Fivebranes Wrapped on SLAG Three-Cycles and Related Geometry

TL;DR

This paper constructs supergravity solutions for fivebranes wrapping special Lagrangian three-cycles, revealing complex geometries with G_2 structures and providing insights into dual gauge theories and related geometric structures.

Contribution

It introduces new supergravity solutions involving G_2 structures for fivebranes on three-cycles, expanding understanding of wrapped branes and their geometries.

Findings

Solutions involve seven-manifolds with two G_2 structures

Derived a general formula for the calibration of these solutions

Discussed geometries with Spin(7) and SU(N) structures

Abstract

We construct ten-dimensional supergravity solutions corresponding to the near horizon limit of IIB fivebranes wrapping special Lagrangian three-cycles of constant curvature. The case of branes wrapping a three-sphere provides a gravity dual of pure N=2 super-Yang-Mills theory in D=3. The non-trivial part of the solutions are seven manifolds that admit two G_2 structures each of which is covariantly constant with respect to a different connection with torsion. We derive a formula for the generalised calibration for this general class of solutions. We discuss analogous aspects of the geometry that arises when fivebranes wrap other supersymmetric cycles which lead to Spin(7) and SU(N) structures. In some cases there are two covariantly constant structures and in others one.