Friday, June 03, 2005

Topological membranes

Martin Schnabl has pointed out a sequence of pretty interesting papers by people like Carlip, Kogan (who sadly passed away in 2003), Szabo, Ferreira, and others. Let me mention one of the recent reviews by Szabo:
The papers in this category elaborate the "holographic" duality between
  • the WZW model in 2 dimensions and
  • the Chern-Simons theory in 3 dimensions.
One of the goals is to formulate the worldsheet description of string theory - arbitrary conformal field theory relevant for string theory (or at least a rational one) - in terms of a three-dimensional theory that may be more fundamental. More precisely, one wants to use "massive" Chern-Simons theory that also has the Maxwell term and whose worldvolume theory describes a "topological membrane".

A success story of this proposal is that one to give a much more geometric and dynamical description of Verlinde's formula, Cardy's condition, and other things. The details of this approach are different from the "N=2" string strategy - the latter offers a higher probability to explain the exceptional duality etc. - but still, some of the results look nontrivial. There are many open questions, too. For example, the original of the conformal bc ghosts is not really understood.

Anyone is familiar with this direction of thinking?

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