Three-charge black holes from the worldsheet

TL;DR

This work provides an exact worldsheet description of the general doubly-rotating, three-charge NS5-F1-P black hole by constructing null-gauged WZW models on $SL(2,\mathbb{R})\times SU(2)\times \mathbb{R}\times U(1)$. The authors map the gauging data to the black hole charges, derive consistency conditions that quantize part of the gauging parameters, and show how horizonless JMaRT solitons arise as analytic continuations of the same worldsheet framework. They extend the construction to the supersymmetric extremal BMPV case via a novel asymmetric null gauging, yielding a worldsheet CFT that captures string dynamics on extremal backgrounds with BTZ factors. The analysis clarifies how the NS5 decoupling limit produces backgrounds with linear dilaton asymptotics and connects to AdS/CFT-type descriptions in the near-horizon regime, offering explicit solvable models for string propagation on nontrivial black hole geometries.

Abstract

We consider the general asymptotically flat, doubly-rotating, three-charge black hole uplifted to a family of NS5-F1-P black brane solutions of Type IIB supergravity. We construct a null-gauged WZW model whose target-space geometry reproduces this background in the NS5 decoupling limit, and show that the gauging parameters precisely satisfy the appropriate consistency conditions on the perturbative string spectrum. Through an analytic continuation and an appropriate limit, this model relates to a recently studied construction describing strings on smooth, horizonless geometries. We further analyze the supersymmetric and extremal three-charge configuration, corresponding to the ten-dimensional uplift of the (NS5-decoupled) BMPV black hole, and show that it requires a novel class of null-gauged WZW models. Our construction provides explicit examples of worldsheet CFTs that capture string dynamics on certain black hole geometries with linear dilaton asymptotics.