Supersymmetric 3-branes on smooth ALE manifolds with flux

We construct a new family of classical BPS solutions of type IIB supergravi ty describing 3-branes transverse to a 6-dimensional space with topology R- 2 x 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. T hey 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 E guchi-Hanson manifold. The equation for H is identified as an instance of t he confluent Heun equation. We write explicit power series solutions and so lve the recurrence relation for the coefficients, discussing also the relev ant asymptotic expansions. While, as in all such N = 2 solutions, supergrav ity breaks down near the brane, the smoothing out of the vacuum geometry ha s 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 char ge "smeared" over the cycle and consider the asymptotic form of the geometr y 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 w ith a discussion of the basic features of the gauge theory dual. (C) 2001 E lsevier Science B.V. All rights reserved.