Constraints on 2d CFT partition functions

TL;DR

This paper systematically explores how modular invariance constrains the spectrum of 2d conformal field theories, deriving new bounds on spectral gaps and implications for Calabi-Yau compactifications.

Contribution

It introduces an improved linear functional method to establish tighter upper bounds on spectral gaps in 2d CFTs and applies these results to superconformal theories and Calabi-Yau threefolds.

Findings

New upper bounds on the lowest spectral gap in 2d CFTs

Non-BPS primary states must have weight ≤ 0.6 in certain Calabi-Yau compactifications

Constraints derived for N=(2,2) superconformal theories

Abstract

Modular invariance is known to constrain the spectrum of 2d conformal field theories. We investigate this constraint systematically, using the linear functional method to put new improved upper bounds on the lowest gap in the spectrum. We also consider generalized partition functions of N = (2,2) superconformal theories and discuss the application of our results to Calabi-Yau compactifications. For Calabi-Yau threefolds with no enhanced symmetry we find that there must always be non-BPS primary states of weight 0.6 or less.