# Superstrings on AdS3 at k=1

## TL;DR

This paper investigates superstring theory in AdS3 at the critical level k=1, proposing a dual conformal field theory that captures the transition from black hole dominance to long string dominance.

## Contribution

It introduces a new holographic dual conformal field theory for superstrings at k=1, explaining the massless modes and the phase transition in AdS3 superstring theory.

## Key findings

- Reproduces the spectrum of long strings at large N
- Identifies massless modes as signals of a phase transition
- Supports the duality with a proposed 2D conformal field theory

## Abstract

We study superstring theory in three dimensional Anti-de Sitter spacetime with NS-NS flux, focusing on the case where the radius of curvature is equal to the string length. This corresponds to the critical level k=1 in the Wess-Zumino-Witten description. Previously, it was argued that a transition takes place at this special radius, from a phase dominated by black holes at larger radius to one dominated by long strings at smaller radius. We argue that the infinite tower of modes that become massless at k=1 is a signal of this transition. We propose a simple two-dimensional conformal field theory as the holographic dual to superstring theory at k=1. As evidence for our conjecture, we demonstrate that at large N our putative dual exactly reproduces the full spectrum of the long strings of the weakly coupled string theory, including states unprotected by supersymmetry.