# Topological quantum field theory

@article{Witten1988TopologicalQF, title={Topological quantum field theory}, author={Edward Witten}, journal={Communications in Mathematical Physics}, year={1988}, volume={117}, pages={353-386} }

A twisted version of four dimensional supersymmetric gauge theory is formulated. The model, which refines a nonrelativistic treatment by Atiyah, appears to underlie many recent developments in topology of low dimensional manifolds; the Donaldson polynomial invariants of four manifolds and the Floer groups of three manifolds appear naturally. The model may also be interesting from a physical viewpoint; it is in a sense a generally covariant quantum field theory, albeit one in which general… Expand

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#### 2,039 Citations

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A topological quantum field theory is introduced which reproduces the Seiberg-Witten invariants of four-manifolds. Dimensional reduction of this topological field theory leads to a new one in three… Expand

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Abstract We present an action which generates the supersymmetric self-dual equations corresponding to euclidean super Yang-Mills theory in four dimensions. By adding additional constraint fields with… Expand

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Abstract We present a detailed description of the three inequivalent twists of N = 4 supersymmetric gauge theories in four dimensions. The resulting topological quantum field theories are reobtained… Expand

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A four-dimensional analog of Chern-Simons theory produces integrable lattice models from Wilson lines and surface operators. We show that this theory describes a quasi-topological sector of maximally… Expand

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- 1997

We review the relations between (twisted) supersymmetric gauge theories in four dimensions and moduli problems in four-dimensional topology, and we study in detail the non-abelian monopole equations… Expand

Algebraic renormalization of the topological Yang-Mills field theory

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Abstract We obtain the most general local counterterm of Witten's topological Yang-Mills field theory in a Landau type gauge. Our results, being based on the algebraic BRS-renormalization technique,… Expand

Duality in Topological Quantum Field Theories 1

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This thesis presents a thorough analysis of the links between the N = 4 supersymmetric gauge theory in four dimensions and its three topological twisted counterparts. Special emphasis is put in… Expand

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A method is presented by which a hidden N=2 superconformal symmetry can be exhibited in a string theory or indeed in a topological conformal field theory. More precisely, we present strong evidence,… Expand

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