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}
}
  • E. Witten
  • Published 1 February 1988
  • Physics
  • Communications in Mathematical Physics
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
Topological Quantum Field Theory and Seiberg-Witten Monopoles
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 threeExpand
Supersymmetric instantons and topological quantum field theory
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 withExpand
Mathai-Quillen formulation of twisted N = 4 supersymmetric gauge theories in four dimensions
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 reobtainedExpand
A Solution of Two-dimensional Topological Quantum Gravity
Abstract We give a formulation of two-dimensional topological gravity without matter in terms of a supersymmetric conformally invariant field theory and derive a path integral expression for theExpand
Unification of integrability in supersymmetric gauge theories
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 maximallyExpand
Green-Schwarz superstring theory in two dimensions and topological field theories
Abstract It is shown that the algebra associated with the local κ-supersymmetry in the Green-Schwarz superstring theory in d =2 dimensions closes off shell. We quantize the theory in a LorentzExpand
The Geometry of Supersymmetric Gauge Theories in Four Dimensions
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 equationsExpand
Algebraic renormalization of the topological Yang-Mills field theory
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
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 inExpand
Untwisting Topological Field Theories
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
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 38 REFERENCES
Vacuum Periodicity in a Yang-Mills Quantum Theory
We propose a description of the vacuum in Yang-Mills theory and arrive at a physical interpretation of the pseudoparticle solution and the attendant violation of symmetries. The existence ofExpand
The structure of the gauge theory vacuum
Abstract The finite action Euclidean solutions of gauge theories are shown to indicate the existence of tunneling between topologically distinct vacuum configurations. Diagonalization of theExpand
Topological sigma models
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,Expand
Supersymmetry and instantons
Abstract We show that the eigenvalue equations for the fluctuation of scalars, fermions and gluon around any classical self-dual solution of the Yang-Mills theory have the same spectrum of non-zeroExpand
Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
We obtain the Ward identities and the gauge-dependence of Green's functions in non-Abelian gauge theories by using only the canonical commutation relations and the equations of motion for theExpand
Conformal invariance, supersymmetry and string theory
Covariant quantization of string theories is developed in the context of conformal field theory and the BRST quantization procedure. The BRST method is used to covariantly quantize superstrings, andExpand
Scale and Conformal Invariance in Quantum Field Theory
We study the relation between invariance under rigid and local changes of length scale. In two dimensions, we complete an argument of Zamolodchikov showing that the rigid invariance implies the localExpand
INTRODUCTION TO STRING AND SUPERSTRING THEORY. 2.
Conformal field theory is reviewed, then conformal invariance is used to rederive the basic results on the embedding dimensionality for bosonic and fermionic strings. The spectrum of the bosonic andExpand
GLOBAL ANOMALIES IN STRING THEORY
This paper addresses various questions involving global anomalies in particle theory and string theory. It is shown that the question of whether a manifold is a spin manifold is equivalent to aExpand
Nonperturbative Aspects in Supersymmetric Gauge Theories
Abstract We review our present understanding of those non-perturbative features of supersymmetric gauge theories that are believed to determine the properties of their ground states (vacua). A wideExpand
...
1
2
3
4
...