Generalized Schur partition functions and RG flows

2025/06/16 by Anirudh Deb, Deb, Anirudh, Shlomo S. Razamat +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2506.13764

openalex publication_date 2025/06/16 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

We revisit a double-scaled limit of the superconformal index of \cal N=2 superconformal field theories (SCFTs) which generalizes the Schur index. The resulting partition function, \cal 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 non-trivial map of the parameters, \cal Z₁(q,α₁)= \cal Z₂(q,α₂(α₁)). 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 \cal N=2 SQCD.

Citations

• Renormalization Group flow in Schur quantization
• A Family of Vertex Algebras from Argyres-Douglas Theory
• Mirror symmetry for circle compactified 4d A₁ class-S theories
• Large Landscape of 4d Superconformal Field Theories from Small Gauge Theories
• Schur Quantization and Complex Chern-Simons theory
• Looking for the G₂ Higgs Branch of 4D Rank 1 SCFTs
• High-temperature expansion of the Schur index and modularity
• On intermediate Lie algebra E_7+1/2
• Construction and classification of Coulomb branch geometries
• Quasi-lisse vertex algebras and modular linear differential equations
• Geometric constraints on the space of N=2 SCFTs III: enhanced Coulomb branches and central charges
• Geometric constraints on the space of N=2 SCFTs II: Construction of special Kähler geometries and RG flows
• Geometric constraints on the space of N=2 SCFTs I: physical constraints\n on relevant deformations
• R-Twisting and 4d/2d Correspondences

Cited by

• Generalized Schur limit, modular differential equations and quantum monodromy traces
• Comments on Class S(YK)

Related

• The exact Schur index in closed form
• High-temperature expansion of the Schur index and modularity
• Index from a point
• Calculating the Superconformal Index and Seiberg Duality
• Modularity in Argyres-Douglas Theories with a=c