English

Vanishing OPE Coefficients in 4d N=2 SCFTs

High Energy Physics - Theory 2019-09-02 v2

Abstract

We compute the superconformal characters of various short multiplets in 4d N=2 superconformal algebra, from which selection rules for operator products are obtained. Combining with the superconformal index, we show that a particular short multiplet appearing in the n-fold product of stress-tensor multiplet is absent in the (A1,A2n)(A_1, A_{2n}) Argyres-Douglas (AD) theory. This implies that the operator product expansion (OPE) coefficients involving this multiplet vanish whenever the central charge cc is identical to that of the AD theory. Similarly, by considering the n-th power of the current multiplet, we show that a particular short multiplet and OPE coefficients vanish for a class of AD theories with ADE flavor symmetry. We also consider the generalized AD theory of type (Ak1,An1)(A_{k-1}, A_{n-1}) for coprime k, n and compute its Macdonald index using the associated W-algebra under a mild assumption. This allows us to show that a number of short multiplets and OPE coefficients vanish in this theory. We also provide a Mathematica file along with this paper, where we implement the algorithm by Cordova-Dumitrescu-Intriligator to compute the spectrum of 4d N=2 superconformal multiplets as well as their superconformal character.

Keywords

Cite

@article{arxiv.1812.04743,
  title  = {Vanishing OPE Coefficients in 4d N=2 SCFTs},
  author = {Prarit Agarwal and Sungjay Lee and Jaewon Song},
  journal= {arXiv preprint arXiv:1812.04743},
  year   = {2019}
}

Comments

25 pages, 1 Mathematica notebook, v2: references added, minor clarification. published version

R2 v1 2026-06-23T06:39:41.724Z