Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1707.00711 · Physical Review Letters

Conformal Dimensions via Large Charge Expansion

Debasish Banerjee, Shailesh Chandrasekharan A, Domenico Orlando

Published Feb 9, 2018• 91 citations
arXivHTMLPDF

Abstract

We construct an efficient Monte Carlo algorithm that overcomes the severe signal-to-noise ratio problems and helps us to accurately compute the conformal dimensions of large-Q fields at the Wilson-Fisher fixed point in the O(2) universality class. Using it, we verify a recent proposal that conformal dimensions of strongly coupled conformal field theories with a global U(1) charge can be obtained via a series expansion in the inverse charge 1/Q. We find that the conformal dimensions of the lowest operator with a fixed charge Q are almost entirely determined by the first few terms in the series.

DOI
10.1103/physrevlett.120.061603

Related papers

Conformal Dimensions in the Large Charge Sectors at the O(4) Wilson-Fisher Fixed Point

Debasish Banerjee, Shailesh Chandrasekharan A, Domenico Orlando +1 more

We study the O(4) Wilson-Fisher fixed point in 2+1 dimensions in fixed large-charge sectors identified by products of two spin-j representations (j_{L},j_{R}). Using effective field theory we derive a formula for the conformal dimensions D(j_{L},j_{R}) of the leading operator in terms of two constants, c_{3/2} and c_{1/2}, when the sum j_{L}+j_{R} is much larger than the difference |j_{L}-j_{R}|. We compute D(j_{L},j_{R}) when j_{L}=j_{R} with Monte Carlo calculations in a discrete formulation of the O(4) lattice field theory, and show excellent agreement with the predicted formula and estimate c_{3/2}=1.068(4) and c_{1/2}=0.083(3).

arXiv:1902.09542•Physical Review Letters•Aug 1, 2019•48 citations

Large-charge Rényi entropy

Masataka Watanabe

A bstract The charged (symmetry-resolved) vacuum Rényi entanglement entropy on a disk is computed in the limit of large U(1) global charge for any Rényi index. We show that it behaves universally for a broad class of conformal field theories including the O (2) Wilson-Fisher fixed-point, by using the effective field theory at large global charge. The result establishes one of the first concrete computations of entanglement quantities in strongly-coupled field theories.

Journal of High Energy Physics•Mar 25, 2026•1 citation

Large-charge Rényi entropy

Masataka Watanabe

The charged (symmetry-resolved) vacuum Rényi entanglement entropy on a disk is computed in the limit of large U(1) global charge for any Rényi index. We show that it behaves universally for a broad class of conformal field theories including the O(2) Wilson-Fisher fixed-point, by using the effective field theory at large global charge. The result establishes one of the first concrete computations of entanglement quantities in strongly-coupled field theories.

arXiv:2506.10072•Jun 11, 2025•0 citations

OPE meets semiclassics

Gabriel Cuomo

We show that the correlator of three large charge operators with minimal scaling dimension can be computed semiclassically in conformal field theories (CFTs) with a $U(1)$ symmetry for arbitrary fixed values of the ratios of their charges. We obtain explicitly the operator product expansion coefficient from the numerical solution of a nonlinear boundary value problem in the conformal superfluid effective field theory in $3d$. The result applies in all three-dimensional CFTs with a $U(1)$ symmetry whose large charge sector is a superfluid.

arXiv:2103.01331•Physical review. D/Physical review. D.•Apr 16, 2021•18 citations

Identifying Large Charge operators

Gil Badel, Alexander Monin, Riccardo Rattazzi A

Abstract The Large Charge sector of Conformal Field Theory (CFT) can generically be described through a semiclassical expansion around a superfluid background. In this work, focussing on U(1) invariant Wilson-Fisher fixed points, we study the spectrum of spinning large charge operators. For sufficiently low spin these correspond to the phonon excitations of the superfluid state. We discuss the organization of these states into conformal multiplets and the form of the corresponding composite operators in the free field theory limit. The latter entails a mapping, built order-by-order in the inverse charge n−1, between the Fock space of vacuum fluctuations and the Fock space of fluctuations around the superfluid state. We discuss the limitations of the semiclassical method, and find that the phonon description breaks down for spins of order n1/2 while the computation of observables is valid up to spins of order n. Finally, we apply the semiclassical method to compute some conformal 3-point and 4-point functions, and analyze the conformal block decomposition of the latter with our knowledge of the operator spectrum.

arXiv:2207.08919•Journal of High Energy Physics•Feb 13, 2023•4 citations

Flux correlators and semiclassics

Eren Firat, Alexander Monin, Riccardo Rattazzi A +1 more

A bstract We consider correlators for the flux of energy and charge in the background of operators with large global U(1) charge in conformal field theory (CFT). It has recently been shown that the corresponding Euclidean correlators generically admit a semiclassical description in terms of the effective field theory (EFT) for a conformal superfluid. We adapt the semiclassical description to Lorentzian observables and compute the leading large charge behavior of the flux correlators in general U(1) symmetric CFTs. We discuss the regime of validity of the large charge EFT for these Lorentzian observables and the subtleties in extending the EFT approach to subleading corrections. We also consider the Wilson-Fisher fixed point in d = 4 − ϵ dimensions, which offers a specific weakly coupled realization of the general setup, where the subleading corrections can be systematically computed without relying on an EFT.

arXiv:2309.14428•Journal of High Energy Physics•Mar 12, 2024•7 citations
We construct an efficient Monte Carlo algorithm that overcomes the severe signal-to-noise ratio problems and helps us to accurately compute the conformal dimensions of large-Q fields at the Wilson-Fisher fixed point in the O(2) universality class. Using it, we verify a recent proposal that conformal dimensions of strongly coupled conformal field theories with a global U(1) charge can be obtained via a series expansion in the inverse charge 1/Q. We find that the conformal dimensions of the lowest operator with a fixed charge Q are almost entirely determined by the first few terms in the series.
We study the O(4) Wilson-Fisher fixed point in 2+1 dimensions in fixed large-charge sectors identified by products of two spin-j representations (j_{L},j_{R}). Using effective field theory we derive a formula for the conformal dimensions D(j_{L},j_{R}) of the leading operator in terms of two constants, c_{3/2} and c_{1/2}, when the sum j_{L}+j_{R} is much larger than the difference |j_{L}-j_{R}|. We compute D(j_{L},j_{R}) when j_{L}=j_{R} with Monte Carlo calculations in a discrete formulation of the O(4) lattice field theory, and show excellent agreement with the predicted formula and estimate c_{3/2}=1.068(4) and c_{1/2}=0.083(3).
We show that the correlator of three large charge operators with minimal scaling dimension can be computed semiclassically in conformal field theories (CFTs) with a U(1)U(1)U(1) symmetry for arbitrary fixed values of the ratios of their charges. We obtain explicitly the operator product expansion coefficient from the numerical solution of a nonlinear boundary value problem in the conformal superfluid effective field theory in 3d3d3d. The result applies in all three-dimensional CFTs with a U(1)U(1)U(1) symmetry whose large charge sector is a superfluid.
Abstract The Large Charge sector of Conformal Field Theory (CFT) can generically be described through a semiclassical expansion around a superfluid background. In this work, focussing on U(1) invariant Wilson-Fisher fixed points, we study the spectrum of spinning large charge operators. For sufficiently low spin these correspond to the phonon excitations of the superfluid state. We discuss the organization of these states into conformal multiplets and the form of the corresponding composite operators in the free field theory limit. The latter entails a mapping, built order-by-order in the inverse charge n−1, between the Fock space of vacuum fluctuations and the Fock space of fluctuations around the superfluid state. We discuss the limitations of the semiclassical method, and find that the phonon description breaks down for spins of order n1/2 while the computation of observables is valid up to spins of order n. Finally, we apply the semiclassical method to compute some conformal 3-point and 4-point functions, and analyze the conformal block decomposition of the latter with our knowledge of the operator spectrum.
A bstract We consider correlators for the flux of energy and charge in the background of operators with large global U(1) charge in conformal field theory (CFT). It has recently been shown that the corresponding Euclidean correlators generically admit a semiclassical description in terms of the effective field theory (EFT) for a conformal superfluid. We adapt the semiclassical description to Lorentzian observables and compute the leading large charge behavior of the flux correlators in general U(1) symmetric CFTs. We discuss the regime of validity of the large charge EFT for these Lorentzian observables and the subtleties in extending the EFT approach to subleading corrections. We also consider the Wilson-Fisher fixed point in d = 4 − ϵ dimensions, which offers a specific weakly coupled realization of the general setup, where the subleading corrections can be systematically computed without relying on an EFT.