We prove mirror symmetry for supersymmetric sigma models on Kahler manifolds in 1+1 dimensions. The proof involves establishing the equivalence of the gauged linear sigma model, embedded in a theory… Expand

We study (2,2) supersymmetric field theories on two-dimensional worldsheet with boundaries. We determine D-branes (boundary conditions and boundary interactions) that preserve half of the bulk… Expand

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… Expand

We compute the elliptic genera of two-dimensional $${\mathcal{N} = (2, 2)}$$N=(2,2) and $${\mathcal{N} = (0, 2)}$$N=(0,2) -gauged linear sigma models via supersymmetric localization, for rank-one… Expand

. We compute the elliptic genera of two-dimensional N = ( 2 , 2 ) and N = ( 0 , 2 ) - gauged linear sigma models via supersymmetric localization, for rank-one gauge groups. The elliptic genus is… Expand

We study B-type D-branes in linear sigma models with Abelian gauge groups. The most important finding is the grade restriction rule. It classifies representations of the gauge group on the Chan-Paton… Expand

A bstractWe compute the Witten index of one-dimensional gauged linear sigma models with at least N$$ \mathcal{N} $$ = 2 supersymmetry. In the phase where the gauge group is broken to a finite group,… Expand

We study parity symmetries and crosscap states in classes ofN =2 supersymmetric quantum eld theories in 1 + 1 dimensions, including non-linear sigma models, gauged WZW models, Landau-Ginzburg models,… Expand