What is the dual of a dipole?

TL;DR

The paper investigates how gravitational solutions carrying dipole charges, specifically black rings in $AdS_3\times S^3$, map to dual CFT descriptions. By extracting one-point functions of scalar operators from the decoupled supergravity solution and comparing with orbifold CFT calculations at large $N$, it shows consistent leading behavior between gravity and the dual theory, especially for 1/2-BPS small black rings. A simple toy model with a dipole operator $D=1/n$ reproduces the small black ring entropy $S \sim 4\sqrt{N-q_3 J}$, supporting a nonlocal interpretation of dipole data in the CFT. The results illuminate how dipole moments are encoded in the boundary theory and suggest nontrivial, testable links between bulk geometries and ensembles in the D1-D5 CFT.

Abstract

We study gravitational solutions that admit a dual CFT description and carry non zero dipole charge. We focus on the black ring solution in AdS_3 x S^3 and extract from it the one-point functions of all CFT operators dual to scalar excitations of the six-dimensional metric. In the case of small black rings, characterized by the level N, angular momentum J and dipole charge q_3, we show how the large N and J dependence of the one-point functions can be reproduced, under certain assumptions, directly from a suitable ensemble in the dual CFT. Finally we present a simple toy model that describes the thermodynamics of the small black ring for arbitrary values of the dipole charge.