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Universal sectors of two-dimensional Carrollian CFTs

Ankit Aggarwal, Arjun Bagchi, Stephane Detournay, Daniel Grumiller, Max Riegler, Joan Simon

TL;DR

The paper analyzes modular invariance in two-dimensional Carrollian CFTs (CCFT$_2$) by expressing the partition function as a sum over Carrollian characters for induced and highest-weight representations. It identifies six sectors in which the vacuum character dominates in the dual ($S$-dual) channel, revealing universal, gravity-like thermodynamics including a negative specific heat in all vacuum-dominated sectors. A central result is the Schwarzian sector, which mirrors near-extremal dynamics and is holographically realized as an $O$-plane orbifold in flat space, with its microstates and density of states computable via the Carrollian modular S-matrix. The work also contrasts induced vs. highest-weight representations, connects the Schwarzian sector to flat space cosmologies, and situates CCFT$_2$ results within broader contexts such as 3d gravity and Warped CFTs. Overall, it provides a comprehensive framework for universal Carrollian thermodynamics and a holographic dictionary for flat-space holography through six vacuum-dominated sectors and their associated density-of-states structures.

Abstract

We revisit modular invariance in two-dimensional Carrollian conformal field theories from a geometric perspective. Focusing on the characters of the induced and highest-weight representations of the theory, we show that there are regions of parameter space where the vacuum character dominates in the dual channel. We use this property to zoom into different subsectors of the Carrollian theory. One of them is reminiscent of the Schwarzian sector of a relativistic CFT2 and has a flat space holographic interpretation as O-plane orbifold. It exists only for the highest-weight representation. We prove that for all sectors with vacuum dominance in the dual channel, the specific heat is negative, concurrent with the holographic interpretation of the negative specific heat of asymptotically flat spacetimes with horizons.

Universal sectors of two-dimensional Carrollian CFTs

TL;DR

The paper analyzes modular invariance in two-dimensional Carrollian CFTs (CCFT) by expressing the partition function as a sum over Carrollian characters for induced and highest-weight representations. It identifies six sectors in which the vacuum character dominates in the dual (-dual) channel, revealing universal, gravity-like thermodynamics including a negative specific heat in all vacuum-dominated sectors. A central result is the Schwarzian sector, which mirrors near-extremal dynamics and is holographically realized as an -plane orbifold in flat space, with its microstates and density of states computable via the Carrollian modular S-matrix. The work also contrasts induced vs. highest-weight representations, connects the Schwarzian sector to flat space cosmologies, and situates CCFT results within broader contexts such as 3d gravity and Warped CFTs. Overall, it provides a comprehensive framework for universal Carrollian thermodynamics and a holographic dictionary for flat-space holography through six vacuum-dominated sectors and their associated density-of-states structures.

Abstract

We revisit modular invariance in two-dimensional Carrollian conformal field theories from a geometric perspective. Focusing on the characters of the induced and highest-weight representations of the theory, we show that there are regions of parameter space where the vacuum character dominates in the dual channel. We use this property to zoom into different subsectors of the Carrollian theory. One of them is reminiscent of the Schwarzian sector of a relativistic CFT2 and has a flat space holographic interpretation as O-plane orbifold. It exists only for the highest-weight representation. We prove that for all sectors with vacuum dominance in the dual channel, the specific heat is negative, concurrent with the holographic interpretation of the negative specific heat of asymptotically flat spacetimes with horizons.

Paper Structure

This paper contains 41 sections, 191 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Carrollian CFTs and Carroll modular invariance
  3. Carroll symmetries and conformal Carroll symmetries
  4. Carroll partition functions
  5. Carroll limit from 2d CFT2
  6. Carroll modular transformations
  7. Carrollian partition functions as sums over Carrollian characters
  8. States and representations
  9. Characters and partition functions
  10. Expectation values, variances, and covariance
  11. Modular aspects of the Dedekind eta-function
  12. Carrollian vacuum characters as limits from CFT vacuum characters
  13. Carrollian vacuum dominance in the dual channel
  14. Six sectors with vacuum dominance in the dual channel
  15. $\beta\Omega \to 0^\pm$:
  16. ...and 26 more sections

Figures (4)

  • Figure 1: Plots of $\sqrt{\epsilon}\,|\eta(x+i\epsilon)|^2$ with $x\in[0,1]$. Left: $\epsilon=10^{-2}$. Right: $\epsilon=10^{-4}$.
  • Figure 2: Analytic structure of partition function in complex $\theta$-plane (see \ref{['fig:description']})
  • Figure 3: 2d slice of Penrose diagram for flat space cosmologies
  • Figure 4: Gravity side of Schwarzian sectors in AdS$_3$/CFT$_2$ (left) and Flat$_3$/CCFT$_2$ (right)