Thursday, April 1, 2004, 2:45pm, 120 Physics, String Theory Seminar at Duke
     Lev Rozansky (UNC, Chapel Hill),
     Defining a topological 2d QFT on a world-wheet foam

 

     The world-sheet foam is (almost) a 2d CW-complex: it is a collection of 2-dimensional surfaces, whose boundaries are glued together at seam lines, which form a graph. Locally a foam is a cone of a graph, so it is a world-sheet for a theory of graph-like strings. Although a foam world-sheet may look ugly, it appeared as a necessary part of Khovanov's work on a categorification of the SU(N) HOMFLY-Jones polynomial. We show that if a QFT can be formulated on a 2d world-sheet with a boundary, then it can also be defined on a world-sheet foam with the help of `non-factorizable' boundary conditions. We give two examples of topological QFTs defined on foams: an A-type topological sigma-model and a B-type Landau-Ginzburg model. In the latter case there is a complete description for the operator spaces and for the correlators.