| Summary: | We explain how equivariant localization may be applied to AdS/CFT to compute various BPS observables in gravity, such as central charges and conformal dimensions of chiral primary operators, without solving the supergravity
equations. The key ingredient is that supersymmetric AdS solutions with an
R-symmetry are equipped with a set of equivariantly closed forms. These may
in turn be used to impose flux quantization and compute observables for supergravity solutions, using only topological information and the Berline–Vergne–
Atiyah–Bott fixed point formula. We illustrate the formalism by considering
AdS5 × M6 and AdS3 × M8 solutions of D = 11 supergravity. As well as recovering results for many classes of well-known supergravity solutions, without
using any knowledge of their explicit form, we also compute central charges for
which explicit supergravity solutions have not been constructed.
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