Constraints on flavored 2d CFT partition functions

• Published in: The journal of high energy physics Vol. 2018; no. 2; pp. 1 - 37
• Main Authors: Dyer, Ethan, Fitzpatrick, A. Liam, Xin, Yuan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2018; Springer Nature B.V; Springer Berlin; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Conformal and W Symmetry; Elementary Particles; Global Symmetries; High energy physics; Integers; Partitions; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Transformations (mathematics); Upper bounds; Global Symmetries; Conformal and W Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2018)148

A bstract We study the implications of modular invariance on 2d CFT partition functions with abelian or non-abelian currents when chemical potentials for the charges are turned on, i.e. when the partition functions are “flavored”. We begin with a new proof of the transformation law for the modular transformation of such partition functions. Then we proceed to apply modular bootstrap techniques to constrain the spectrum of charged states in the theory. We improve previous upper bounds on the state with the greatest “mass-to-charge” ratio in such theories, as well as upper bounds on the weight of the lightest charged state and the charge of the weakest charged state in the theory. We apply the extremal functional method to theories that saturate such bounds, and in several cases we find the resulting prediction for the occupation numbers are precisely integers. Because such theories sometimes do not saturate a bound on the full space of states but do saturate a bound in the neutral sector of states, we find that adding flavor allows the extremal functional method to solve for some partition functions that would not be accessible to it otherwise.