Comments on $Ad{S}_2$ solutions from M2-branes on complex curves and the backreacted Kähler geometry

Abstract

We consider $Ad{S}_2$ solutions of M-theory which are obtained by twisted compactifications of M2-branes on a complex curve. They are of a generalized class, in the sense that the non-abelian part of the connection for the holomorphic bundle over the supersymmetric cycle is nontrivial. They are solutions of $U(1{)}^4$ gauged supergravity in $D=4$, with magnetic flux over the curve, and then uplifted to $D=11$. We discuss the behavior of conformal fixed points as a function of the non-abelian connection. We also describe how they fit into the general description of wrapped M2-brane $Ad{S}_2$ solutions and their higher-order generalizations, by showing that they satisfy the master equation for the eight-dimensional Kähler base space.

v2: title changed, refs added. 13 pages, 2 figures; v3: refs and discussion added

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• New AdS${}_2$ backgrounds and $\mathcal{N}=4$ Conformal Quantum Mechanics
• Non-integrability in AdS${}_3$ vacua
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