Topic
Mirror symmetry
About: Mirror symmetry is a research topic. Over the lifetime, 2422 publications have been published within this topic receiving 90786 citations.
Papers published on a yearly basis
Papers
More filters
07 Feb 2008
20 citations
Posted Content•
TL;DR: In this article, a homological mirror symmetry equivalence for pairs of multiplicative hypertoric varieties was proved by matching holomorphic Lagrangian skeleta with non-commutative resolutions on the B-model side.
Abstract: In this paper, we prove a homological mirror symmetry equivalence for pairs of multiplicative hypertoric varieties, and we calculate monodromy autoequivalences of these categories by promoting our result to an equivalence of perverse schobers. We prove our equivalence by matching holomorphic Lagrangian skeleta, on the A-model side, with non-commutative resolutions on the B-model side. The hyperkahler geometry of these spaces provides each category with a natural t-structure, which helps clarify SYZ duality in a hyperkahler context. Our results are a prototype for mirror symmetry statements relating pairs of K-theoretic Coulomb branches.
20 citations
Posted Content•
TL;DR: In this paper, the authors introduced the notion of gravitational descendants of the cotangent bundle of a manifold, which are augmentations of the Chas-Sullivan algebra structure of the loop space.
Abstract: This paper introduces new operations on the string topology of a smooth manifold: gravitational descendants of its cotangent bundle, which are augmentations of the Chas-Sullivan $L_\infty$ algebra structure of the loop space. The definition extends to Liouville domains. Descendants of the $n$-torus are computed.
To a monotone Lagrangian torus in a symplectic manifold, one associates a Laurent polynomial called the Landau-Ginzburg potential, by counting holomorphic disks. This paper proves the following mirror symmetry prediction: the constant terms of the powers of an LG potential are equal to descendant Gromov-Witten invariants of the ambient manifold.
19 citations
TL;DR: In this article, the authors describe explicit relations in the symplectomorphism groups of toric hypersurfaces, which arise through the study of the one dimensional strata of this stack.
Abstract: In this paper, we describe explicit relations in the symplectomorphism groups of toric hypersurfaces. To define the elements involved, we construct a proper stack of toric hypersurfaces with compactifying boundary representing toric hypersurface degenerations. Our relations arise through the study of the one dimensional strata of this stack. The results are then examined from the perspective of homological mirror symmetry where we view sequences of relations as maximal degenerations of Landau-Ginzburg models. We then study the B-model mirror to these degenerations, which gives a new mirror symmetry approach to the minimal model program.
19 citations
TL;DR: In this paper, the equivalence of the SL(2,R)/U(1) Kazama-Suzuki model, which is a fermionic generalization of the 2D Black Hole, and N=2 Liouville theory was proved.
Abstract: We prove the equivalence of the SL(2,R)/U(1) Kazama-Suzuki model, which is a fermionic generalization of the 2d Black Hole, and N=2 Liouville theory. We show that this duality is an example of mirror symmetry. The essential part of the derivation is to realize the fermionic 2d Black Hole as the low energy limit of a gauged linear sigma-model. Liouville theory is obtained by dualizing the charged scalar fields and taking into account the vortex-instanton effects, as proposed recently in non-dilatonic models. The gauged linear sigma-model we study has many useful generalizations which we briefly discuss. In particular, we show how to construct a variety of dilatonic superstring backgrounds which generalize the fermionic 2d Black Hole and admit a mirror description in terms of Toda-like theories.
19 citations