Sigma Models for Bundles on Calabi-Yau: A Proposal for Matrix String Compactifications

TL;DR

This paper introduces a supersymmetric gauged linear sigma-model targeting the space of bundles on Calabi-Yau manifolds, proposing its use for matrix string theory compactifications and exploring its topological variants.

Contribution

It presents a novel sigma-model framework for describing D-branes on Calabi-Yau spaces and connects it to matrix string theory and topological string theories.

Findings

Infrared limit yields a superconformal sigma-model on the moduli space of BPS brane configurations.

Topological models relate to holomorphic Chern-Simons theory and compute quantum cohomology and elliptic genus.

Bulk degrees of freedom decouple under semi-stability conditions.

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.