Magnetic Brane Solutions in AdS

TL;DR

This paper constructs and analyzes asymptotically AdS_5 solutions in Einstein-Maxwell theory, revealing how magnetic fields influence the dual N=4 SYM theory's near horizon geometry, entropy, and central charge, with generalizations to other dimensions.

Contribution

It introduces new magnetic brane solutions in AdS that connect to near horizon geometries and generalizes these solutions across various spacetime dimensions.

Findings

Near horizon geometry is AdS_3×T^2 with magnetic fields.

Entropy vanishes at zero temperature.

Near horizon central charge is  4/3 times that of free N=4 SYM.

Abstract

We construct asymptotically AdS_5 solutions of Einstein-Maxwell theory dual to N=4 SYM theory on R^{3,1} in the presence of a background magnetic field. The solutions interpolate between AdS_5 and a near horizon AdS_3\times T^2. The central charge of the near horizon region, and hence low temperature entropy of the solution, is found to be \sqrt{4\over 3} times that of free N=4 SYM theory. The entropy vanishes at zero temperature. We also present the generalization of these solutions to arbitrary spacetime dimensionality.