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Journal of High Energy Physics

Fermionic CFTs at large charge and large N

Nicola Andrea Dondi, Simeon Hellerman, Ioannis Kalogerakis, Rafael Moser, Domenico Orlando, Susanne Reffert

Published Aug 28, 2023• 14 citations
Publisher

Abstract

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.

DOI
10.1007/jhep08(2023)180

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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.
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This thesis aims to explore the structure of CFTs with global internal symmetries and beyond via the Large-Charge Expansion (LCE), a semi-classical expansion applicable for states with large global quantum numbers. In the first part of this thesis we study CFT and SSB. We discuss the symmetry-constraints imposed by conformal invariance, introduce the concept of CFT data and the OPE. Concerning SSB, we discuss the existence of NG modes, the general counting rule for the number of NG modes under the spontaneous breaking of global internal symmetries and a generalization of the Goldstone theorem at finite density. In the second part of this thesis we discuss the current state-of-the-art understanding of the LCE and systematically study CFTs with a global O(2) symmetry in the context of the LCE. We discuss the emergence of effective condensed-matter descriptions, in particular superfluids, in correlators involving states with large global quantum numbers. We then use the superfluid EFT description to systematically study two-, three- and four-point functions for CFTs with a global O(2) symmetry. In the last part of this thesis we study CFTs in the double-scaling limit of large charge and large N . We discuss the D = 3 WF fixed point at large N and derive the leading order asymptotics at large charge Q in the double scaling limit Q/N fixed. Next, we use a fixed-charge approach to gain access to the leading order effective potential for the quartic theory, which we then study for spacetime dimensions 2 < D < 6. In D = 3, we reproduce and extend old results originally found by re-summing Feynman diagrams. Finally, we discuss the interacting fixed points of three-dimensional fermionic CFTs in the double-scaling limit. While the GN model exhibits a Fermi-sphere description at large charge, whose fate at finite N is yet to be determined, for the NJL-type models we find a BEC.
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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.