STRING FIELD THEORY AND GAUGE THEORIES

Abstract

AbstractThis chapter shows that both Chern-Simons gauge theories and matrix models with polynomial potentials can be realized as open string theories. To show that Chern-Simons theory and matrix models with polynomial potentials are open string theories the strategy is to prove that these gauge theories describe the spacetime dynamics of topological open strings on certain backgrounds. To do this, string field theory is used. Some basic ingredients of the cubic string field theory introduced by Witten (1986) to describe the spacetime dynamics of open bosonic strings are described. The same model is used to describe topological strings. In bosonic open string field theory, the worldsheet of the string is considered to be an infinite strip parameterized by a spatial coordinate and a time coordinate.