Supersymmetric 3-branes on smooth ALE manifolds with flux

TL;DR

This paper constructs new supersymmetric 3-brane solutions in type IIB supergravity on ALE manifolds with flux, analyzing their properties and implications for gauge theory duals.

Contribution

It introduces a family of explicit BPS solutions with flux on ALE manifolds, including detailed analysis of the warp factor and its mathematical properties.

Findings

Solutions preserve N=2 supersymmetry.

Warp factor regular near the cycle, indicating smeared brane charge.

Conformal invariance is broken despite vanishing 3-form flux.

Abstract

We construct a new family of classical BPS solutions of type IIB supergravity describing 3-branes transverse to a 6-dimensional space with topology R^2*ALE. They are characterized by a non-trivial flux of the supergravity 2-forms through the homology 2-cycles of a generic smooth ALE manifold. Our solutions have two Killing spinors and thus preserve N=2 supersymmetry. They are expressed in terms of a quasi harmonic function H (the ``warp factor''), whose properties we study in the case of the simplest ALE, namely the Eguchi-Hanson manifold. The equation for H is identified as an instance of the confluent Heun equation. We write explicit power series solutions and solve the recurrence relation for the coefficients, discussing also the relevant asymptotic expansions. While, as in all such N=2 solutions, supergravity breaks down near the brane, the smoothing out of the vacuum geometry has the effect that the warp factor is regular in a region near the cycle. We interpret the behavior of the warp factor as describing a three-brane charge ``smeared'' over the cycle and consider the asymptotic form of the geometry in that region, showing that conformal invariance is broken even when the complex type IIB 3-form field strength is assumed to vanish. We conclude with a discussion of the basic features of the gauge theory dual.