Abstract
We study 4d \( \mathcal{N} \) = 1 supersymmetric theories of class \( {\mathcal{S}}_k \), obtained from flux compactifications on a Riemann surface of 6d (1, 0) conformal theories describing the low energy physics on a stack of M5 branes probing a \( \frac{@}{@}{\mathrm{\mathbb{Z}}}_k \) singularity. We conjecture that the protected spectrum of class \( {\mathcal{S}}_k \) theories contains a freely generated ring, generalizing the Coulomb branch of the \( \mathcal{N} \) = 2 theories. We derive this by examining a limit of the supersymmetric index of 4d \( \mathcal{N} \) = 1 class \( {\mathcal{S}}_k \) theories. The limit generalizes the Coulomb limit of \( \mathcal{N} \) = 2 theories, which coincides with the case of k = 1 for a particular choice of flux. We conjecture a general simple formula for the index in the aforementioned limit.
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Razamat, S.S., Sabag, E. A freely generated ring for \( \mathcal{N} \) = 1 models in class \( {\mathcal{S}}_k \). J. High Energ. Phys. 2018, 150 (2018). https://doi.org/10.1007/JHEP07(2018)150
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DOI: https://doi.org/10.1007/JHEP07(2018)150