Witten's Topological Field Theory Research Articles

A new action principle for Witten's topological field theory

In this letter a new gauge invariant, metric independent action is introduced from which Witten's topological quantum field theory may be obtained after gauge fixing using standard BRST techniques. In our model the BRST algebra of transformations, under which the effective action is invariant, close off-shell in distinction with what occurs in the one proposed by Labastida and Pernici. Our approach provides the geometrical principle for the quantum theory. We also compare our results with an alternative formulation presented by Baulieu and Singer.

Self-dual supersymmetric Yang-Mills theory generates Witten's topological field theory

We show that the recently constructed N=4 supersymmetric self-dual Yang-Mills theory as the consistent background of the N=2 open superstring will generate Witten's topological field theory in two dimensions as a descendant theory after appropriate twisted dimensional reduction/truncations. We also show that this topological field theory further generates supersymmetric Korteweg de Vries equations, SL ( n)-Toda theory and W ∞-gravity in the n→∞ limit. Considering also that this topological field theory is to generate other integrable and topological systems, our resutls give supporting evidence for the conjecture that the N=2 open superstring theory is the underlying “master theory” of integrable and topological systems, via the intermediate N=4 supersymmetric self-dual Yang-Mills theory as its consistent target space-time background.

POLYMERS AND TOPOLOGICAL FIELD THEORY

We show that the generating function for self-avoiding paths is formally obtainable from a Witten topological field theory, even if the physical quantities for polymers are not the physical quantities in the BRST approach. We argue that in the dense phase the BRST invariance should generally be broken at the quantum level.

Topological quantum field theory and N=2 conformal supergravity

We show how the BRST symmetry of Witten's topological field theory arises as a Killing spinor in N=2 conformal supergravity. We extend the model to include the twisted N=2 scalar multiplet, thus including commuting and anticommuting spinors.