Spectral flow and application to unitarity of representations of minimal $W$-algebras

Fuente: arXiv
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Autori principali: Kac, Victor G., Frajria, Pierluigi Möseneder, Papi, Paolo
Natura: Preprint
Pubblicazione: 2025
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author Kac, Victor G.
Frajria, Pierluigi Möseneder
Papi, Paolo
author_facet Kac, Victor G.
Frajria, Pierluigi Möseneder
Papi, Paolo
contents Using spectral flow, we provide a proof of [11, Theorem 9.17] on unitarity of Ramond twisted non-extremal representations of unitary minimal $W$-algebras that does not rely on the still conjectural exactness of the twisted quantum reduction functor (see Conjecture 9.11 of [11]). When $\mathfrak g = spo(2|2n)$, $F (4$), $D(2, 1; \frac{m}{n})$, it is also proven that the unitarity of extremal (=massless) representations of the unitary minimal $W$-algebra $W^k_{\min}(\mathfrak g)$ in the Ramond sector is equivalent to the unitarity of extremal representations in the Neveu-Schwarz sector.
format Preprint
id arxiv_https___arxiv_org_abs_2508_06873
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Spectral flow and application to unitarity of representations of minimal $W$-algebras
Kac, Victor G.
Frajria, Pierluigi Möseneder
Papi, Paolo
Representation Theory
Mathematical Physics
Using spectral flow, we provide a proof of [11, Theorem 9.17] on unitarity of Ramond twisted non-extremal representations of unitary minimal $W$-algebras that does not rely on the still conjectural exactness of the twisted quantum reduction functor (see Conjecture 9.11 of [11]). When $\mathfrak g = spo(2|2n)$, $F (4$), $D(2, 1; \frac{m}{n})$, it is also proven that the unitarity of extremal (=massless) representations of the unitary minimal $W$-algebra $W^k_{\min}(\mathfrak g)$ in the Ramond sector is equivalent to the unitarity of extremal representations in the Neveu-Schwarz sector.
title Spectral flow and application to unitarity of representations of minimal $W$-algebras
topic Representation Theory
Mathematical Physics
url https://arxiv.org/abs/2508.06873