Mirror symmetry

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

D_n Quivers From Branes

Abstract: D-branes can end on orbifold planes if the action of the orbifold group includes (-1)^{F_L}. We consider configurations of D-branes ending on such orbifolds and study the low-energy theory on their worldvolume. We apply our results to gauge theories with eight supercharges in three and four dimensions. We explain how mirror symmetry for N=4 d=3 gauge theories with gauge group Sp(k) and matter in the antisymmetric tensor and fundamental representations follows from S-duality of IIB string theory. We argue that some of these theories have hidden Fayet-Iliopoulos deformations, not visible classically. We also study a class of finite N=2 d=4 theories (so-called D_n quiver theories) and find their exact solution. The integrable model corresponding to the exact solution is a Hitchin system on an orbifold Riemann surface. We also give a simple derivation of the S-duality group of these theories based on their relationship to SO(2n) instantons on R^2\times T^2.

Mirror symmetry in 2+1 and 1+1 dimensions

Abstract: We study the Coulomb-Higgs duality of = 2 supersymmetric abelian Chern-Simons theories in 2+1 dimensions, by compactifying dual pairs on a circle of radius R and comparing the resulting = (2,2) theories in 1+1 dimensions. Below the compactification scale, the theory on the Higgs branch reduces to the non-linear sigma model on a toric manifold. In the dual theory on the Coulomb branch, the Kaluza-Klein modes generate an infinite tower of contributions to the superpotential. After resummation, in the limit R?0 the superpotential becomes that of the Landau-Ginzburg model which is the two-dimensional mirror of the toric sigma model. We further examine the conjecture of all-scale three-dimensional mirror symmetry and observe that it is consistent with mirror symmetry in 1+1 dimensions.

Generalized complex geometry, generalized branes and the Hitchin sigma model

Abstract: Hitchin's generalized complex geometry has been shown to be relevant in compactifications of superstring theory with fluxes and is expected to lead to a deeper understanding of mirror symmetry. Gualtieri's notion of generalized complex submanifold seems to be a natural candidate for the description of branes in this context. Recently, we introduced a Batalin–Vilkovisky field theoretic realization of generalized complex geometry, the Hitchin sigma model, extending the well known Poisson sigma model. In this paper, exploiting Gualtieri's formalism, we incorporate branes into the model. A detailed study of the boundary conditions obeyed by the world sheet fields is provided. Finally, it is found that, when branes are present, the classical Batalin–Vilkovisky cohomology contains an extra sector that is related non trivially to a novel cohomology associated with the branes as generalized complex submanifolds.

Local mirror symmetry and type IIA monodromy of Calabi-Yau manifolds

Abstract: We propose a monodromy invariant pairing Khol(X) H3(X _ ;Z) ! Q for a mirror pair of Calabi-Yau manifolds, (X; X _ ). This pairing is utilized implicitly in the previous calculations of the prepotentials for Gromov-Witten invariants. After identifying the pairing explicitly we interpret some hypergeometric series from the viewpoint of homo- logical mirror symmetry due to Kontsevich. Also we consider the local mirror symmetry limit to del Pezzo surfaces in Calabi-Yau 3-folds.