AdS${}_3$ and AdS${}_2$ Magnetic Brane Solutions

Abstract

We investigate AdS${}_3$ and AdS${}_2$ magnetic brane solutions within the consistent truncation of AdS${}_5\times S^5$ supergravity. The AdS${}_3$ solution extends earlier work by allowing a general embedding of the magnetic $U(1)$ in $SO(6)$. We determine the ratio of strong- and weak-coupling entropies as a function of this embedding. Further, by considering crossed magnetic fields in different $U(1)$'s we are able to construct a solution that runs from AdS${}_5$ in the UV to AdS${}_2\times R^3$ in the IR. We find the notable result that there is a zero temperature entropy at strong coupling but not at weak coupling. We also show that the AdS${}_2$ solution and at least some of the AdS${}_3$ solutions are stable within the truncation.

15 pages, 2 figures

References in corpus (3)

• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• Hall conductivity from dyonic black holes
• Ohm's Law at strong coupling: S duality and the cyclotron resonance