Branes, Calibrations and Supergravity

TL;DR

This paper provides an accessible overview of constructing supergravity solutions for branes wrapping calibrated cycles in special holonomy manifolds, emphasizing geometric aspects and their relation to supersymmetry and the AdS/CFT correspondence.

Contribution

It introduces a method to construct supergravity solutions for wrapped branes using auxiliary gauged supergravity and explores their geometric and supersymmetric properties.

Findings

Supergravity solutions for branes on calibrated cycles are constructed.

Wrapped branes preserve supersymmetry in special holonomy backgrounds.

Connection between supergravity solutions and AdS/CFT correspondence is discussed.

Abstract

These notes are based on lectures given at the Clay School on Geometry and String Theory, Isaac Newton Institute, Cambridge, 25 March - 19 April 2002. They attempt to provide an elementary and somewhat self contained discussion of the construction of supergravity solutions describing branes wrapping calibrated cycles, emphasising the geometrical aspects and focusing on D=11 supergravity. Following a discussion of the role of special holonomy backgrounds in D=11 supergravity, the basic membrane and fivebrane solutions are reviewed and the connection with the AdS/CFT correspondence is made. The world-volume description of branes is introduced and used to argue that branes wrapping calibrated cycles in special holonomy manifolds preserve supersymmetry. The corresponding supergravity solutions are constructed first in an auxiliary gauged supergravity theory which is obtained via Kaluza-Klein reduction.