Past String Theory Seminar

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It is suggested that topological membranes play a fundamental role

in the recently proposed topological M-theory. We formulate a topological theory

of membranes wrapping associative three-cycles in a seven-dimensional target

space with G_2 holonomy. The topological BRST rules and BRST invariant action

are constructed via the Mathai-Quillen formalism. We construct a set of local

and non-local observables for the topological membrane theory. As the BRST

cohomology of local operators turns out to be isomorphic to the de Rham

cohomology of the G_2 manifold, our observables agree with the spectrum of

d=4, N=1 G_2 compactifications of M-theory.

I aim to give some review of how generalised geometries provide a natural

framework for describing supersymmetric string backgrounds. In particular I

will focus on a rewriting of type II supergravity in terms of generalised

structures. Hitchin functions appear naturally along with generalised

extensions of the Gukov-Vafa-Witten superpotential.

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