Gravitational Instantons and Moduli Spaces of Topological 2-form Gravity

Abstract

A topological version of four-dimensional (Euclidean) Einstein gravity which we propose regards anti-self-dual 2-forms and an anti-self-dual part of the frame connections as fundamental fields. The theory describes the moduli spaces of conformally self-dual Einstein manifolds for the non-zero cosmological constant case and Einstein-Kahlerian manifold with the vanishing real first Chern class for the zero cosmological constant. In the non-zero cosmological constant case, we evaluate the index of the elliptic complex associated with the moduli space and calculate the partition function. We also clarify the moduli space and its dimension for the zero cosmological constant case which are related to the Plebansky's heavenly equations.

36pages, LaTex, TIT/HEP-247/COSMO-42

References in corpus (5)

• Twisted N=2 Supergravity as Topological Gravity in Four Dimensions
• Topological Sigma-Models in Four Dimensions and Triholomorphic Maps
• Topological 2-form Gravity in Four Dimensions
• Topological Conformal Gravity in Four Dimensions
• Moduli Space of Topological 2-form Gravity

Cited by in corpus (10)

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• Towards a Gravitational Analog to S-duality in Non-abelian Gauge Theories
• The Phillips - Barger model for the elastic cross section and the Odderon
• Topological Symmetry of forms, N=1 Supersymmetry and S-duality on Special Manifolds
• Open-string singlet interaction as pomeron in elastic $pp,p\bar{p}$ scattering
• Exact helicoidal and catenoidal solutions in Einstein-Maxwell theory
• Plebanski-like action for general relativity and anti-self-dual gravity
• Symmetries and observables in topological gravity
• A semiclassical interpretation of the topological solutions for canonical quantum gravity
• NUT Solutions in Einstein-Maxwell-scalar-Gauss-Bonnet Gravity