 100 [arXiv:1405.6046] [INSPIRE].
F. Benini and A. Zaffaroni, Supersymmetric partition functions on Riemann surfaces, arXiv:1605.06120 [INSPIRE].
C. Closset and H. Kim, Comments on twisted indices in 3d supersymmetric gauge theories, JHEP 08 (2016) 059 [arXiv:1605.06531] [INSPIRE].
C. Closset, H. Kim and B. Willett, Supersymmetric partition functions and the three-dimensional A-twist, JHEP 03 (2017) 074 [arXiv:1701.03171] [INSPIRE].
N.A. Nekrasov and S.L. Shatashvili, Supersymmetric vacua and Bethe ansatz, Nucl. Phys. Proc. Suppl. 192-193 (2009) 91 [arXiv:0901.4744] [INSPIRE].
L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, Strings on Orbifolds, Nucl. Phys. B 261 (1985) 678 [INSPIRE].
L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, Strings on Orbifolds. 2., Nucl. Phys. B 274 (1986) 285 [INSPIRE].
O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, The long flow to freedom, JHEP 02 (2017) 056 [arXiv:1611.02763] [INSPIRE].
G. Festuccia and N. Seiberg, Rigid Supersymmetric Theories in Curved Superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
C. Closset, T.T. Dumitrescu, G. Festuccia and Z. Komargodski, From Rigid Supersymmetry to Twisted Holomorphic Theories, Phys. Rev. D 90 (2014) 085006 [arXiv:1407.2598] [INSPIRE].
M. Brion and M. Vergne, Arrangements of hyperplanes I: Rational functions and Jeffrey-Kirwan residue, math/9903178.
D. Gaiotto, S. Gukov and N. Seiberg, Surface Defects and Resolvents, JHEP 09 (2013) 070 [arXiv:1307.2578] [INSPIRE].
N. Chair, Explicit computations for the intersection numbers on Grassmannians and on the space of holomorphic maps from CP 1 into G r (C n), hep-th/9808170 [INSPIRE].
M.S. Ravi, J. Rosenthal and X. Wang, Dynamic pole assignment and schubert calculus, SIAM J. Control Optim. 34 (1996) 813.
K.A. Intriligator, Fusion residues, Mod. Phys. Lett. A 6 (1991) 3543 [hep-th/9108005] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1705.04137
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Closset, C., Mekareeya, N. & Park, D.S. A-twisted correlators and Hori dualities. J. High Energ. Phys. 2017, 101 (2017). https://doi.org/10.1007/JHEP08(2017)101
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2017)101