The Chiral Algebra of Genus Two Class $\mathcal{S}$ Theory

Abstract

We construct the chiral algebra associated with the $A_1$-type class $\mathcal{S}$ theory for 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.

arXiv comment41 pages, 1 figure; minor typos corrected, results unchanged

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Cited by in corpus (5)

• The exact Schur index in closed form
• Schur Indices of Class $\mathcal{S}$ and Quasimodular Forms
• Surface defects, flavored modular differential equations and modularity
• A geometric free field realisation for the genus-two class $\mathcal{S}$ theory of type ${\mathfrak{a}}_1$
• Defects, modular differential equations, and free field realization of N = 4 VOAs