Abstract
We construct the chiral algebra associated with the A1-type class \( \mathcal{S} \) theory for the genus two Riemann surface without punctures. By solving the BRST cohomology problem corresponding to a marginal gauging in four dimensions, we find a set of chiral algebra generators that form closed OPEs. Given the fact that they reproduce the spectrum of chiral algebra operators up to large dimensions, we conjecture that they are the complete set of generators. Remarkably, their OPEs are invariant under an action of SU(2) which is not associated with any conserved one-form current in four dimensions. We find that this novel SU(2) strongly constrains the OPEs of non-scalar Schur operators. For completeness, we also check the equivalence of Schur indices computed in two S-dual descriptions with a non-vanishing flavor fugacity turned on.
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Kiyoshige, K., Nishinaka, T. The chiral algebra of genus two class \( \mathcal{S} \) theory. J. High Energ. Phys. 2021, 199 (2021). https://doi.org/10.1007/JHEP02(2021)199
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DOI: https://doi.org/10.1007/JHEP02(2021)199