Equivariant branes and equivariant homological mirror symmetry

Equivariant Localization and Mirror Symmetry

Dirichlet branes, homological mirror symmetry, and stability

We discuss some mathematical conjectures which have come out of the study of Dirichlet branes in superstring theory, focusing on the case of supersymmetric branes in Calabi-Yau compactification. This has led to the formulation of a notion of stability for objects in a derived category, contact with Kontsevich’s homological mirror symmetry conjecture, and ”physics proofs” for many of the subsequ...

The quantum equivariant cohomology of toric manifolds through mirror symmetry

Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten invariants of the target manifold. e-mail address: [email protected] address: Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands

Meet Homological Mirror Symmetry

In this paper, we introduce the interested reader to homological mirror symmetry. After recalling a little background knowledge, we tackle the simplest cases of homological mirror symmetry: curves of genus zero and one. We close by outlining the current state of the field and mentioning what homological mirror symmetry has to say about other aspects of mirror symmetry.

Planar Homological Mirror Symmetry

In this article, we formulate a planar limited version of the B-side in homological mirror symmetry that formularizes Chern-Simons-type topological open string field theory using homotopy associative algebra (A∞ algebra). This formulation is based on the works by Dijkgraaf and Vafa. We show that our formularization includes gravity/gauge theory correspondence which originates in the AdS/CFT dua...