Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

EVERY CFT$_3$ HAS AN $ \mathcal{L}_Λw_{1+\infty}$ SYMMETRY

Andrew Strominger, Hongji Wei

Abstract

Recently a one-parameter family of deformed $ \mathcal{L} w_{1+\infty}$ soft symmetry algebras, denoted $ \mathcal{L}_Λw_{1+\infty}$, acting on tree-level gravitational theories in AdS$_4$ has been discovered. Here we show that all CFT$_3$s, including those dual to quantum gravity on AdS$_4$, admit an $\mathcal{L}_Λw_{1+\infty}$ action generated by the ANEC operator, its conformal descendants and their commutators. This extends the previous tree-level results on these soft symmetries to the strongly-coupled quantum regime.

EVERY CFT$_3$ HAS AN $ \mathcal{L}_Λw_{1+\infty}$ SYMMETRY

Abstract

Recently a one-parameter family of deformed soft symmetry algebras, denoted , acting on tree-level gravitational theories in AdS has been discovered. Here we show that all CFTs, including those dual to quantum gravity on AdS, admit an action generated by the ANEC operator, its conformal descendants and their commutators. This extends the previous tree-level results on these soft symmetries to the strongly-coupled quantum regime.

Paper Structure

This paper contains 8 sections, 39 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Cordova-Shao Light Ray Operators
  3. $SO(3,2)$ Conformal Action
  4. The Wedge
  5. AdS$_4$
  6. Conformal mappings EC$^3\leftrightarrow$M$^3$
  7. Plane model algebra
  8. Constructive proof of the wedge algebra

Figures (3)

  • Figure 1: The dark grey region depicts the set of all light rays in the $S^2\times R$ Einstein cylinder EC$^3$ (forming the boundary of AdS$_4$) beginning at an initial point $x_i$ and reconverging at the antipodal point $x_f$. These comprise a null $S^2$ and are a Cauchy surface for EC$^3$. The sphere $S^2$ is shown schematically as a disk.
  • Figure 2: Lattice of states. The green dots are modes of ANEC operator. These are lowest weight states at the edge of the wedge \ref{['swedge']}, which is the shaded region. The arrow is the "forbidden" operations along which all the $SO(3,2)$ generators have vanishing coefficients.
  • Figure 3: Objects used in the construction. Green dots denote the ANEC modes $A_q$. Other objects are indicated as vertical strips in the figure. The arrow is the "forbidden" operations along which all the $SO(3,2)$ generators have vanishing coefficients.