N=1 Field Theories and Fluxes in IIB String Theory

TL;DR

This paper explores how complex three-form fluxes in IIB string theory influence the moduli space and fixed points of deformed N=2 quiver gauge theories, revealing geometric structures like ALE spaces and generalized conifolds.

Contribution

It provides a detailed analysis of the role of fluxes and superpotentials in shaping the moduli space and fixed points of N=1 theories derived from N=2 quivers, including new insights into their geometric and quantum properties.

Findings

Moduli space is either ALE space or generalized conifold depending on flux type.

Exactly marginal operators parameterize fixed manifolds and preserve moduli space dimension.

Moduli space at the end of Seiberg duality cascade is a three-dimensional generalized conifold.

Abstract

Deformation of N=2 quiver gauge theories by adjoint masses leads to fixed manifolds of N=1 superconformal field theories. We elaborate on the role of the complex three-form flux in the IIB duals to these fixed point theories, primarily using field theory techniques. We study the moduli space at a fixed point and find that it is either the two (complex) dimensional ALE space or three-dimensional generalized conifold, depending on the type of three-form flux that is present. We describe the exactly marginal operators that parameterize the fixed manifolds and find the operators which preserve the dimension of the moduli space. We also study deformations by arbitrary superpotentials W(\Phi_i) for the adjoints. We invoke the a-theorem to show that there are no dangerously irrelevant operators like Tr\Phi_i^{k+1}, k>2 in the N=2 quiver gauge theories. The moduli space of the IR fixed point theory generally contains orbifold singularities if W(\Phi_i) does not give a mass to the adjoints. Finally we examine some nonconformal N=1 quiver theories. We find evidence that the moduli space at the endpoint of a Seiberg duality cascade is always a three-dimensional generalized conifold. In general, the low-energy theory receives quantum corrections. In several non-cascading theories we find that the moduli space is a generalized conifold realized as a monodromic fibration.