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:1906.07283 · Journal of High Energy Physics

Superfluids, vortices and spinning charged operators in 4d CFT

Gabriel Cuomo

Published Feb 1, 2020• 17 citations
arXivHTMLPDF

Abstract

Abstract We include vortices in the superfluid EFT for four dimensional CFTs at large global charge. Using the state-operator correspondence, vortices are mapped to charged operators with large spin and we compute their scaling dimensions. Different regimes are identified: phonons, vortex rings, Kelvin waves, and vortex crystals. We also compute correlators with a Noether current insertion in between vortex states. Results for the scaling dimensions of traceless symmetric operators are given in arbitrary spacetime dimensions.

DOI
10.1007/jhep02(2020)119

Related papers

Rotating superfluids and spinning charged operators in conformal field theory

Gabriel Cuomo, Anton de la Fuente, Alexander Monin +2 more

We compute the scaling dimensions of operators with large global charge and spin in $2+1$ dimensional conformal field theories. By the state-operator correspondence, these operators correspond to superfluids with vortices and can be systematically studied using effective field theory. As the spin increases from zero to the unitarity bound, the superfluid state corresponding to the lowest dimension operator passes through three distinct regimes: (i) a single phonon, (ii) two vortices, and (iii) multiple vortices. We also compute correlation functions with two such operators and the Noether current.

arXiv:1711.02108•Physical review. D/Physical review. D.•Feb 15, 2018•39 citations

The spinful large charge sector of non-relativistic CFTs: from phonons to vortex crystals

Shauna Kravec, Sridip Pal

Abstract We study operators in Schrödinger invariant field theories (non-relativistic conformal field theories or NRCFTs) with large charge (particle number) and spin. Via the state-operator correspondence for NRCFTs, such operators correspond to states of a superfluid in a harmonic trap with phonons or vortices. Using the effective field theory of the Goldstone mode, we compute the dimensions of operators to leading order in the angular momentumLand chargeQ. We find a diverse set of scaling behaviors for NRCFTs in bothd= 2 andd= 3 spatial dimensions. These results apply to theories with a superfluid phase, such as unitary fermions or critical anyon systems.

arXiv:1904.05462•Journal of High Energy Physics•May 1, 2019•22 citations

Spinning correlators in large-charge CFTs

Nicola Andrea Dondi, Ioannis Kalogerakis, Rafael Moser +2 more

We systematically study correlators of a generic conformal field theory with a global O(2) symmetry in a sector of large global charge. We focus in particular on three- and four-point correlators with conserved current insertions sandwiched between spinful excited states corresponding to phonons over the large-charge vacuum. We also discuss loop corrections to the scaling dimensions and observe the presence of multiple logarithms in even dimensions.

arXiv:2203.12624•Nuclear Physics B•Aug 11, 2022•12 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

Fermionic CFTs at large charge and large N

Nicola Andrea Dondi, Simeon Hellerman, Ioannis Kalogerakis +3 more

Abstract We study the large-charge sector of large-N fermionic cfts in three dimensions. Depending on the model and the nature of the fixed charge, we find two types of descriptions: in terms of a superfluid or a Fermi sphere. We explicitly compute the conformal dimensions of the lowest operator of fixed charge and in the superfluid case verify the eft predictions for the phonon spectrum.

Journal of High Energy Physics•Aug 28, 2023•14 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
Abstract We include vortices in the superfluid EFT for four dimensional CFTs at large global charge. Using the state-operator correspondence, vortices are mapped to charged operators with large spin and we compute their scaling dimensions. Different regimes are identified: phonons, vortex rings, Kelvin waves, and vortex crystals. We also compute correlators with a Noether current insertion in between vortex states. Results for the scaling dimensions of traceless symmetric operators are given in arbitrary spacetime dimensions.
We compute the scaling dimensions of operators with large global charge and spin in 2+12+12+1 dimensional conformal field theories. By the state-operator correspondence, these operators correspond to superfluids with vortices and can be systematically studied using effective field theory. As the spin increases from zero to the unitarity bound, the superfluid state corresponding to the lowest dimension operator passes through three distinct regimes: (i) a single phonon, (ii) two vortices, and (iii) multiple vortices. We also compute correlation functions with two such operators and the Noether current.
Abstract We study operators in Schrödinger invariant field theories (non-relativistic conformal field theories or NRCFTs) with large charge (particle number) and spin. Via the state-operator correspondence for NRCFTs, such operators correspond to states of a superfluid in a harmonic trap with phonons or vortices. Using the effective field theory of the Goldstone mode, we compute the dimensions of operators to leading order in the angular momentumLand chargeQ. We find a diverse set of scaling behaviors for NRCFTs in bothd= 2 andd= 3 spatial dimensions. These results apply to theories with a superfluid phase, such as unitary fermions or critical anyon systems.
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.
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.