Mirror symmetry

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

Two-Sphere Partition Functions and Gromov-Witten Invariants

Abstract: Many N=(2,2) two-dimensional nonlinear sigma models with Calabi-Yau target spaces admit ultraviolet descriptions as N=(2,2) gauge theories (gauged linear sigma models). We conjecture that the two-sphere partition function of such ultraviolet gauge theories -- recently computed via localization by Benini et al. and Doroud et al. -- yields the exact Kahler potential on the quantum Kahler moduli space for Calabi-Yau threefold target spaces. In particular, this allows one to compute the genus zero Gromov-Witten invariants for any such Calabi-Yau threefold without the use of mirror symmetry. More generally, when the infrared superconformal fixed point is used to compactify string theory, this provides a direct method to compute the spacetime Kahler potential of certain moduli (e.g., vector multiplet moduli in type IIA), exactly in {\alpha}'. We compute these quantities for the quintic and for Rodland's Pfaffian Calabi-Yau threefold and find agreement with existing results in the literature. We then apply our methods to a codimension four determinantal Calabi-Yau threefold in P^7, recently given a nonabelian gauge theory description by the present authors, for which no mirror Calabi-Yau is currently known. We derive predictions for its Gromov-Witten invariants and verify that our predictions satisfy nontrivial geometric checks.

N=2 strings and the twistorial Calabi-Yau

Abstract: We interpret the A and B model topological strings on CP^{3|4} as equivalent to open N=2 string theory on spacetime with signature (2,2), when covariantized with respect to SO(2,2) and supersymmetrized a la Siegel. We propose that instantons ending on Lagrangian branes wrapping RP^{3|4} deform the self-dual N=4 Yang-Mills sector to ordinary Yang-Mills by generating a `t Hooft like expansion. We conjecture that the A and B versions are S-dual to each other. We also conjecture that mirror symmetry may explain the recent observations of Witten that twistor transformed N=4 Yang-Mills amplitudes lie on holomorphic curves.

D-Branes on Calabi-Yau Manifolds

Abstract: We give an overview of recent work on Dirichlet branes on CalabiYau threefolds which makes contact with Kontsevich’s homological mirror symmetry proposal, proposes a new definition of stability which is appropriate in string theory, and provides concrete quiver categories equivalent to certain categories of branes on CY.

Strings on pp-waves and massive two dimensional field theories

Abstract: We find a general class of pp-wave solutions of type IIB string theory such that the light cone gauge worldsheet lagrangian is that of an interacting massive field theory. When the light cone Lagrangian has (2,2) supersymmetry we can find backgrounds that lead to arbitrary superpotentials on the worldsheet. We consider situations with both flat and curved transverse spaces. We describe in some detail the background giving rise to the N=2 sine Gordon theory on the worldsheet. Massive mirror symmetry relates it to the deformed $CP^1$ model (or sausage model) which seems to elude a purely supergravity target space interpretation.