RG Flow of Magnetic Brane Correlators

TL;DR

This paper analyzes the RG flow in a holographic model with magnetic branes, revealing emergent IR symmetries and confirming the structure of the low energy conformal field theory through correlator computations.

Contribution

It provides a detailed holographic analysis of the IR limit of a magnetic brane solution, demonstrating the emergence of chiral current and Virasoro algebras, and connecting IR correlators to double-trace interactions.

Findings

Confirmation of a single chiral current algebra in IR

Matching of the Virasoro central charge with Brown-Henneaux formula

Relation of current algebra level to Chern-Simons coupling

Abstract

The magnetic brane solution to five-dimensional Einstein-Maxwell-Chern-Simons theory provides a holographic description of the RG flow from four-dimensional Yang-Mills theory in the presence of a constant magnetic field to a two-dimensional low energy CFT. We compute two-point correlators involving the U(1) current and the stress tensor, and use their leading IR behavior to confirm the existence of a single chiral current algebra, and of left- and right-moving Virasoro algebras in the low energy CFT. The common central charge of the Virasoro algebras is found to match the Brown-Henneaux formula, while the level of the current algebra is related to the Chern-Simons coupling. The coordinate reparametrizations produced by the Virasoro algebras on the AdS_3 near-horizon geometry arise from physical non-pure gauge modes in the asymptotic AdS_5 region, thereby providing a concrete example for the emergence of IR symmetries. Finally, we interpret the infinite series of sub-leading IR contributions to the correlators in terms of certain double-trace interactions generated by the RG flow in the low energy CFT.