$\mathcal{N}=2^{\ast }$ Schur indices

Abstract

We find closed-form expressions for the Schur indices of 4d $\mathcal{N}=2^{\ast }$ super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas formulation. They can be written as a sum over the Young diagrams associated with spectral zeta functions of an ideal Fermi-gas system. These functions are expressed in terms of the twisted Weierstrass functions, generating functions for quasi-Jacobi forms. The indices lie in the polynomial ring generated by the Kronecker theta function and the Weierstrass functions which contains the polynomial ring of the quasi-Jacobi forms. The grand canonical ensemble allows for another simple exact form of the indices as infinite series. In addition, we find that the unflavored Schur indices and their limits can be expressed in terms of several generating functions for combinatorial objects, including sum of triangular numbers, generalized sums of divisors and overpartitions.

61 pages

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Cited by in corpus (10)

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• On Classification of Fermionic Rational Conformal Field Theories
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• Giant graviton expansions and ETW brane
• ADHM Wilson line defect indices
• Asymptotic degeneracies of M2-brane SCFTs
• $\mathcal{N}=4$ line defect correlators of type BCD
• A landscape of 4d N=1 SCFTs with a=c
• $SL(2,\mathbb{Z})$ dualities of boundary conditions in Abelian M2-brane SCFTs