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We study some (conformal) field theories with global symmetries in the sector where the value of the global charge Q is large. We find (as expected) that the low energy excitations of this sector are described by the general form of Goldstone's theorem in the non-relativistic regime. We also derive the unexpected result, first presented in [1], that the effective field theory describing such sector of fixed Q contains effective couplings λ ∼ λ / Q , where λ is the original coupling. Hence, large charge leads to weak coupling. In the last section of the paper we present an outline of how to compute anomalous dimensions of the O( n) model in this limit. [ABSTRACT FROM AUTHOR]

Abstract In this note we search for the ground state of the D = 3 Wilson-Fisher conformal O(4) model, at nonzero values of the two independent charge densities ρ 1,2, on the torus spatial slice. Using an effective theory valid on scales longer than the scale defined by the charge density, we show that the ground-state configuration is inhomogeneous for generic ratios ρ 1/ρ 2. This result confirms, within the context of a well-defined effective theory, a recent no-go result of [1]. We also show that any spatially periodic ground state solutions have an energetic preference towards longer periods, within some range of ρ 1/ρ 2 containing a neighborhood of zero. This suggests that the scale of variation of the ground state solution in finite volume will be the infrared scale, and that the use of the effective theory at large charge in finite volume is self-consistent. Note added: the statements in this paper are true for arbitrary ratio of ρ 1/ρ 2, which we proved after we uploaded this paper. See [2].

The unitary Fermi gas, by virtue of its description as a nonrelativistic conformal field theory, has proven an interesting system by which the quantum properties of CFTs can be held to experimental verification. Here, we examine the structure of conformal dimensions of charge-Q operators in nonrelativistic CFTs, in the large-Q regime, from the non-linear sigma model perspective. We discuss in detail the renormalization of edge divergences using dimensional regularization, elucidating the presence of log(Q) terms in the large-charge expansion. Finally, we use dimensional regularization to compute the universal one-loop Q0 log Q contribution to the ground-state energy in d = 3 spatial dimensions, with the result Δ Q Q 0 = 1 3 3 log Q + const. [ABSTRACT FROM AUTHOR]

In this note we discuss the phase space of the O(2N) vector model in the presence of a quadratic and a quartic interaction by writing the large-N effective potential using large charge methods in dimensions 2 < D < 4 and 4 < D < 6. Based on a simple discussion of the convexity properties of the grand potential, we find very different behavior in the two regimes: while in 2 < D < 4, the theory is well-behaved, the model in 4 < D < 6 leads to a complex CFT in the UV, consistently with earlier results. We also find a new metastable massive phase in the high-energy regime for the theory on the cylinder. [ABSTRACT FROM AUTHOR]

We study operators with large internal charge in boundary conformal field theories (BCFTs) with internal symmetries. Using the state-operator correspondence and the existence of a macroscopic limit, we find a non-trivial relation between the scaling dimension of the lowest dimensional CFT and BCFT charged operators to leading order in the charge. We also construct the superfluid effective field theory for theories with boundaries and use it to systematically calculate the BCFT spectrum in a systematic expansion. We verify explicitly many of the predictions from the EFT analysis in concrete examples including the classical conformal scalar field with a |ϕ|6 interaction in three dimensions and the O(2) Wilson-Fisher model near four dimensions in the presence of boundaries. In the appendices we additionally discuss a systematic background field approach towards Ward identities in general boundary and defect conformal field theories, and clarify its relation with Noether's theorem in perturbative theories. [ABSTRACT FROM AUTHOR]

Infrared divergences in perturbative gravitational scattering amplitudes have been recently argued to be governed by the two-point function of the supertranslation Goldstone mode on the celestial sphere. We show that the form of this celestial two-point function simply derives from an effective action that also controls infrared divergences in the symplectic structure of General Relativity with asymptotically flat boundary conditions. This effective action finds its natural place in a path integral formulation of a celestial conformal field theory, as we illustrate by re-deriving the infrared soft factors in terms of celestial correlators. Our analysis relies on a well-posed action principle close to spatial infinity introduced by Compère and Dehouck. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Carrying to higher precision the large- J expansion of [1], we calculate to all orders in 1 / J the power-law corrections to the two-point functions Y n ≡ x − y 2 n Δ O ⋅ ≤ O n x O ¯ n y for generators O of Coulomb branch chiral rings in four-dimensional N = 2 superconformal field theories. We show these correlators have the universal large-n expansion log Y n ≃ J A + B + log Γ J + α + 1 , where J ≡ n Δ O is the total R-charge of O n, the A and B are theory-dependent coefficients, α is the coefficient of the Wess-Zumino term for the Weyl a-anomaly, and the ≃ denotes equality up to terms exponentially small in J . Our methods combine the structure of the Coulomb-branch eft with the supersymmetric recursion relations. However, our results constrain the power-law corrections to all orders, even for non-Lagrangian theories to which the recursion relations do not apply. For the case of N = 2 sqcd, we also comment on the nature of the exponentially small corrections, which can be calculated to high precision in the double-scaling limit recently discussed by Bourget et al. in [2]. We show the exponentially small correction is consistent with the interpretation of the eft breaking down due to the propagation of massive bps particles over distances of order of the infrared scale |x − y|. [ABSTRACT FROM AUTHOR]

Abstract We study some (conformal) field theories with global symmetries in the sector where the value of the global charge Q is large. We find (as expected) that the low energy excitations of this sector are described by the general form of Goldstone’s theorem in the non-relativistic regime. We also derive the unexpected result, first presented in [1], that the effective field theory describing such sector of fixed Q contains effective couplings λ eff ∼ λ b /Q a , where λ is the original coupling. Hence, large charge leads to weak coupling. In the last section of the paper we present an outline of how to compute anomalous dimensions of the O(n) model in this limit.