A note on the large charge expansion in 4d CFT
Abstract
In this letter, we discuss certain universal predictions of the large charge expansion in conformal field theories with symmetry, mainly focusing on four-dimensional theories. We show that, while in three dimensions quantum fluctuations are responsible for the existence of a theory-independent term in the scaling dimension of the lightest operator with fixed charge , in four dimensions the same mechanism provides a universal correction to . Previous works discussing four-dimensional theories failed in identifying this term. We also compute the first subleading correction to the OPE coefficient corresponding to the insertion of an arbitrary primary operator with small charge in between the minimal energy states with charge and , both in three and four dimensions. This contribution does not depend on the operator insertion and, similarly to the quantum effects in , in four dimensions it scales logarithmically with .
Cite
@article{arxiv.2010.00407,
title = {A note on the large charge expansion in 4d CFT},
author = {Gabriel Cuomo},
journal= {arXiv preprint arXiv:2010.00407},
year = {2020}
}
Comments
6 pages v2 7 pages, added ref.s and results in d=5,6, paper matches journal version