Sigma models for bundles on Calabi–Yau: A proposal for Matrix string compactifications

Abstract

We describe a class of supersymmetric gauged linear sigma-model, whose target space is the infinite-dimensional space of bundles on a Calabi–Yau 3- or 2-fold. This target space can be considered the configuration space of D-branes wrapped around the Calabi–Yau. We propose that this model can be used to define matrix string theory compactifications. In the infrared limit the model flows to a superconformal non-linear sigma-model whose target space is the moduli space of BPS configurations of branes on the compact space, containing the moduli space of semi-stable bundles. We argue that the bulk degrees of freedom decouple in the infrared limit if semi-stability implies stability. We study topological versions of the model on Calabi–Yau 3-folds. The resulting B-model is argued to be equivalent to the holomorphic Chern–Simons theory proposed by Witten. The A-model and half-twisted model define the quantum cohomology ring and the elliptic genus, respectively, of the moduli space of stable bundles on a Calabi–Yau 3-fold.