Can I read Equivariant localization for $D=4$ gauged supergravity on EtoBox?

Equivariant localization for $D=4$ gauged supergravity by Genolini, Pietro Benetti; Gauntlett, Jerome P.; Jiao, Yusheng; Lüscher, Alice; Sparks, James is a scholarly article available to read on EtoBox.

What is Equivariant localization for $D=4$ gauged supergravity about?

We consider supersymmetric solutions of $D=4$, $\mathcal{N}=2$ Euclidean gauged supergravity coupled to an arbitrary number of vector multiplets. Such solutions admit an R-symmetry Killing vector, $\xi$, constructed as a bilinear in the Killing spinor. The Killing spinor bilinears can also be used to construct polyforms that are equivariantly closed under the action of the equivariant exterior derivative $\mathrm{d}_\xi=\mathrm{d}-\xi\mathbin{\rule[.2ex]{.4em}{.03em}\rule[.2ex]{.03em}{.9ex}}\,$. This allows one to compute various flux integrals and the on-shell action using localization, without solving any supergravity equations, just assuming the supersymmetric solutions exist. The flux integrals allow one to obtain important UV-IR relations, relating fixed point data in the bulk to data on the asymptotic AdS boundary, allowing one to express the gravitational free energy in terms of boundary SCFT data. We illustrate the formalism with a number of examples, including classes of solutions which are unlikely to ever be constructed in closed form.

Author

Genolini, Pietro Benetti; Gauntlett, Jerome P.; Jiao, Yusheng; Lüscher, Alice; Sparks, James

Published

2024

Language

EN