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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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TL;DR: In this article, a generalization of the SL(2, ℤ) action on a 3D CFT with a U(1) 0-form global symmetry is presented.
Abstract: Mirror symmetry, a three dimensional $$ \mathcal{N} $$
= 4 IR duality, has been studied in detail for quiver gauge theories of the ADE-type (as well as their affine versions) with unitary gauge groups. The A-type quivers (also known as linear quivers) and the associated mirror dualities have a particularly simple realization in terms of a Type IIB system of D3-D5-NS5-branes. In this paper, we present a systematic field theory prescription for constructing 3d mirror pairs beyond the ADE quiver gauge theories, starting from a dual pair of A-type quivers with unitary gauge groups. The construction involves a certain generalization of the S and the T operations, which arise in the context of the SL(2, ℤ) action on a 3d CFT with a U(1) 0-form global symmetry. We implement this construction in terms of two supersymmetric observables — the round sphere partition function and the superconformal index on S2 × S1. We discuss explicit examples of various (non-ADE) infinite families of mirror pairs that can be obtained in this fashion. In addition, we use the above construction to conjecture explicit 3d $$ \mathcal{N} $$
= 4 Lagrangians for 3d SCFTs, which arise in the deep IR limit of certain Argyres-Douglas theories compactified on a circle.
17 citations
TL;DR: In this article, a list of known four-dimensional Fano manifolds and their quantum periods was collected and their index greater than one was computed. And this list includes all 4D Fano manifold types.
Abstract: We collect a list of known four-dimensional Fano manifolds and compute their quantum periods. This list includes all four-dimensional Fano manifolds of index greater than one, all four-dimensional ...
17 citations
TL;DR: In this article, the authors describe mirror symmetry in N = 2 superconformal field theories in terms of a dynamical topology changing process of the principal fiber bundle associated with a topological membrane.
16 citations
TL;DR: In this article, an algebra on the space of perturbative BPS states in toroidal compactification of the heterotic string is defined, which is closely related to a generalized Kac-Moody algebra.
Abstract: We define an algebra on the space of BPS states in theories with extended supersymmetry. We show that the algebra of perturbative BPS states in toroidal compactification of the heterotic string is closely related to a generalized Kac-Moody algebra. We use D-brane theory to compare the formulation of RR-charged BPS algebras in type II compactification with the requirements of string/string duality and find that the RR charged BPS states should be regarded as cohomology classes on moduli spaces of coherent sheaves. The equivalence of the algebra of BPS states in heterotic/IIA dual pairs elucidates certain results and conjectures of Nakajima and Gritsenko & Nikulin, on geometrically defined algebras and furthermore suggests nontrivial generalizations of these algebras. In particular, to any Calabi-Yau 3-fold there are two canonically associated algebras exchanged by mirror symmetry.
16 citations
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TL;DR: For the resolved conifold with one outer D-brane in arbitrary framing, the authors proved local mirror symmetry for the resolved confolds for holomorphic disc invariants and proved integrality conjecture of such invariants by Ooguri-Vafa in this case.
Abstract: For the resolved conifold with one outer D-brane in arbitrary framing, we present some results for the open string partition functions obtained by some operator manipulations. We prove some conjectures by Aganagic-Vafa and Aganagic-Klemm-Vafa that relates such invariants to the mirror curve of the resolved conifold. This establishes local mirror symmetry for the resolved confolds for holomorphic disc invariants. We also verify an integrality conjecture of such invariants by Ooguri-Vafa in this case and present closed formulas for some Ooguri-Vafa type invariants in genus 0 and arbitrary genera.
16 citations