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 $U(1)$ 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 $Q^0$ term in the scaling dimension ${\Delta }_Q$ of the lightest operator with fixed charge $Q\gg 1$, in four dimensions the same mechanism provides a universal $Q^0\log Q$ correction to ${\Delta }_Q$. 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 $q\ll Q$ in between the minimal energy states with charge $Q$ and $Q+q$, both in three and four dimensions. This contribution does not depend on the operator insertion and, similarly to the quantum effects in ${\Delta }_Q$, in four dimensions it scales logarithmically with $Q$.

arXiv comment6 pages v2 7 pages, added ref.s and results in d=5,6, paper matches journal version

References in corpus (15)

• On Renormalization Group Flows in Four Dimensions
• Generalized Dimensional Analysis
• Semiclassics, Goldstone Bosons and CFT data
• Compensating strong coupling with large charge
• The Epsilon Expansion Meets Semiclassics
• Low-Energy Quantum Effective Action for Relativistic Superfluids
• Conformal dimensions via large charge expansion
• Conformal Bootstrap At Large Charge
• On the CFT Operator Spectrum at Large Global Charge
• Selected Topics in the Large Quantum Number Expansion
• Five lectures on effective field theory
• Feynman diagrams and the large charge expansion in $3-\epsilon$ dimensions
• Operator Dimensions from Moduli
• Partition function on spheres: how (not) to use zeta function regularization
• Charging the Conformal Window

Cited by in corpus (24)

• Positivity bounds on effective field theories with spontaneously broken Lorentz invariance
• Resurgence of the large-charge expansion
• Charging the Conformal Window
• Anomalous dimensions of monopole operators at the transitions between Dirac and topological spin liquids
• Untangling scaling dimensions of fixed charge operators in Higgs Theories
• The OPE meets semiclassics
• Yukawa interactions at Large Charge
• Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements
• Numerical tests of the large charge expansion
• Operator spectrum of nonrelativistic CFTs at large charge
• Spinning correlators in large-charge CFTs
• Long Range, Large Charge, Large $N$
• The analytic structure of the fixed charge expansion
• On the exponentially small corrections to $\mathcal{N}=2$ superconformal correlators at large R-charge
• Applied nonrelativistic conformal field theory: scattering-length and effective-range corrections to unnuclear physics
• The Breakdown of Resummed Perturbation Theory at High Energies
• Large R-charge EFT correlators in N=2 SQCD
• Droplet-Edge Operators in Nonrelativistic Conformal Field Theories
• On Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture
• Charging the conformal window at nonzero $\theta$ angle
• IR side of bounds on Theories with Spontaneously Broken Lorentz Symmetry
• Boundary Conformal Field Theory at Large Charge
• Exact evaluation of large-charge correlation functions in non-relativistic conformal field theory
• Higher-form anomalies and state-operator correspondence beyond conformal invariance