Saturday, July 23, 2005

D-branes, Superpotentials and A-Infinity Algebras

The meeting in Durham is under way and the first two talks of the symposium have finished. They were both given (two 45 minute sessions, separated by one hour's worth of coffee) by Paul Aspinwall, hailing from the "other Durham", under the title "D-branes, Superpotentials and A-Infinity Algebras". The talk was based on work completed with Sheldon Katz in hep-th/0412209.

The aim of the talk was to find a generalised method for finding superpotentials through the medium of category theory looking at the topological field theory B-model (i.e. IIB string theory). It was all very new to me, and involved looking at chain complexes as brane coordinates in the Calabi-Yau 3-fold part of space-time. There were very many neat commutative diagrams relating the complex chains and the maps extending between them were identified as open strings extending between the branes in these coordinates. When it came to looking at decaying branes quivers turned up and there were some more neat diagrams showing the decay of a stack of D-branes down to other new stacks, and the resulting changes of gauge symmetry. So Paul Aspinwall did a good job of intertwining the mathematics of categories with results from string theory, but it would require a lot of work on my part to understand the talk well. Next is matrix factorisations, in fact in 8 minutes so I had better dash.

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