The Spectrum of Permutation Orbifolds

TL;DR

This paper investigates the spectrum of permutation orbifolds in 2D conformal field theories, revealing cases with faster-than-Hagedorn growth and providing methods to compute their partition functions.

Contribution

It introduces a new approach to analyze permutation orbifolds, including cases with unconventional spectral growth, and generalizes Hecke operators for partition function calculations.

Findings

Identified permutation orbifolds with super-Hagedorn spectrum growth

Developed a generalized method for computing partition functions

Provided examples contrasting known symmetric orbifold behavior

Abstract

We study the spectrum of permutation orbifolds of 2d CFTs. We find examples where the light spectrum grows faster than Hagedorn, which is different from known cases such as symmetric orbifolds. We also describe how to compute their partition functions using a generalization of Hecke operators.