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 Yₙ≡ |x-y|^2nΔO (O(x))ⁿ(Ō(y))ⁿ in the limit where the operator insertion Oⁿ has large total R-charge J=nΔO . We show that Yₙ has a nontrivial but universal asymptotic expansion at large J , of the form Yₙ=J!(|NO|2)2JJαỸₙ, where Ỹₙ approaches a consstant as n → ∞, and NO 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 Bₙ= log (Yₙ) , up to and including order log J against exact results from supersymmetric localization [2-5]. 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 S4 partition function. We also give predictions for the growth of two-point functions in all rank-one SCFT in the classification of [6-9]. 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 ssof the moduli space of vacua.
No takes yet. Share an insight, caveat, or question.
A 2017 study studied this question.