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Conformal Chern-Simons holography - lock, stock and barrel

Hamid Afshar, Branislav Cvetković, Sabine Ertl, Daniel Grumiller, Niklas Johansson

TL;DR

This work analyzes conformal Chern–Simons gravity (CSG) as a nonlinear realization of linearized partial masslessness in three dimensions. It develops a complete canonical framework, derives gauge generators and boundary charges, and classifies boundary conditions yielding distinct holographic setups. In asymptotically AdS holography, it computes 1-, 2-, and 3-point functions, obtaining central charges $c_R=12k$ and $c_L=-12k$, and reveals a boundary scalar sector in generalized holography that can carry a background charge and modify the Virasoro structure via a Sugawara shift. The study shows how Weyl invariance on the boundary changes the holographic map, leading to cases with pure diffeomorphism symmetry, an extended Virasoro$ imes$U(1) algebra, or additional scalar degrees of freedom, and points toward extensions to supersymmetric or higher-spin theories as well as non-AdS holography.

Abstract

We discuss a fine-tuning of rather generic three dimensional higher-curvature gravity actions that leads to gauge symmetry enhancement at the linearized level via partial masslessness. Requiring this gauge symmetry to be present also non-linearly reduces such actions to conformal Chern-Simons gravity. We perform a canonical analysis of this theory and construct the gauge generators and associated charges. We provide and classify admissible boundary conditions. The boundary conditions on the conformal equivalence class of the metric render one chirality of the partially massless Weyl gravitons normalizable and the remaining one non-normalizable. There are three choices - trivial, fixed or free - for the Weyl factors of the bulk metric and of the boundary metric. This proliferation of boundary conditions leads to various physically distinct scenarios of holography that we study in detail, extending considerably the discussion initiated in 1106.6299. In particular, the dual CFT may contain an additional scalar field with or without background charge, depending on the choices above.

Conformal Chern-Simons holography - lock, stock and barrel

TL;DR

This work analyzes conformal Chern–Simons gravity (CSG) as a nonlinear realization of linearized partial masslessness in three dimensions. It develops a complete canonical framework, derives gauge generators and boundary charges, and classifies boundary conditions yielding distinct holographic setups. In asymptotically AdS holography, it computes 1-, 2-, and 3-point functions, obtaining central charges and , and reveals a boundary scalar sector in generalized holography that can carry a background charge and modify the Virasoro structure via a Sugawara shift. The study shows how Weyl invariance on the boundary changes the holographic map, leading to cases with pure diffeomorphism symmetry, an extended VirasoroU(1) algebra, or additional scalar degrees of freedom, and points toward extensions to supersymmetric or higher-spin theories as well as non-AdS holography.

Abstract

We discuss a fine-tuning of rather generic three dimensional higher-curvature gravity actions that leads to gauge symmetry enhancement at the linearized level via partial masslessness. Requiring this gauge symmetry to be present also non-linearly reduces such actions to conformal Chern-Simons gravity. We perform a canonical analysis of this theory and construct the gauge generators and associated charges. We provide and classify admissible boundary conditions. The boundary conditions on the conformal equivalence class of the metric render one chirality of the partially massless Weyl gravitons normalizable and the remaining one non-normalizable. There are three choices - trivial, fixed or free - for the Weyl factors of the bulk metric and of the boundary metric. This proliferation of boundary conditions leads to various physically distinct scenarios of holography that we study in detail, extending considerably the discussion initiated in 1106.6299. In particular, the dual CFT may contain an additional scalar field with or without background charge, depending on the choices above.

Paper Structure

This paper contains 33 sections, 223 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Canonical analysis
  3. Field equations and gauge symmetries
  4. Hamiltonian and constraints
  5. Gauge generators and boundary charges
  6. Boundary conditions
  7. Statement and classification of boundary conditions
  8. Asymptotic symmetry group
  9. Asymptotic AdS holography
  10. 1-point functions
  11. Charges
  12. Graviton modes
  13. 2- and 3-point functions
  14. Generalized holography
  15. Case II: Weyl factor fixed
  16. ...and 18 more sections

Figures (1)

  • Figure 1: Spectrum of Weyl gravitons. Physical modes are denoted by full circles, pure gauge modes by X, and non-normalizable modes by empty circles. Primaries are additionally encircled. Arrows denote the action of ladder operators $L_+$ (up), $L_-$ (down), $\bar{L}_+$ (right) and $\bar{L}_-$ (left). Dotted lines are semi-permeable barriers.