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Main Authors: Ardehali, Arash Arabi, Martone, Mario, Rosselló, Martí
Format: Preprint
Published: 2023
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Online Access:https://arxiv.org/abs/2308.09738
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author Ardehali, Arash Arabi
Martone, Mario
Rosselló, Martí
author_facet Ardehali, Arash Arabi
Martone, Mario
Rosselló, Martí
contents High-temperature ($q\to1$) asymptotics of 4d superconformal indices of Lagrangian theories have been recently analyzed up to exponentially suppressed corrections. Here we use RG-inspired tools to extend the analysis to the exponentially suppressed terms in the context of Schur indices of $N=2$ SCFTs. In particular, our approach explains the curious patterns of logarithms (polynomials in $1/\log q$) found by Dedushenko and Fluder in their numerical study of the high-temperature expansion of rank-$1$ theories. We also demonstrate compatibility of our results with the conjecture of Beem and Rastelli that Schur indices satisfy finite-order, possibly twisted, modular linear differential equations (MLDEs), and discuss the interplay between our approach and the MLDE approach to the high-temperature expansion. The expansions for $q$ near roots of unity are also treated. A byproduct of our analysis is a proof (for Lagrangian theories) of rationality of the conformal dimensions of all characters of the associated VOA, that mix with the Schur index under modular transformations.
format Preprint
id arxiv_https___arxiv_org_abs_2308_09738
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle High-temperature expansion of the Schur index and modularity
Ardehali, Arash Arabi
Martone, Mario
Rosselló, Martí
High Energy Physics - Theory
High-temperature ($q\to1$) asymptotics of 4d superconformal indices of Lagrangian theories have been recently analyzed up to exponentially suppressed corrections. Here we use RG-inspired tools to extend the analysis to the exponentially suppressed terms in the context of Schur indices of $N=2$ SCFTs. In particular, our approach explains the curious patterns of logarithms (polynomials in $1/\log q$) found by Dedushenko and Fluder in their numerical study of the high-temperature expansion of rank-$1$ theories. We also demonstrate compatibility of our results with the conjecture of Beem and Rastelli that Schur indices satisfy finite-order, possibly twisted, modular linear differential equations (MLDEs), and discuss the interplay between our approach and the MLDE approach to the high-temperature expansion. The expansions for $q$ near roots of unity are also treated. A byproduct of our analysis is a proof (for Lagrangian theories) of rationality of the conformal dimensions of all characters of the associated VOA, that mix with the Schur index under modular transformations.
title High-temperature expansion of the Schur index and modularity
topic High Energy Physics - Theory
url https://arxiv.org/abs/2308.09738