Constraints on flavored 2d CFT partition functions
We study the implications of modular invariance on 2d CFT partition functions with abelian or nonabelian 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 “masstocharge” 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.
 Authors:

^{[1]};
^{[2]};
^{[2]}
 Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics; Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Physics and Astronomy
 Boston Univ., MA (United States). Physics Dept.
 Publication Date:
 Grant/Contract Number:
 SC0010025; PHY1316699
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 2; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Boston Univ., MA (United States); Johns Hopkins Univ., Baltimore, MD (United States); Stanford Univ., CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25); National Science Foundation (NSF)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; conformal and W symmetry; global symmetries
 OSTI Identifier:
 1501933
Dyer, Ethan, Fitzpatrick, A. Liam, and Xin, Yuan. Constraints on flavored 2d CFT partition functions. United States: N. p.,
Web. doi:10.1007/jhep02(2018)148.
Dyer, Ethan, Fitzpatrick, A. Liam, & Xin, Yuan. Constraints on flavored 2d CFT partition functions. United States. doi:10.1007/jhep02(2018)148.
Dyer, Ethan, Fitzpatrick, A. Liam, and Xin, Yuan. 2018.
"Constraints on flavored 2d CFT partition functions". United States.
doi:10.1007/jhep02(2018)148. https://www.osti.gov/servlets/purl/1501933.
@article{osti_1501933,
title = {Constraints on flavored 2d CFT partition functions},
author = {Dyer, Ethan and Fitzpatrick, A. Liam and Xin, Yuan},
abstractNote = {We study the implications of modular invariance on 2d CFT partition functions with abelian or nonabelian 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 “masstocharge” 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.},
doi = {10.1007/jhep02(2018)148},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2018,
place = {United States},
year = {2018},
month = {2}
}