High-temperature expansion of the Schur index and modularity
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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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 |