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Probing higher spin black holes from CFT

Matthias R. Gaberdiel, Kewang Jin, Eric Perlmutter

TL;DR

The paper tests higher-spin holography by computing thermal two-point functions of scalar operators deformed by a holomorphic spin-3 current, comparing bulk propagators in hs[λ] black hole backgrounds with CFT torus correlators. It extends previous linear-order results to generic λ, derives second-order corrections, and provides all-orders results in a zero-temperature, fixed-μ limit; it also cross-checks with higher scalar representations (antisymmetric two-box) to validate the multi-trace operator prescription. The bulk calculations rely on the master-field formalism and holonomy constraints, while the boundary theory uses perturbation theory in the W_3 deformation and modular transformations to access high-temperature regimes. Overall, the results reinforce the proposed dualities between W_N minimal models at large c and 3D higher spin gravity, and clarify the CFT deformation framework for higher-spin holography.

Abstract

In a class of 2D CFTs with higher spin symmetry, we compute thermal two-point functions of certain scalar primary operators in the presence of nonzero chemical potential for higher spin charge. These are shown to agree with the same quantity calculated holographically using scalar fields propagating in a charged black hole background of 3D higher spin gravity. This match serves as further evidence for the duality between W_N minimal models at large central charge and 3D higher spin gravity. It also supports a recent prescription for computing boundary correlators of multi-trace scalar primary operators in higher spin theories.

Probing higher spin black holes from CFT

TL;DR

The paper tests higher-spin holography by computing thermal two-point functions of scalar operators deformed by a holomorphic spin-3 current, comparing bulk propagators in hs[λ] black hole backgrounds with CFT torus correlators. It extends previous linear-order results to generic λ, derives second-order corrections, and provides all-orders results in a zero-temperature, fixed-μ limit; it also cross-checks with higher scalar representations (antisymmetric two-box) to validate the multi-trace operator prescription. The bulk calculations rely on the master-field formalism and holonomy constraints, while the boundary theory uses perturbation theory in the W_3 deformation and modular transformations to access high-temperature regimes. Overall, the results reinforce the proposed dualities between W_N minimal models at large c and 3D higher spin gravity, and clarify the CFT deformation framework for higher-spin holography.

Abstract

In a class of 2D CFTs with higher spin symmetry, we compute thermal two-point functions of certain scalar primary operators in the presence of nonzero chemical potential for higher spin charge. These are shown to agree with the same quantity calculated holographically using scalar fields propagating in a charged black hole background of 3D higher spin gravity. This match serves as further evidence for the duality between W_N minimal models at large central charge and 3D higher spin gravity. It also supports a recent prescription for computing boundary correlators of multi-trace scalar primary operators in higher spin theories.

Paper Structure

This paper contains 23 sections, 132 equations, 1 figure.

Table of Contents

  1. Introduction
  2. CFT correlators from scalars in the hs[$\lambda$] black hole background
  3. The hs[$\lambda$] black hole
  4. A zero temperature limit
  5. Scalar fields in higher spin gravity
  6. Scalar correlators in the black hole background
  7. First order: Universal structure
  8. Second order
  9. All orders in zero temperature, fixed $\mu$ limit
  10. The dual CFT point of view
  11. The unperturbed answer
  12. First order correction
  13. The structure of the first order result
  14. Second order correction
  15. A further test: higher scalar representations
  16. ...and 8 more sections

Figures (1)

  • Figure 1: Domain of the 2d integral.