Vanishing OPE coefficients in 4d N=2 SCFTs

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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 (A(1), A(2n)) 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 4dN=2 superconformal multiplets as well as their superconformal character.
Publisher
SPRINGER
Issue Date
2019-06
Language
English
Article Type
Article
Citation

JOURNAL OF HIGH ENERGY PHYSICS, no.06

ISSN
1029-8479
DOI
10.1007/JHEP06(2019)102
URI
http://hdl.handle.net/10203/273992
Appears in Collection
PH-Journal Papers(저널논문)
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