Topological A-models on seamed Riemann surfaces

TL;DR

This paper introduces a class of topological A-models on seamed Riemann surfaces with Grassmannian target spaces, providing a quantum field theory perspective on Khovanov's categorification of the sl(3) HOMFLY polynomial.

Contribution

It constructs topological A-models on seamed Riemann surfaces with specific boundary conditions related to Grassmannians, linking topological quantum field theory to knot polynomial categorification.

Findings

Defines topological A-models on seamed Riemann surfaces.

Connects the models to Khovanov's categorification of the sl(3) HOMFLY polynomial.

Provides a QFT interpretation of knot polynomial categorification.

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.