MG11 
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Abstract

AdS limits of wrapped M5 branes

I will discuss the derivation of a complete geometrical characterisation of a large class of $AdS_3$, $AdS_4$ and $AdS_5$ supersymmetric spacetimes in eleven-dimensional supergravity using $G$-structures. These are obtained as special cases of a class of supersymmetric $\mathbb{R}^{1,1}$, $\mathbb{R}^{1,2}$ and $\mathbb{R}^{1,3}$ geometries, naturally associated to M5-branes wrapping calibrated cycles in manifolds with $G_2$, $\SU(3)$ or $\SU(2)$ holonomy. Specifically, the latter class is defined by requiring that the Killing spinors satisfy the same set of projection conditions as for the wrapped brane, and that there is no electric flux. I will show how the R-symmetries of the dual field theories are encoded by the supergravity description of the wrapped branes, and appear as isometries of the general $AdS$ geometries. I will discuss how known solutions previously constructed in gauged supergravity satisfy our more general $G$-structure conditions, explain that our conditions for half-BPS $AdS_5$ geometries are precisely those of LLM, and construct some new solutions.