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Towards mirror symmetry as duality for two dimensional Abelian gauge theories

Publication ,  Journal Article
Morrison, DR; Plesser, MR
Published in: Nuclear Physics B - Proceedings Supplements
January 1, 1996

Superconformal sigma models with Calabi-Yau target spaces described as complete intersection subvarieties in toric varieties can be obtained as the low-energy limit of certain abelian gauge theories in two dimensions. We formulate mirror symmetry for this class of Calabi-Yau spaces as a duality in the abelian gauge theory, giving the explicit mapping relating the two Lagrangians. The duality relates inequivalent theories which lead to isomorphic theories in the low-energy limit. This formulation suggests that mirror symmetry could be derived using abelian duality. The application of duality in this context is complicated by the presence of nontrivial dynamics and the absence of a global symmetry. We propose a way to overcome these obstacles, leading to a more symmetric Lagrangian. The argument, however, fails to produce a derivation of the conjecture.

Duke Scholars

Published In

Nuclear Physics B - Proceedings Supplements

DOI

ISSN

0920-5632

Publication Date

January 1, 1996

Volume

46

Issue

1-3

Start / End Page

177 / 186
 

Citation

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Morrison, D. R., & Plesser, M. R. (1996). Towards mirror symmetry as duality for two dimensional Abelian gauge theories. Nuclear Physics B - Proceedings Supplements, 46(1–3), 177–186. https://doi.org/10.1016/0920-5632(96)00020-5
Morrison, D. R., and M. R. Plesser. “Towards mirror symmetry as duality for two dimensional Abelian gauge theories.” Nuclear Physics B - Proceedings Supplements 46, no. 1–3 (January 1, 1996): 177–86. https://doi.org/10.1016/0920-5632(96)00020-5.
Morrison DR, Plesser MR. Towards mirror symmetry as duality for two dimensional Abelian gauge theories. Nuclear Physics B - Proceedings Supplements. 1996 Jan 1;46(1–3):177–86.
Morrison, D. R., and M. R. Plesser. “Towards mirror symmetry as duality for two dimensional Abelian gauge theories.” Nuclear Physics B - Proceedings Supplements, vol. 46, no. 1–3, Jan. 1996, pp. 177–86. Scopus, doi:10.1016/0920-5632(96)00020-5.
Morrison DR, Plesser MR. Towards mirror symmetry as duality for two dimensional Abelian gauge theories. Nuclear Physics B - Proceedings Supplements. 1996 Jan 1;46(1–3):177–186.
Journal cover image

Published In

Nuclear Physics B - Proceedings Supplements

DOI

ISSN

0920-5632

Publication Date

January 1, 1996

Volume

46

Issue

1-3

Start / End Page

177 / 186