Superstring Theories and Unification of Knot Homologies

Abstract

The quantum field theory has been playing important roles in the research of the knot invariants since a connection between the Chern-Simons gauge theory and the Jones polynomial was uncovered. In developments for the past decade, the novel class of knot invariants has been found via the concept of "categorification" in mathematics. On the other hand in the string theory, the concept of "D-brane" has been introduced, and we get new physical interpretation for such knot invariants. In recent years, the unification of various categorified knot invariants has been discussed by combining new approaches in physics and mathematics. In this article, we will survey on recent developments in this researc area.