Operator dimensions from moduli

Self Cite

154

In this note we study two point functions of Coulomb branch chiral ring elements with large R-charge, in quantum field theories with N = 2 superconformal symmetry in four spacetime dimensions. Focusing on the case of one-dimensional Coulomb branch, we use the effective-field-theoretic methods of [1], to estimate the two-point correlation function Y n ≡ |x − y| 2n∆ O (O(x)) n (Ō(y)) n in the limit where the operator insertion O n has large total R-charge J = n∆ O . We show that Y n has a nontrivial but universal asymptotic expansion at large J , of the formwhereỸ n approaches a constant as n → ∞, and N O is an n-independent constant describing on the normalization of the operator relative to the effective Abelian gauge coupling. The exponent α is a positive number proportional to the difference between the a-anomaly coefficient of the underlying CFT and that of the effective theory of the Coulomb branch. For Lagrangian SCFT, we check our predictions for the logarithm B n = log(Y n ), up to and including order log(J ) against exact results from supersymmetric localization [2][3][4][5]. In the case of N = 4 we find precise agreement and in the case N = 2 we find reasonably good numerical agreement at J 60 using the no-instanton approximation to the S 4 partition function. We also give predictions for the growth of two-point functions in all rank-one SCFT in the classification of [6][7][8][9]. In this way, we show the large-R-charge expansion serves as a bridge from the world of unbroken superconformal symmetry, OPE data, and bootstraps, to the world of the low-energy dynamics of the moduli space of vacua.

Section: Introductionmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

On the Large R-charge Expansion in N = 2 $$ \mathcal{N}=2 $$ Superconformal Field Theories

Hellerman

Maeda

2017

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154

“…This appears to be related to the existence of a nontrivial moduli space of vacua, as we briefly explained using the example of a free complex scalar. It would be extremely interesting to generalize the analysis of the present case to the more nontrivial scenarios of [30], [31]. Another direction would be to consider generic heavy states, as in [13], and try to understand how universal hydrodynamic properties emerge, see, e.g., [32].…”

Section: Discussionmentioning

confidence: 99%

Conformal bootstrap at large charge

Jafferis

Mukhametzhanov

Zhiboedov

2018

We consider unitary CFTs with continuous global symmetries in d > 2. We consider a state created by the lightest operator of large charge Q ≫ 1 and analyze the correlator of two light charged operators in this state. We assume that the correlator admits a welldefined large Q expansion and, relatedly, that the macroscopic (thermodynamic) limit of the correlator exists. We find that the crossing equations admit a consistent truncation, where only a finite number N of Regge trajectories contribute to the correlator at leading nontrivial order. We classify all such truncated solutions to the crossing. For one Regge trajectory N = 1, the solution is unique and given by the effective field theory of a Goldstone mode. For two or more Regge trajectories N ≥ 2, the solutions are encoded in roots of a certain degree N polynomial. Some of the solutions admit a simple weakly coupled EFT description, whereas others do not. In the weakly coupled case, each Regge trajectory corresponds to a field in the effective Lagrangian.

“…Examples include superconformal theories with vacuum manifolds, such as the 1 See also more recent work [5,6]. 3D N = 2 superconformal XYZ model at large R-charge and [17], 4D N = 2 rank 1 SCFTs at large R-charge [18,19].…”

Section: Introductionmentioning

confidence: 99%

A note on inhomogeneous ground states at large global charge

Hellerman

Kobayashi

Maeda

et al. 2019

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As a sequel to previous work, we extend the study of the ground state configuration of the D = 3, Wilson-Fisher conformal O(4) model. In this work, we prove that for generic ratios of two charge densities, ρ 1 /ρ 2 , the ground-state configuration is inhomogeneous and that the inhomogeneity expresses itself towards longer spatial periods. This is the direct extension of the similar statements we previously made for ρ 1 /ρ 2 1. We also compute, at fixed set of charges, ρ 1 , ρ 2 , the ground state energy and the two-point function(s) associated with this inhomogeneous configuration on the torus. The ground state energy was found to scale (ρ 1 + ρ 2 ) 3/2 , as dictated by dimensional analysis and similarly to the case of the O(2) model. Unlike the case of the O(2) model, the ground also strongly violates cluster decomposition in the large-volume, fixed-density limit, with a two-point function that is negative definite at antipodal points of the torus at leading order at large charge.