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Mirror symmetry

About: Mirror symmetry is a research topic. Over the lifetime, 2422 publications have been published within this topic receiving 90786 citations.


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Journal ArticleDOI
TL;DR: In this paper, the authors give a mathematical account of a recent string theory calcula- tion which predicts the number of rational curves on the generic quintic three-fold, using the interpretation of Yukawa couplings in terms of variations of Hodge structure, a new q-expansion principle for functions on the moduli space of Calabi-Yau manifolds, and the mirror symmetry.
Abstract: We give a mathematical account of a recent string theory calcula- tion which predicts the number of rational curves on the generic quintic three- fold. Our account involves the interpretation of Yukawa couplings in terms of variations of Hodge structure, a new q-expansion principle for functions on the moduli space of Calabi-Yau manifolds, and the "mirror symmetry" phe- nomenon recently observed by string theorists. DEPARTMENT OF MATHEMATICS, DUKE UNIVERSITY, DURHAM, NORTH CAROLINA 27706 E-mail address: drm@math.duke.edu This content downloaded from 157.55.39.224 on Wed, 14 Dec 2016 04:59:36 UTC All use subject to http://about.jstor.org/terms

203 citations

Journal ArticleDOI
TL;DR: In this article, the interpretation in classical geometry of conformal field theories constructed from orbifolds with discrete torsion is considered, and examples of stringy regions that from a classical point of view are singularities that are to be neither resolved nor blown up are given.
Abstract: We consider the interpretation in classical geometry of conformal field theories constructed from orbifolds with discrete torsion. In examples we can analyze, these spacetimes contain ``stringy regions'' that from a classical point of view are singularities that are to be neither resolved nor blown up. Some of these models also give particularly simple and clear examples of mirror symmetry.

202 citations

Journal ArticleDOI
TL;DR: In this paper, the chiral ring and moduli space on the Coulomb branch of an N = 4 superconformal field theory in 2+1 dimensions were identified.
Abstract: This paper addresses a long standing problem - to identify the chiral ring and moduli space (i.e. as an algebraic variety) on the Coulomb branch of an N = 4 superconformal field theory in 2+1 dimensions. Previous techniques involved a computation of the metric on the moduli space and/or mirror symmetry. These methods are limited to sufficiently small moduli spaces, with enough symmetry, or to Higgs branches of sufficiently small gauge theories. We introduce a simple formula for the Hilbert series of the Coulomb branch, which applies to any good or ugly three-dimensional N = 4 gauge theory. The formula counts monopole operators which are dressed by classical operators, the Casimir invariants of the residual gauge group that is left unbroken by the magnetic flux. We apply our formula to several classes of gauge theories. Along the way we make various tests of mirror symmetry, successfully comparing the Hilbert series of the Coulomb branch with the Hilbert series of the Higgs branch of the mirror theory.

201 citations

Journal ArticleDOI
TL;DR: In this article, the moduli spaces of vacua of supersymmetric deformations of the N=4 super Yang-Mills theory were interpreted as symmetric products of non-commutative spaces.

200 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied the dynamics of 3D N = 2 Chern-Simons gauge theories and their possible phases, and showed that solitons are compatible with a mirror symmetry exchange of Higgs and Coulomb branches.
Abstract: We comment on various aspects of the the dynamics of 3d N=2 Chern-Simons gauge theories and their possible phases. Depending on the matter content, real masses and FI parameters, there can be non-compact Higgs or Coulomb branches, compact Higgs or Coulomb branches, and isolated vacua. We compute the Witten index of the theories, and show that it does not change when the system undergoes a phase transition. We study aspects of monopole operators and solitons in these theories, and clarify subtleties in the soliton collective coordinate quantization. We show that solitons are compatible with a mirror symmetry exchange of Higgs and Coulomb branches, with BPS solitons on one branch related to the modulus of the other. Among other results, we show how to derive Aharony duality from Giveon-Kutasov duality.

200 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202351
2022116
2021138
2020130
2019139
2018125