Holographic Duals of a Family of N=1 Fixed Points

TL;DR

This paper constructs a family of supergravity solutions that serve as holographic duals to a set of N=1 fixed points in a Z_2 quiver gauge theory, interpolating between known geometries with different flux configurations.

Contribution

It introduces a new family of warped AdS_5 compactifications with a general Ansatz, providing insights into N=1 holographic RG-flows and calculating their central charges.

Findings

Constructed interpolating supergravity solutions with varying flux.

Calculated the central charge as 27/32 of the parent theory.

Derived projection conditions useful for broader N=1 holographic flows.

Abstract

We construct a family of warped AdS_5 compactifications of IIB supergravity that are the holographic duals of the complete set of N=1 fixed points of a Z_2 quiver gauge theory. This family interpolates between the T^{1,1} compactification with no three-form flux and the Z_2 orbifold of the Pilch-Warner geometry which contains three-form flux. This family of solutions is constructed by making the most general Ansatz allowed by the symmetries of the field theory. We use Killing spinor methods because the symmetries impose two simple projection conditions on the Killing spinors, and these greatly reduce the problem. We see that generic interpolating solution has a nontrivial dilaton in the internal five-manifold. We calculate the central charge of the gauge theories from the supergravity backgrounds and find that it is 27/32 of the parent N=2, quiver gauge theory. We believe that the projection conditions that we derived here will be useful for a much larger class of N=1 holographic RG-flows.