# Topological sigma models

@article{Witten1988TopologicalSM, title={Topological sigma models}, author={Edward Witten}, journal={Communications in Mathematical Physics}, year={1988}, volume={118}, pages={411-449} }

A variant of the usual supersymmetric nonlinear sigma model is described, governing maps from a Riemann surfaceΣ to an arbitrary almost complex manifoldM. It possesses a fermionic BRST-like symmetry, conserved for arbitraryΣ, and obeyingQ2=0. In a suitable version, the quantum ground states are the 1+1 dimensional Floer groups. The correlation functions of the BRST-invariant operators are invariants (depending only on the homotopy type of the almost complex structure ofM) similar to those that… Expand

#### 894 Citations

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We construct and study a closed, two-dimensional, quasi-topological (0,2) gauged sigma model with target space a smooth G-manifold, where G is any compact and connected Lie group. When the target… Expand

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We identify and examine a generalization of topological sigma models suitable for coupling to topological open strings. The targets are Kahler manifolds with a real structure, i.e. with an involution… Expand

2D sigma models and differential Poisson algebras

- Physics, Mathematics
- 2015

A bstractWe construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and… Expand

String holonomy and extrinsic geometry in four-dimensional topological gauge theory

- Physics, Mathematics
- 1998

Abstract The most general gauge-invariant marginal deformation of four-dimensional abelian BF-type topological field theory is studied. It is shown that the deformed quantum field theory is… Expand

Infinite conformal algebras in supersymmetric theories on four manifolds

- Physics
- 1994

Abstract We study a supersymmetric theory twisted on a Kahler four-manifold M = Σ 1 × Σ 2 , where Σ 1,2 are two-dimensional Riemann surfaces. We demonstrate that it possesses a “left-moving”… Expand

BRST and Topological Gauge Theories

- Mathematics
- 2002

In this thesis, the BRST-quantization of gauge theories is discussed. A detailed analysis of the BRST-quantization on inner product spaces is performed for a class of abelian models, including… Expand

The topological B model as a twisted spinning particle

- Physics
- 1994

Abstract The B-twisted topological sigma model coupled to topological gravity is supposed to be described by an ordinary field theory: a type of holomorphic Chern-Simons theory for the open string,… Expand

SL(n, R) topological field theories

- Physics
- 1991

Abstract We detail the BRST quantization of zero-dimensional string theory, by using Singer's observation of a SL(2, R ) gauge symmetry. This provides a supersymmetric action, involving a pair of… Expand

A renormalizable topological quantum field theory for gravity

- 2019

In 1989 E. Witten, using traditional QFT techniques, develop an exact path integral representation to many classes of topological invariants. These QFTs, so-called Topological QFTs (TQFTs), share the… Expand

Topological Gauge Theories of Antisymmetric Tensor Fields

- Physics
- 1991

Abstract We introduce a new class of topological gauge field theories in any dimension, based on anti-symmetric tensor fields, and discuss the BRST-quantization of these reducible systems as well as… Expand

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