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

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