Localizing $\mathcal{N}=(2,0)$ $AdS_3$ solutions of M-theory

Abstract

We apply equivariant localization to supersymmetric $AdS_3\times M_8$ solutions of eleven-dimensional supergravity, dual to two-dimensional $\mathcal N=(2,0)$ SCFTs. We construct equivariantly closed polyforms encoding the magnetic flux and its dual, calibrated M2-branes and the warped volume, reducing protected observables to fixed point data of the $U(1)$ R-symmetry action. We apply the framework to $S^4$ bundles over coassociative four-cycles and $S^2$ bundles over compact six-manifolds, obtaining topological formulae for leading central charges and gravitational anomalies in terms of quantized fluxes and topological data. We recover the known results for $T^2\times KE_4$ solutions and construct a compact numerical solution with quantized flux that lies outside the known polynomial branch.