Warped Weyl fermion partition functions

TL;DR

This work analyzes warped conformal field theories through the explicit example of a massive Weyl fermion in 1+1 dimensions, deriving the spectrum and modular properties of WCFT partition functions. It introduces two novel Ramond-sector partition functions with no CFT2 analogs and develops a rigorous torus-based framework to study modular transformations, anomalies, and frame dependence. The authors show that angular momentum is bounded in WCFTs, construct modular invariant combinations requiring specific fermion counts, and connect high-temperature entropy to spectral-flow–invariant quantities, with implications for holography and black hole entropy. They also discuss the microcanonical density of states and the conditions under which universal Cardy-like growth holds, outlining directions for further generalization to $\mathcal{W}_N$ algebras and potential bosonization in WCFTs.

Abstract

Warped conformal field theories (WCFTs) are a novel class of non-relativistic theories. A simple, yet non-trivial, example of such theory is a massive Weyl fermion in $(1+1)$-dimensions, which we study in detail. We derive general properties of the spectrum and modular properties of partition functions of WCFTs. The periodic (Ramond) sector of this fermionic system is non-trivial, and we build two novel partition functions for this sector which have no counterpart in a CFT$_2$. The thermodynamical properties of WCFTs are revisited in the canonical and micro-canonical ensemble.