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Vanishing OPE Coefficients in 4d N=2 SCFTs

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arxiv 1812.04743 v2 pith:PG642ZDZ submitted 2018-12-11 hep-th

classification hep-th
keywords multipletsuperconformalcoefficientsshorttheorycomputemultipletsvanish
verification ladder T0 review T1 audit T2 compute T3 formal
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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 $(A_1, A_{2n})$ Argyres-Douglas (AD) theory. This implies that the operator product expansion (OPE) coefficients involving this multiplet vanish whenever the central charge $c$ 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 4d N=2 superconformal multiplets as well as their superconformal character.

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  1. A landscape of 4d N=1 SCFTs with a=c

    hep-th 2024-12 conditional novelty 6.0 of 10

    Starting from an SU(3) gauging of three D2(SU(3)) Argyres-Douglas theories with an adjoint chiral multiplet, the authors map the tree of relevant deformations that preserve a=c and find 21 fixed points, including flow...

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