Branes wrapped on quadrilaterals

Abstract

We construct new families of supersymmetric \({\textrm{AdS}}_2\times \mathbb {M}_4\) solutions of \(D=6\) gauged supergravity and \({\textrm{AdS}}_3\times \mathbb {M}_4\) solutions of \(D=7\) gauged supergravity, where \(\mathbb {M}_4\) are four-dimensional toric orbifolds with four fixed points. These are presented in a unified fashion that highlights their common underlying geometry. The \(D=6\) solutions uplift to massive type IIA and describe the near-horizon limit of D4-branes wrapped on \(\mathbb {M}_4\), while the \(D=7\) solutions uplift to \(D=11\) supergravity and describe the near-horizon limit of M5-branes wrapped on \(\mathbb {M}_4\). We reproduce the entropy and gravitational central charge of the two families by extremizing a function constructed gluing the orbifold gravitational blocks proposed in Faedo et al. (Lett Math Phys 113:51, 2023. https://doi.org/10.1007/s11005-023-01671-1. arXiv:2210.16128).