Nonperturbative effects in $T\bar{T}$-deformed conformal field theories: A toy model for Planckian physics

TL;DR

This paper develops a nonperturbative approach to two-point correlators in $Tar{T}$-deformed CFTs, revealing how short-distance behavior mimics quantum gravitational effects and suggests a transition to a regime with suppressed correlations and erased geometric structure.

Contribution

It introduces a nonperturbative completion of correlators in $Tar{T}$-deformed CFTs and explores their short-distance behavior as a toy model for Planckian physics.

Findings

Short-distance correlators exhibit trans-Planckian oscillations.

Correlations are suppressed and become exponentially weaker at sub-fundamental scales.

Geometric structure appears largely erased at trans-Planckian regimes.

Abstract

We propose a nonperturbative completion of two-point correlators in $T\bar{T}$-deformed conformal field theories (CFTs), and analyze their behavior at distance scales shorter than the fundamental length scale set by the $T\bar{T}$ deformation. Building on the interpretation of the $T\bar{T}$ deformation as a coupling to two-dimensional quantum gravity with a unique built-in length scale, we advance the study of $T\bar{T}$-deformed CFTs as a toy model for Planckian physics. As we probe shorter distances, trans-Planckian oscillations are followed by a super-Planckian regime in which correlations are typically suppressed by geometric randomness, in contrast to the power-law growth characteristic of CFTs. Moreover, their dependence on distance becomes exponentially weaker, suggesting that the underlying geometric structure has been largely erased -- a behavior broadly consistent with expectations for quantum spacetime in this regime.