Adding momentum to supersymmetric geometries

TL;DR

This paper introduces a method to add traveling-wave deformations to supersymmetric solutions in six-dimensional supergravity, providing explicit microstate examples and linking deformations to CFT current actions.

Contribution

It develops a general framework for deforming supersymmetric geometries with harmonic functions and connects these deformations to CFT operators in the D1-D5 system.

Findings

Deformation solutions are harmonic functions in the background geometry.

Explicit microstate geometries for D1-D5 system are constructed.

Deformations correspond to U(1) current actions in the dual CFT.

Abstract

We consider general supersymmetric solutions to minimal supergravity in six dimensions, trivially lifted to IIB supergravity. To any such solution we add a travelling-wave deformation involving the additional directions. The deformed solution is given in terms of a function which is harmonic in the background geometry. We also present a family of explicit examples describing microstates of the D1-D5 system on T^4. In the case where the background contains a large AdS region, the deformation is identified as corresponding to an action of a U(1) current of the D1-D5 orbifold CFT on a given state.