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arXiv · hep-th/9904150

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

C. Hofman·J. -S. Park
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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.

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C. Hofman, J. -S. Park. 1999-08-25. Sigma Models for Bundles on Calabi-Yau: A Proposal for Matrix String Compactifications. https://doi.org/10.1016/s0550-3213(99)00548-9

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