Topological A-models on seamed Riemann surfaces

Abstract

We define a class of topological A-models on a collection of Riemann surfaces, whose boundaries are sewn together along the seams. The target spaces for the Riemann surfaces are the Grassmanians Gr_{m_i,n} with the common value of n, and the boundary conditions at the seams demand that the spaces C^{m_i}\subset C^n present the orthogonal decomposition of C^n. The whole construction is a QFT interpretation of a part of Khovanov's categorification of the sl(3) HOMFLY polynomial.