# Little Strings, Long Strings, and Fuzzballs

## TL;DR

This paper investigates the relationship between little strings, fuzzballs, and black hole thermodynamics in string theory, using D-brane probes and exactly solvable models to reveal the nature of long strings near black hole regimes.

## Contribution

It introduces a formalism for null gauging with boundaries and demonstrates that D-branes in supertube backgrounds represent long string structures relevant to black hole thermodynamics.

## Key findings

- D-branes wrapping supertube bottoms are long string analogs.
- Null gauged WZW models describe string dynamics on these backgrounds.
- Long strings near black hole regimes are linked to D-brane excitations.

## Abstract

At high energy densities, fivebranes are populated by a Hagedorn phase of so-called "little strings", whose statistical mechanics underlies black fivebrane thermodynamics. A particular limit of this phase yields BTZ black holes in $AdS_3$, leading us to the idea that in this context fuzzballs and highly excited little strings are one and the same. We explore these ideas through an analysis of D-brane probes of fivebrane supertube backgrounds. String theory dynamics on these backgrounds is described by an exactly solvable null-gauged WZW model. We develop the formalism of null gauging on worldsheets with boundaries, and find that D-branes wrapping topology at the bottom of the supertube throat are avatars of the "long string" structure that dominates the thermodynamics of the black hole regime, appearing here as excitations of supertubes lying near but slightly outside the black hole regime.