Comments on $$AdS_2$$ A d S 2 solutions from M2-branes on complex curves and the backreacted Kähler geometry

Nakwoo Kim

doi:10.1140/epjc/s10052-014-2778-6

Abstract

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. We also describe how they fit into the general description of wrapped M2-brane $$AdS_2$$ solutions and their higher-order generalizations, by showing that they satisfy the master equation for the eight-dimensional Kähler base space.

Highlights

For such magnetic brane solutions relevant to 2-cycles, more general solutions were constructed with multiple nonvanishing U (1) charges, where the sum of magnetic fields still exactly cancel the spin-connection part in the Killing equations [8,9,10]
In gauged supergravity the implementation is quite simple: originally for 2-cycles in Calabi–Yau 3-manifold (CY3) we take the diagonal U (1) among S O(4) gauge fields and assign it the same value as the spin connection of the 2cycle
As a consistency check we have verified that the uplifted D = 11 solutions satisfy the general supersymmetry condition (22) and we presented a generalization to other dimensions

Summary

Introduction

For such magnetic brane solutions relevant to 2-cycles, more general solutions were constructed with multiple nonvanishing U (1) charges, where the sum of magnetic fields still exactly cancel the spin-connection part in the Killing equations [8,9,10]. Their interpretation as general wrapped branes and the description of the dual conformal field theory are given in [11,12]. Solutions in canonical form immediately give full information on the Killing spinors This can be very useful for instance when one looks for supersymmetric brane embeddings in a given supersymmetric background.

Ad S2 solutions

Discussion