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Generalized Schur partition functions and RG flows

Anirudh Deb

Shlomo S. Razamat

C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, New York 11794-3840, USA

Department of Physics, Technion, Haifa 32000, Israel

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Phys. Rev. D 113, 045011 – Published 11 February, 2026

DOI: https://doi.org/10.1103/ldxd-2jm5

Abstract

We revisit a double-scaled limit of the superconformal index of $N = 2$ superconformal field theories (SCFTs) which generalizes the Schur index. The resulting partition function, $\hat{Z} (q, α)$ , has a standard $q$ -expansion with coefficients depending on a continuous parameter $α$ . The Schur index is a special case with $α = 1$ . Through explicit computations we argue that this partition function is an invariant of certain mass deformations and vacuum expectation value (vev) deformations of the SCFT. In particular, two SCFTs residing in different corners of the same Coulomb branch, satisfying certain restrictive conditions, have the same partition function with a nontrivial map of the parameters, ${\hat{Z}}_{1} (q, α_{1}) = {\hat{Z}}_{2} (q, α_{2} (α_{1}))$ . For example, we show that the Schur index of all the SCFTs in the Deligne-Cvitanović series is given by special values of $α$ of the partition function of the $SU (2) N_{f} = 4$ $N = 2$ SQCD.

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Phys. Rev. D 113, 045011– Published 11 February, 2026

Vol. 113, Iss. 4 — 15 February 2026

Received 14 August 2025
Accepted 5 January 2026

DOI: https://doi.org/10.1103/ldxd-2jm5

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Generalized Schur partition functions and RG flows

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