Vanishing OPE coefficients in 4d $$ \mathcal{N}=2 $$ SCFTs

• Published in: The journal of high energy physics 2019-06, Vol.2019 (6), Article 102
• Main Authors: Agarwal, Prarit, Lee, Sungjay, Song, Jaewon
• Format: Article
• Language: English
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP06(2019)102

We compute the superconformal characters of various short multiplets in 4d $$ \mathcal{N}=2 $$ 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 ( A 1 , A 2 n ) Argyres-Douglas (AD) theory. This implies that certain operator product expansion (OPE) coefficients involving this multiplet vanish whenever the central charge c 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 ( 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 4 d $$ \mathcal{N}=2 $$ N = 2 superconformal multiplets as well as their superconformal character.