Superpotentials for Quiver Gauge Theories

TL;DR

This paper computes superpotentials for quiver gauge theories from D-brane decay on del Pezzo cycles in Calabi-Yau manifolds using advanced algebraic geometry tools, confirming expected relations in the moduli space.

Contribution

It introduces a method to derive superpotentials for quiver gauge theories via A-infinity products in derived categories, linking geometric decay processes to algebraic structures.

Findings

Superpotentials are linear in Ext2 fields and relate to Ext1 polynomials.

The derived category approach confirms expected moduli space relations.

Method applies to quiver gauge theories from D-brane decay.

Abstract

We compute superpotentials for quiver gauge theories arising from marginal D-Brane decay on collapsed del Pezzo cycles S in a Calabi-Yau X. This is done using the machinery of A-infinity products in the derived category of coherent sheaves of X, which in turn is related to the derived category of S and quiver path algebras. We confirm that the superpotential is what one might have guessed from analyzing the moduli space, i.e., it is linear in the fields corresponding to the Ext2's of the quiver and that each such Ext2 multiplies a polynomial in Ext1's equal to precisely the relation represented by the Ext2.