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Probing thermality beyond the diagonal

Enrico M. Brehm, Diptarka Das, Shouvik Datta

TL;DR

The paper analytically probes the off-diagonal sector of eigenstate thermalization in 2d CFTs by combining modular bootstrap of torus two-point functions with semi-classical heavy-light Virasoro blocks. It derives asymptotics for averaged off-diagonal OPE coefficients, showing entropic suppression consistent with ETH, and refines these results to primary OPE data, including a central-charge shift c→c−1. A universal bound on light data emerges from variance considerations, constraining coefficients like C_{χ O χ}. The off-diagonal two-point functions are analyzed via the monodromy method, revealing thermal features and a bulk holographic interpretation in terms of geodesic networks in AdS3 with conical defects or BTZ backgrounds.

Abstract

We investigate the off-diagonal sector of eigenstate thermalization using both local and non-local probes in 2-dimensional conformal field theories. A novel analysis of the asymptotics of OPE coefficients via the modular bootstrap is performed to extract the behaviour of the off-diagonal matrix elements. We also probe this sector using semi-classical heavy-light Virasoro blocks. The results demonstrate signatures of thermality and confirms the entropic suppression of the off-diagonal elements as necessitated by the eigenstate thermalization hypothesis.

Probing thermality beyond the diagonal

TL;DR

The paper analytically probes the off-diagonal sector of eigenstate thermalization in 2d CFTs by combining modular bootstrap of torus two-point functions with semi-classical heavy-light Virasoro blocks. It derives asymptotics for averaged off-diagonal OPE coefficients, showing entropic suppression consistent with ETH, and refines these results to primary OPE data, including a central-charge shift c→c−1. A universal bound on light data emerges from variance considerations, constraining coefficients like C_{χ O χ}. The off-diagonal two-point functions are analyzed via the monodromy method, revealing thermal features and a bulk holographic interpretation in terms of geodesic networks in AdS3 with conical defects or BTZ backgrounds.

Abstract

We investigate the off-diagonal sector of eigenstate thermalization using both local and non-local probes in 2-dimensional conformal field theories. A novel analysis of the asymptotics of OPE coefficients via the modular bootstrap is performed to extract the behaviour of the off-diagonal matrix elements. We also probe this sector using semi-classical heavy-light Virasoro blocks. The results demonstrate signatures of thermality and confirms the entropic suppression of the off-diagonal elements as necessitated by the eigenstate thermalization hypothesis.

Paper Structure

This paper contains 11 sections, 71 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Off-diagonal one point functions
  3. Modular properties of correlation functions on the torus
  4. Asymptotics of OPE coefficients
  5. Refining asymptotics for primaries
  6. A bound from the statistics of OPE coefficients
  7. Off-diagonal two-point functions
  8. Off-diagonal conformal blocks using the monodromy method
  9. Comparison with other approaches
  10. Conclusions
  11. Mellin-Barnes integrals

Figures (2)

  • Figure 1: Schematic representation of the decomposition of the torus 2-point function in projection/necklace channel using torus blocks.
  • Figure 2: Geodesic configuration at the $AdS_3$ time slice equivalent to the semi-classical Virasoro blocks result \ref{['exp-block']} calculated using the monodromy method.