Article

Communications in Mathematical Physics

, Volume 117, Issue 3, pp 353-386

First online:

Topological quantum field theory

  • Edward WittenAffiliated withSchool of Natural Sciences, Institute for Advanced Study

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Abstract

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 covariance is unbroken, there are no gravitons, and the only excitations are topological.