English

A note on the large charge expansion in 4d CFT

High Energy Physics - Theory 2020-12-15 v2 Statistical Mechanics Strongly Correlated Electrons

Abstract

In this letter, we discuss certain universal predictions of the large charge expansion in conformal field theories with U(1)U(1) 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 Q0Q^0 term in the scaling dimension ΔQ\Delta_Q of the lightest operator with fixed charge Q1Q\gg 1, in four dimensions the same mechanism provides a universal Q0logQQ^0\log Q correction to ΔQ\Delta_Q. 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 qQq\ll Q in between the minimal energy states with charge QQ and Q+qQ+q, both in three and four dimensions. This contribution does not depend on the operator insertion and, similarly to the quantum effects in ΔQ\Delta_Q, in four dimensions it scales logarithmically with QQ.

Keywords

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

R2 v1 2026-06-23T18:56:10.986Z