Localization of the free energy in supergravity

Abstract

We derive a general formula for the gravitational free energy of Euclidean supersymmetric solutions to $D=4$, $\mathcal{N}=2$ gauged supergravity coupled to vector multiplet matter. This allows one to compute the free energy without solving any supergravity equations, just assuming the solutions exist. As well as recovering some known results in the literature with ease, we also present new supergravity results that match with holographically dual field theory computations.

6 pages; v3: corrected typos

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Cited by in corpus (3)

• Toric gravitational instantons in gauged supergravity
• NUTs, Bolts, and Spindles
• Bubbling saddles of the gravitational index