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Superstrings on AdS3 at k=1

G. Giribet, C. Hull, M. Kleban, M. Porrati, E. Rabinovici

TL;DR

The paper analyzes superstrings on AdS$_3$ with NS-NS flux at the special k=1 regime, identifying a phase where long strings dominate and a continuum of massless higher-spin states emerges. It proposes a concrete holographic dual: a symmetric-product SCFT on $(R imes c{N})^N/S_N$ with a carefully chosen seed, and demonstrates that, in the large-N limit, this dual reproduces the full long-string spectrum (including non-BPS states) of the bulk theory. The work provides strong evidence for a concrete, exactly-matchable holographic description at a string-scale curvature, offering insights into tensionless-like phases and stringy symmetries in AdS$_3$. It also discusses subtleties in comparing bulk amplitudes to boundary correlators and outlines avenues for refining the dual and understanding interactions. Overall, it reveals that a simple symmetric-orbifold CFT captures the intricate long-string physics at the AdS$_3$ transition point, with potential implications for broader holographic dualities at highly curved or tensionless limits.

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.

Superstrings on AdS3 at k=1

TL;DR

The paper analyzes superstrings on AdS with NS-NS flux at the special k=1 regime, identifying a phase where long strings dominate and a continuum of massless higher-spin states emerges. It proposes a concrete holographic dual: a symmetric-product SCFT on with a carefully chosen seed, and demonstrates that, in the large-N limit, this dual reproduces the full long-string spectrum (including non-BPS states) of the bulk theory. The work provides strong evidence for a concrete, exactly-matchable holographic description at a string-scale curvature, offering insights into tensionless-like phases and stringy symmetries in AdS. It also discusses subtleties in comparing bulk amplitudes to boundary correlators and outlines avenues for refining the dual and understanding interactions. Overall, it reveals that a simple symmetric-orbifold CFT captures the intricate long-string physics at the AdS transition point, with potential implications for broader holographic dualities at highly curved or tensionless limits.

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.

Paper Structure

This paper contains 17 sections, 60 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Phase Structure of String theory in $AdS_3$.
  3. String Theory in AdS$_3$
  4. The Bosonic String on $AdS_3$.
  5. Superstrings on AdS$_{3}$
  6. Holographic dual
  7. The permutation orbifold $(\mathbb{R} \times {\cal N})^N/S_N$.
  8. Fermionic boundary conditions
  9. Comparison of spectra
  10. Multiplicities
  11. Invariant states of the symmetric orbifold
  12. Shift in the conformal weight
  13. An Equivalent Construction
  14. Odd $n$
  15. Even $n$
  16. ...and 2 more sections

Figures (1)

  • Figure 1: The behavior of the entropy $S$ at high energies, as a function of the WZW level $k$. The black solid line is the entropy of black holes, which do not exist for $k<1$. The dashed line is the entropy of long strings, that dominate for $k<1$ (see gkrs for details).