N=1 and N=2 Geometry from Fluxes

TL;DR

This paper proves the equivalence between N=1 supersymmetric gauge theories deformed from N=2 theories and type IIB string theory on Calabi-Yau threefolds with fluxes, linking superpotential minimization to geometric properties.

Contribution

It establishes a precise correspondence between gauge theory superpotentials and Calabi-Yau flux geometries, extending the understanding of N=2 and N=1 dynamics.

Findings

Superpotential minimization corresponds to Seiberg-Witten curve factorization.

Turning off superpotential recovers full N=2 gauge dynamics from flux geometries.

Provides a geometric framework for analyzing supersymmetric gauge theories.

Abstract

We provide a proof of the equivalence of N=1 dynamics obtained by deforming N=2 supersymmetric gauge theories by addition of certain superpotential terms, with that of type IIB superstring on Calabi-Yau threefold geometries with fluxes. In particular we show that minimization of the superpotential involving gaugino fields is equivalent to finding loci where Seiberg-Witten curve has certain factorization property. Moreover, by considering the limit of turning off of the superpotential we obtain the full low energy dynamics of N=2 gauge systems from Calabi-Yau geometries with fluxes.