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.

41 pages

References in corpus (9)

• Matrix String Theory
• Why is the Matrix Model Correct?
• Six-Dimensional Supergravity on S^3 X AdS_3 and 2d Conformal Field Theory
• Instanton Strings and HyperKaehler Geometry
• D-branes and Matrix Theory in Curved Space
• Chern-Simons and Twisted Supersymmetry in Higher Dimensions
• Large N Elliptic Genus and AdS/CFT Correspondence
• 5D Black Holes and Matrix Strings
• Limits of Matrix Theory in Curved Space

Cited by in corpus (2)

• Cohomological Yang-Mills Theories on Kahler 3-Folds
• Higgs Bundles and Four Manifolds