Comments on $AdS_2$ solutions from M2-branes on complex curves and the backreacted K\"ahler geometry

Understand

We consider $AdS_2$ 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.