Currents and Moduli in the (4,0) theory

TL;DR

The paper analyzes a 4,0 CFT describing five-dimensional black strings, detailing a decoupled scaling limit, a 42-dimensional moduli space with 14 fixed scalars and 28 free moduli, and a rich spectrum of 27 U(1) charges organized by dualities and current algebras. It derives a microscopic entropy formula for near-extremal four-dimensional black holes that reduces to the E7(7) quartic invariant in the BPS limit, linking conformal weights to a detailed U(1) charge lattice. The work advances understanding of the (4,0) theory by describing backgrounds, fragmentation instabilities, and the potential for an exactly solvable CFT, while highlighting the parallels and distinctions with the better-understood (4,4) D1-D5 system. Overall, it provides a structured framework for constructing and constraining the spacetime CFT underlying (4,0) backgrounds and for testing microscopic entropy against macroscopic area formulas.

Abstract

We consider black strings in five dimensions and their description as a (4,0) CFT. The CFT moduli space is described explicitly, including its subtle global structure. BPS conditions and global symmetries determine the spectrum of charged excitations, leading to an entropy formula for near-extreme black holes in four dimensions with arbitrary charge vector. In the BPS limit, this formula reduces to the quartic E(7,7) invariant. The prospects for a description of the (4,0) theory as a solvable CFT are explored.