Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-11-14
Nucl.Phys. B401 (1993) 206-238
Physics
High Energy Physics
High Energy Physics - Theory
35 pages, harvmac, DAMTP R92/42
Scientific paper
10.1016/0550-3213(93)90303-7
In this paper, we present a new formulation of topological conformal gravity in four dimensions. Such a theory was first considered by Witten as a possible gravitational counterpart of topological Yang-Mills theory, but several problems left it incomplete. The key in our approach is to realise a theory which describes deformations of conformally self-dual gravitational instantons. We first identify the appropriate elliptic complex which does precisely this. By applying the Atiyah-Singer index theorem, we calculate the number of independent deformations of a given gravitational instanton which preserve its self-duality. We then quantise topological conformal gravity by BRST gauge-fixing, and discover how the quantum theory is naturally described by the above complex. Indeed, it is a process which closely parallels that of the Yang-Mills theory, and we show how the partition function generates an uncanny gravitational analogue of the first Donaldson invariant.
Perry Malcolm J.
Teo Edward
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