Chern-Simons gauge theory as a string theory. (English) Zbl 0844.58018

Witten, E.

Hofer, Helmut (ed.) et al., The Floer memorial volume. Basel: Birkhäuser. Prog. Math. 133, 637-678 (1995).

It is described how Chern-Simons gauge theory in three dimensions can be viewed as a string theory which is constructed by using a topological sigma model associated with a degenerate case of Floer/Gromov theory of symplectic manifolds whose target space is \(T^*M\) where \(M\) is a 3-manifold. The instantons considered in Floer theory give rise to Wilson line insertions in the space-time Chern-Simons theory. It is stressed that a holomorphic analog of Chern-Simons theory can arise as a string theory.
For the entire collection see [Zbl 0824.00019].

Reviewer: A.V.Aminova (Kazan’)

MSC:

58D30	Applications of manifolds of mappings to the sciences
81T13	Yang-Mills and other gauge theories in quantum field theory
81T30	String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T40	Two-dimensional field theories, conformal field theories, etc. in quantum mechanics

Keywords:

Chern-Simons gauge theory; string theory; topological sigma model; Floer/Gromov theory