Magnetic AdS x R^2: Supersymmetry and stability

TL;DR

The paper builds a top-down holographic model in which a background magnetic field coupled to a KK $U(1)$ stabilizes an $AdS_5$ theory into an infrared $AdS_3\times \mathbb{R}^2$ region, enabling controlled study of supersymmetric and nonsupersymmetric embeddings. It derives the gravity dual from the $U(1)^3$ truncation of IIB supergravity, analyzes the Coulomb branch, and shows that the low-energy LLL sector exhibits nontrivial interactions essential for a gravitational dual, with a central charge matching $c$-extremization results in a $(0,2)$ LG description. Stability is mapped out across neutral and charged modes, Coulomb-branch dynamics, and dilaton instabilities, revealing regions of absolute or near-absolute stability in the nonsupersymmetric theory and identifying the dilaton tadpole as a generic obstacle. The work also discusses implications for AdS$_2$ analogues and potential condensed-matter connections, including non-Fermi-liquid behavior and the role of orbifolds in enlarging stable parameter regions.

Abstract

We study AdS/CFT with a Kaluza-Klein magnetic field in one plane. By appropriate choice of magnetic U(1), and by balancing the magnetic field against the background D field, we obtain a supersymmetric field theory. We find the dual geometry for an AdS_5 to AdS_3 x R^2 example, and we compare the moduli spaces and entropies. For the entropy, the interactions are important even at weak coupling. We also consider nonsupersymmetric embeddings of the U(1), and show that over a regime of parameter space all known instabilities appear to be absent, aside from a dilaton tadpole that may be removed in a number of ways.