Unitarizable highest weight modules over the twisted sector of the \(N=2\) super Virasoro algebra
type: Item
instance of: scholarly article
title: Unitarizable highest weight modules over the twisted sector of the \(N=2\) super Virasoro algebra
zbMATH Open document ID: 1174.17021
author: Kenji Iohara
publication date: 2008-07-04T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/10332
review text: In this paper, the author classifies unitarizable highest weight modules over the twisted sector of the \(N=2\) Virasoro super-algebra \(\mathfrak{g}\). The problem has been considered before by \textit{W. Boucher}, \textit{D. Friedan} and \textit{A. Kent} in [Phys. Lett. B 172, 316--322 (1986; Zbl 1174.81319)], where the authors gave without proof a necessary condition for unitarizability of a Verma module over \(\mathfrak{g}\). Here the author gives a proof of this result, and shows by explicit construction that the condition is also sufficient. More precisely, there are two families of unitarizable Verma modules over \(\mathfrak{g}\). The \textit{minimal unitary series} is realised via an action of \(\mathfrak{g}\) on simple integrable highest weight modules over the affine Lie algebra \(\widehat{\mathfrak{sl}_2}\). For the other family a direct proof of unitarizability is given using the determinant formula from [\textit{K. Iohara} and \textit{Y. Koga}, J. Funct. Anal. 214, No. 2, 450--518 (2004; Zbl 1155.17309)].
reviewed by: Jean-Marie Bois
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 5298319
zbMATH Keywords: twisted sector of the \(N=2\) Virasoro super-algebra
zbMATH Keywords: unitarizable module
zbMATH Keywords: parafermion
MaRDI profile type: Publication
OpenAlex ID: W1535586588
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DOI: 10.5802/AIF.2367
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 5298319