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Title: Constraints on flavored 2d CFT partition functions

Abstract

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.

Authors:
 [1];  [2]; ORCiD logo [2]
  1. Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics; Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Physics and Astronomy
  2. Boston Univ., MA (United States). Physics Dept.
Publication Date:
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) (SC-25); National Science Foundation (NSF)
OSTI Identifier:
1501933
Grant/Contract Number:  
SC0010025; PHY-1316699
Resource 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 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; conformal and W symmetry; global symmetries

Citation Formats

Dyer, Ethan, Fitzpatrick, A. Liam, and Xin, Yuan. Constraints on flavored 2d CFT partition functions. United States: N. p., 2018. 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. Fri . "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 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.},
doi = {10.1007/jhep02(2018)148},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2018,
place = {United States},
year = {2018},
month = {2}
}

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Cited by: 11 works
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