Forthcoming events in this series


Mon, 23 Oct 2006
12:00
L3

Einstein Geometry and Conformal Field Theory

James Sparks
(Oxford)
Abstract
I shall describe two recent results in Sasaki-Einstein geometry, which is the odd-dimensional cousin of Kahler-Einstein geometry, and how they are related to four-dimensional superconformal field theory (SCFT) via the AdS/CFT correspondence. The first is a proof that the volumes of such Einstein manifolds are always algebraic numbers, which reflects a similar statement about central charges in SCFTs due to Intriligator and Wecht. The second descibes two simple holomorphic obstructions to the existence of such Einstein metrics. In such obstructed cases the non-existence of the dual superconformal fixed point may be proven by a simle application of the unitarity bound and the “a-theorem”, respectively, and these may be related directly to the geometrical obstructions via AdS/CFT arguments. On the mathematical side, these are new simple obstructions to the existence of Kahler-Einstein metrics on Fano orbifolds.

 /notices/events/abstracts/string-theory/mt06/sparks.shtml

  

  

Mon, 28 Nov 2005
12:00
L3

Topological membranes

Annamaria Sinkovics
Abstract

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.

Mon, 21 Nov 2005
12:00
L3

Generalised geometries and supergravity

Dan Waldram
(Imperial)
Abstract

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.