zbMATH — the first resource for mathematics

Non abelian T-duality in Gauged Linear Sigma Models. (English) Zbl 1390.81488
Summary: Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by K. Hori et al. [Mirror symmetry. Providence, RI: American Mathematical Society (AMS) (2003; Zbl 1044.14018)]. We consider an alternative formulation of abelian T-duality on GLSM’s as a gauging of a global U(1) symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa loc. cit. We extend the construction to formulate non-abelian T-duality on GLSMs with global non-abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they depend in general on semi-chiral superfields; for cases such as SU(2) they depend on twisted chiral superfields. We solve the equations of motion for an SU(2) gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-abelian sector that can be described by a family of abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the U(1) field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T13 Yang-Mills and other gauge theories in quantum field theory
Full Text: DOI arXiv
[1] Morrison, DR; Plesser, MR, Towards mirror symmetry as duality for two-dimensional abelian gauge theories, Nucl. Phys. Proc. Suppl., 46, 177, (1996) · Zbl 0957.81656
[2] Strominger, A.; Yau, S-T; Zaslow, E., Mirror symmetry is T duality, Nucl. Phys., B 479, 243, (1996) · Zbl 0896.14024
[3] K. Hori and C. Vafa, Mirror symmetry, hep-th/0002222 [INSPIRE].
[4] K. Hori et al., Mirror symmetry. Volume 1, Clay mathematics monographs, AMS, Providence U.S.A. (2003). · Zbl 1069.81562
[5] Giveon, A.; Porrati, M.; Rabinovici, E., Target space duality in string theory, Phys. Rept., 244, 77, (1994)
[6] Ossa, XC; Quevedo, F., Duality symmetries from nonabelian isometries in string theory, Nucl. Phys., B 403, 377, (1993) · Zbl 1030.81513
[7] Sfetsos, K.; Thompson, DC, On non-abelian T-dual geometries with Ramond fluxes, Nucl. Phys., B 846, 21, (2011) · Zbl 1208.81173
[8] Y. Lozano, E. O Colgain, K. Sfetsos and D.C. Thompson, Non-abelian T-duality, Ramond Fields and Coset Geometries, JHEP06 (2011) 106 [arXiv:1104.5196] [INSPIRE]. · Zbl 1274.14047
[9] Itsios, G.; Lozano, Y.; Montero, J.; Núñez, C., the AdS_{5}non-abelian T-dual of Klebanov-Witten as a\( \mathcal{N} \) = 1 linear quiver from M5-branes, JHEP, 09, 038, (2017) · Zbl 1382.81182
[10] J. van Gorsel and S. Zacarías, A Type IIB Matrix Model via non-Abelian T-dualities, JHEP12 (2017) 101 [arXiv:1711.03419] [INSPIRE]. · Zbl 1383.83194
[11] K. Hori and D. Tong, Aspects of Non-Abelian Gauge Dynamics in Two-Dimensional N = (2\(,\)2) Theories, JHEP05 (2007) 079 [hep-th/0609032] [INSPIRE].
[12] 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
[13] Hori, K., duality in two-dimensional (2\(,\) 2) supersymmetric non-abelian gauge theories, JHEP, 10, 121, (2013) · Zbl 1342.81635
[14] Jockers, H.; Kumar, V.; Lapan, JM; Morrison, DR; Romo, M., nonabelian 2D gauge theories for determinantal Calabi-Yau varieties, JHEP, 11, 166, (2012) · Zbl 1397.81378
[15] Gates, SJ; Grisaru, MT; Roček, M.; Siegel, W., Superspace or one thousand and one lessons in supersymmetry, Front. Phys., 58, 1, (1983) · Zbl 0986.58001
[16] Witten, E., phases of N = 2 theories in two-dimensions, Nucl. Phys., B 403, 159, (1993) · Zbl 0910.14020
[17] Bogaerts, J.; Sevrin, A.; Loo, S.; Gils, S., Properties of semichiral superfields, Nucl. Phys., B 562, 277, (1999) · Zbl 0958.81194
[18] Gates, SJ; Merrell, W., \(D\) = 2 \(N\) = (2\(,\) 2) semi chiral vector multiplet, JHEP, 10, 035, (2007)
[19] Gates, SJ; Hull, CM; Roček, M., Twisted multiplets and new supersymmetric nonlinear σ-models, Nucl. Phys., B 248, 157, (1984)
[20] Giveon, A.; Roček, M., On nonabelian duality, Nucl. Phys., B 421, 173, (1994) · Zbl 0990.81690
[21] Roček, M.; Verlinde, EP, Duality, quotients and currents, Nucl. Phys., B 373, 630, (1992)
[22] J. Wess and J. Bagger, Supesymmetry and Supergravity, Princeton Series in Physics, Princeton University Press, Princeton U.S.A. (1992). · Zbl 1382.81182
[23] Rødland, EA, the pfaffian Calabi-Yau, its mirror, and their link to the Grassmannian G(2\(,\) 7), Compos. Math., 122, 135, (2000) · Zbl 0974.14026
[24] Kanazawa, A., Pfaffian Calabi-Yau threefolds and mirror symmetry, Commun. Num. Theor. Phys., 6, 661, (2012) · Zbl 1274.14047
[25] A. Caldararu, J. Knapp and E. Sharpe, GLSM realizations of maps and intersections of Grassmannians and Pfaffians, arXiv:1711.00047 [INSPIRE]. · Zbl 1390.81310
[26] Hosono, S.; Konishi, Y., Higher genus Gromov-Witten invariants of the grassmannian and the Pfaffian Calabi-Yau threefolds, Adv. Theor. Math. Phys., 13, 463, (2009) · Zbl 1218.81089
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.