# Fuzzballs with internal excitations

## TL;DR

This paper constructs and analyzes horizon-free fuzzball solutions with internal excitations in IIB supergravity, demonstrating their duality to specific superpositions of R ground states and capturing internal excitations via chiral primary vevs.

## Contribution

It introduces a general class of fuzzball solutions with internal excitations characterized by arbitrary curves, extending the understanding of microstates in supergravity.

## Key findings

- Internal excitations are captured by vevs of chiral primaries.
- Solutions correspond to superpositions of R ground states.
- Internal excitations are characterized by arbitrary curves.

## Abstract

We construct general 2-charge D1-D5 horizon-free non-singular solutions of IIB supergravity on T^4 and K3 describing fuzzballs with excitations in the internal manifold; these excitations are characterized by arbitrary curves. The solutions are obtained via dualities from F1-P solutions of heterotic and type IIB on T^4 for the K3 and T^4 cases, respectively. We compute the holographic data encoded in these solutions, and show that the internal excitations are captured by vevs of chiral primaries associated with the middle cohomology of T^4 or K3. We argue that each geometry is dual to a specific superposition of R ground states determined in terms of the Fourier coefficients of the curves defining the supergravity solution. We compute vevs of chiral primaries associated with the middle cohomology and show that they indeed acquire vevs in the superpositions corresponding to fuzzballs with internal excitations, in accordance with the holographic results. We also address the question of whether the fuzzball program can be implemented consistently within supergravity.