Near-Extremal Limits of Warped CFTs

TL;DR

This paper investigates the near-extremal limit of warped conformal field theories (WCFTs), revealing that it requires large central charges and is consistent only for non-unitary cases, with implications for related warped-Schwarzian theories.

Contribution

It provides a detailed derivation of the near-extremal limit for WCFTs and compares it with previous studies and analogous limits in 2D CFTs.

Findings

Near-extremal limit requires large central charge

Limit is only consistent for non-unitary WCFTs

Comparison with warped-Schwarzian theory and 2D CFTs

Abstract

Warped conformal field theories (WCFTs) are two-dimensional non-relativistic systems, with a chiral scaling and shift symmetry. We present a detailed derivation of the near-extremal limit for their torus partition function. This limit requires large values of the central charge, and is only consistent for non-unitary WCFT. We compare our analysis with previous studies of WCFT and its relation to a one-dimensional warped-Schwarzian theory. We discuss different ensembles of warped CFTs and contrast our results with analogous limits in two-dimensional CFTs.