Character Identities Between Affine and Virasoro Vertex Operator Algebra Modules

[2511.20121] Character Identities Between Affine and Virasoro Vertex Operator Algebra Modules Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Quantum Algebra arXiv:2511.20121 (math) [Submitted on 25 Nov 2025 ( v1 ), last revised 24 Jun 2026 (this version, v2)] Title: Character Identities Between Affine and Virasoro Vertex Operator Algebra Modules Authors: Dražen Adamović , Sven Möller View a PDF of the paper titled Character Identities Between Affine and Virasoro Vertex Operator Algebra Modules, by Dra\v{z}en Adamovi\'c and 1 other authors View PDF HTML (experimental) Abstract: The affine vertex operator algebras for $\mathfrak{sl}_2$ and the Virasoro minimal models are related by Drinfeld-Sokolov reduction and by the Goddard-Kent-Olive coset construction. In this work, we propose another connection based on certain character identities between these vertex operator algebras and their modules. This relates the simple affine vertex operator algebras $L_k(\mathfrak{sl}_2)$ at admissible levels $k=-2+q/p$ to the rational $(q,3p)$-minimal models $L_\mathrm{Vir}(c_{q,3p},0)$, and also extends to the nonadmissible levels with $q=1$. Several special cases are particularly interesting. In the nonadmissible case $q=1$, the character identities extend to certain abelian intertwining algebras, specifically $\mathcal{V}^{(p)}$ and the doublet $\mathcal{A}^{(3p)}$. Specialising further to $p=2$, where $\mathcal{V}^{(2)}$ is the simple small $\mathcal{N}=4$ superconformal algebra of central charge $c=-9$, this recovers, via the 4d/2d-correspondence, a known identity between the Schur indices of the 4d $\mathcal{N}=4$ supersymmetric Yang-Mills theory for $\mathrm{SU}(2)$ and the 4d $\mathcal{N}=2$ $(3,2)$ Argyres-Douglas theory. In the boundary admissible case $q=2$, in a similar vein, we obtain an identity between the Schur indices of 4d $\mathcal{N}=2$ Argyres-Douglas theories of types $(A_1,D_{2n+1})$ and $(A_1,A_{6n})$. On the other hand, for integral levels, $p=1$, where both involved vertex operator algebras are strongly rational, our character identity induces a Galois conjugation between the representation categories $\mathrm{Rep}(L_{-2+q}(\mathfrak{sl}_2))$ and $\mathrm{Rep}(L_\mathrm{Vir}(c_{q,3},0))$; and for small values of $q$, the characters are related by the action of certain Hecke operators. Finally, we also sketch how to extend the results of this paper to relaxed highest-weight and Whittaker modules. Comments: 45 pages, LaTeX; minor changes; to appear in Math. Z Subjects: Quantum Algebra (math.QA) ; High Energy Physics - Theory (hep-th); Representation Theory (math.RT) MSC classes: 17B69, 17B65, 17B67, 18M15, 18M20, 11F27 Cite as: arXiv:2511.20121 [math.QA] (or arXiv:2511.20121v2 [math.QA] for this version) https://doi.org/10.48550/arXiv.2511.20121 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Math. Z., 313:87, 2026 Related DOI : https://doi.org/10.1007/s00209-026-04078-5 Focus to learn more DOI(s) linking to related resources Submission history From: Sven Möller [ view email ] [v1] Tue, 25 Nov 2025 09:42:27 UTC (42 KB) [v2] Wed, 24 Jun 2026 16:26:23 UTC (45 KB) Full-text links: Access Paper: View a PDF of the paper titled Character Identities Between Affine and Virasoro Vertex Operator Algebra Modules, by Dra\v{z}en Adamovi\'c and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.QA < prev | next > new | recent | 2025-11 Change to browse by: hep-th math math.RT References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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