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arXiv · hep-th/9208029

Twisted N=2 Supergravity as Topological Gravity in Four Dimensions

Damiano Anselmi·Pietro Fre
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Abstract

We show that the BRST quantum version of pure D=4 N=2 supergravity can be topologically twisted, to yield a formulation of topological gravity in four dimensions. The topological BRST complex is just a rearrangement of the old BRST complex, that partly modifies the role of physical and ghost fields: indeed, the new ghost number turns out to be the sum of the old ghost number plus the internal U(1) charge. Furthermore, the action of N=2 supergravity is retrieved from topological gravity by choosing a gauge fixing that reduces the space of physical states to the space of gravitational instanton configurations, namely to self-dual spin connections. The descent equations relating the topological observables are explicitly exhibited and discussed. Ours is a first step in a programme that aims at finding the topological sector of matter coupled N=2 supergravity, viewed as the effective Lagrangian of type II superstrings and, as such, already related to 2D topological field-theories. As it stands the theory we discuss may prove useful in describing gravitational instantons moduli-spaces.

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Damiano Anselmi, Pietro Fre. 1992-08-11. Twisted N=2 Supergravity as Topological Gravity in Four Dimensions. https://doi.org/10.1016/0550-3213(93)90679-j

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