Gravity Duals of Fractional Branes in Various Dimensions

TL;DR

This paper constructs supergravity solutions for fractional Dp and M2 branes on conical spaces, revealing their geometric and gauge theory interpretations, and highlighting conditions for their existence based on topological properties.

Contribution

It provides explicit supergravity solutions for fractional branes in various dimensions, linking geometric conditions to the presence of fractional branes and their gauge theory duals.

Findings

Solutions exist only if the cone's base has non-zero Betti number b_2 or b_3.

Fractional Dp-branes are wrapped D(p+2)-branes; fractional M2-branes are M5-branes wrapped over 3-cycles.

Discusses gauge theory interpretations of these supergravity solutions.

Abstract

We derive type II supergravity solutions corresponding to space-filling regular and fractional Dp branes on (9-p)-dimensional conical transverse spaces. Fractional Dp-branes are wrapped D(p+2)-branes; therefore, our solutions exist only if the base of the cone has a non-vanishing Betti number b_2. We also consider 11-dimensional SUGRA solutions corresponding to regular and fractional M2 branes on 8-dimensional cones whose base has a non-vanishing b_3. (In this case a fractional M2-brane is an M5-brane wrapped over a 3-cycle.) We discuss the gauge theory intepretation of these solutions, as well as of the solutions constructed by Cvetic et al. in hep-th/0011023 and hep-th/0012011.