Adding momentum to D1-D5 system

TL;DR

This work constructs the first completely regular, asymptotically flat geometry carrying three charges (D1, D5, and momentum) by leveraging a near-horizon map that relates flat and AdS$_3\times S^3$ asymptotics and applying spectral flow in the dual CFT. Starting from a known regular D1-D5 geometry, the authors move to the AdS region, induce momentum via spectral flow, and map back to flat space, producing an explicit three-charge solution that remains regular. They verify crucial properties—regularity, absence of horizons, and supersymmetry—and compute the D1, D5, and momentum charges, connecting the geometry to microstates of the three-charge black hole and to the AdS/CFT correspondence. The results provide a concrete example in the microstate geometry program and offer a framework for generating additional regular geometries with multiple charges. This work thus advances understanding of how black hole entropy can emerge from smooth gravity solutions in string theory and suggests directions for extending these geometric constructions to a broader set of microstates and CFT states.

Abstract

We construct the first example of asymptotically flat solution which carries three charges (D1,D5 and momentum) and which is completely regular everywhere. The construction utilizes the relation between gravity solutions and spectral flow in the dual CFT. We show that the solution has the right properties to describe one of the microscopic states which are responsible for the entropy of the black hole with three charges.