Sigma models for bundles on Calabi-Yau: a proposal for matrix string compactifications

Abstract

W e describe a class of supersymmetric gauged linear sigma-model, whose target space is the infinite dimensional space of bundles on a Calabi-Y au 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 o ws to a superconformal non-linear sigma-model whose target space is the moduli space of BPS configurations of branes on the compact space, con taining the moduli space of semi-stable bundles. W e argue that the bulk degrees of freedom decouple in the infrared limit if semi-stabilit y implies stabilit y. W e study topological versions of the model on Calabi-Y au 3-folds. The resulting B-model is argued to be equivalent to the holomorphic Chern-Simons theory proposed b y Witten. TheA-model and half-twisted model define the quan tum cohomology ring and the elliptic gen us, respectively, of the moduli space of stable bundles on a Calabi-Y au 3-fold.