The topological structure of supergravity: an application to supersymmetric localization

Abstract

The BRST algebra of supergravity is characterized by two different bilinears of the commuting supersymmetry ghosts: a vector ${\gamma }^{\mu }$ and a scalar $\varphi$, the latter valued in the Yang-Mills Lie algebra. We observe that under BRST transformations $\gamma$ and $\varphi$ transform as the superghosts of, respectively, topological gravity and topological Yang-Mills coupled to topological gravity. This topological structure sitting inside any supergravity leads to universal equivariant cohomological equations for the curvatures 2-forms which hold on supersymmetric bosonic backgrounds. Additional equivariant cohomological equations can be derived for supersymmetric backgrounds of supergravities for which certain gauge invariant scalar bilinears of the commuting ghosts exist. Among those, $N=(2,2)$ in $d=2$, which we discuss in detail in this paper, and $N=2$ in $d=4$.

38 pages

References in corpus (3)

• Comments on N=(2,2) Supersymmetry on Two-Manifolds
• The Coupling of Chern-Simons Theory to Topological Gravity
• The coupling of Poisson sigma models to topological backgrounds

Cited by in corpus (7)

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• Twisting and localization in supergravity: equivariant cohomology of BPS black holes
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• Deformations of Supergravity and Supersymmetry Anomalies
• Anomalies and Supersymmetry
• Boundary Conditions in Topological AdS${}_4$/CFT${}_3$