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Superstrings on NS5 backgrounds, deformed AdS3 and holography

Dan Israel, Costas Kounnas, Marios P Petropoulos

TL;DR

The paper constructs and analyzes a new decoupling limit of the D1/D5 system that yields an exact, regular CFT description based on null-deformed SL(2,$\mathbb{R}$) x SU(2) x T^4/K3, connecting NS5 and D5 near-horizon geometries. It develops both bosonic and supersymmetric formulations, deriving modular-invariant partition functions for the undeformed and marginally deformed theories (including J^3J^3, J^2J^2, and null deformations) and clarifying the spectral content via discrete/continuous SL(2,$\mathbb{R}$) representations and spectral flow. The work then analyzes the supersymmetric null deformation, the resulting N=2 algebras, and the space-time SUSY projections, yielding a coherent IIB partition function on the deformed background with T^4/\mathbb{Z}_2 or K3. Finally, it discusses holographic implications, framing the geometry as an RG flow from Little String Theory in the UV to 6D string-like instanton dynamics in the IR, and outlines future directions in brane realizations and correlation-function computations on these exact backgrounds.

Abstract

We study a non-standard decoupling limit of the D1/D5-brane system, which interpolates between the near-horizon geometry of the D1/D5 background and the near-horizon limit of the pure D5-brane geometry. The S-dual description of this background is actually an exactly solvable two-dimensional (worldsheet) conformal field theory: {null-deformed SL(2,R)} x SU(2) x T^4 or K3. This model is free of strong-coupling singularities. By a careful treatment of the SL(2,R), based on the better-understood SL(2,R) / U(1) coset, we obtain the full partition function for superstrings on SL(2,R) x SU(2) x K3. This allows us to compute the partition functions for the J^3 and J^2 current-current deformations, as well as the full line of supersymmetric null deformations, which links the SL(2,R) conformal field theory with linear dilaton theory. The holographic interpretation of this setup is a renormalization-group flow between the decoupled NS5-brane world-volume theory in the ultraviolet (Little String Theory), and the low-energy dynamics of super Yang--Mills string-like instantons in six dimensions.

Superstrings on NS5 backgrounds, deformed AdS3 and holography

TL;DR

The paper constructs and analyzes a new decoupling limit of the D1/D5 system that yields an exact, regular CFT description based on null-deformed SL(2,) x SU(2) x T^4/K3, connecting NS5 and D5 near-horizon geometries. It develops both bosonic and supersymmetric formulations, deriving modular-invariant partition functions for the undeformed and marginally deformed theories (including J^3J^3, J^2J^2, and null deformations) and clarifying the spectral content via discrete/continuous SL(2,) representations and spectral flow. The work then analyzes the supersymmetric null deformation, the resulting N=2 algebras, and the space-time SUSY projections, yielding a coherent IIB partition function on the deformed background with T^4/\mathbb{Z}_2 or K3. Finally, it discusses holographic implications, framing the geometry as an RG flow from Little String Theory in the UV to 6D string-like instanton dynamics in the IR, and outlines future directions in brane realizations and correlation-function computations on these exact backgrounds.

Abstract

We study a non-standard decoupling limit of the D1/D5-brane system, which interpolates between the near-horizon geometry of the D1/D5 background and the near-horizon limit of the pure D5-brane geometry. The S-dual description of this background is actually an exactly solvable two-dimensional (worldsheet) conformal field theory: {null-deformed SL(2,R)} x SU(2) x T^4 or K3. This model is free of strong-coupling singularities. By a careful treatment of the SL(2,R), based on the better-understood SL(2,R) / U(1) coset, we obtain the full partition function for superstrings on SL(2,R) x SU(2) x K3. This allows us to compute the partition functions for the J^3 and J^2 current-current deformations, as well as the full line of supersymmetric null deformations, which links the SL(2,R) conformal field theory with linear dilaton theory. The holographic interpretation of this setup is a renormalization-group flow between the decoupled NS5-brane world-volume theory in the ultraviolet (Little String Theory), and the low-energy dynamics of super Yang--Mills string-like instantons in six dimensions.

Paper Structure

This paper contains 36 sections, 222 equations.

Table of Contents

  1. Introduction
  2. A new decoupling limit for the D1/D5-brane system
  3. The supergravity solution and a partial near-horizon limit
  4. Exact conformal-field-theory description: a null deformation of $SL(2,\mathbb{R})$
  5. Bosonic strings on AdS$_3$
  6. $SL(2,\mathbb{R})$ from $SL(2,\mathbb{R})/U(1)_{\mathrm{A}}$
  7. Uncovering the spectrum
  8. About the structure of the partition function
  9. Superstrings on AdS$_3 \times S^3 \times T^4$
  10. Extended superconformal algebras
  11. NS5 background
  12. NS5/F1 background
  13. The $N=2$ algebras of $SL(2,\mathbb{R}) \times SU(2)$.
  14. Space--time supersymmetry.
  15. The required projections in $SL(2,\mathbb{R}) \times SU(2) \times U(1)^4$.
  16. ...and 21 more sections