A Topological Field Theory of Gravitational Instantons
Physics Letters B
A topological field theory modeling the moduli space of conformally (anti-) self-dual gravitational instantons is presented. The classical action is a functional of an SU((2) gauge field and a totally symmetric rank-four SU (2) spinor. Classical extrema of the action correspond to euclidean signature Einstein spaces with (anti-) self-dual Weyl tensor as well as a condition which governs the appearance of singularities in the space of instantons modulo the action of diffeomorphisms and local SU (2) transformations. A suitable fermionic supersymmetry is constructed as well as a supersymmetric extension of the classical bosonic action, both of which are a natural generalization (to include diffeomorphisms) of their counterparts in Witten's topological gauge theory. We discuss relevant properties of the moduli space and their implications for the quantized version of the theory.
C.G. Torre, A topological field theory of gravitational instantons, Physics Letters B, Volume 252, Issue 2, 13 December 1990, Pages 242-246, ISSN 0370-2693, 10.1016/0370-2693(90)90867-6.