Unitarizable Highest Weight Modules of the N = 2 Super Virasoro Algebras: Untwisted Sectors

Iohara, Kenji

doi:10.1007/s11005-010-0375-7

Cited by 9 publications

(7 citation statements)

References 12 publications

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“…As in the cases N = 0, 1, unitarity gives restrictions on the possible values of c, h, q. The situation is described in Theorem 3.2 ([5], [18], [40]). For any irreducible unitary representation of the Neveu-Schwarz N = 2 super-Virasoro algebra SVir N =2,0 the corresponding values of c, h, q satisfy one of the following conditions:…”

Section: Moreover the Unitary Representationmentioning

confidence: 99%

N =2 Superconformal Nets

Carpi

Hillier

Kawahigashi

et al. 2014

Commun. Math. Phys.

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We provide an Operator Algebraic approach to N = 2 chiral Conformal Field Theory and set up the Noncommutative Geometric framework. Compared to the N = 1 case, the structure here is much richer. There are naturally associated nets of spectral triples and the JLO cocycles separate the Ramond sectors. We construct the N = 2 superconformal nets of von Neumann algebras in general, classify them in the discrete series c < 3, and we define and study an operator algebraic version of the N = 2 spectral flow. We prove the coset identification for the N = 2 superVirasoro nets with c < 3, a key result whose equivalent in the vertex algebra context has seemingly not been completely proved so far. Finally, the chiral ring is discussed in terms of net representations.

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Section: Moreover the Unitary Representationmentioning

confidence: 99%

N =2 Superconformal Nets

Carpi

Hillier

Kawahigashi

et al. 2014

Commun. Math. Phys.

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“…In this paper we only deal with the untwisted sector. See [Ioh10] and references therein for the details.…”

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confidence: 99%

“…In 1980s many physicists extensively studied unitarizable highest weight modules over the N = 2 SCA in order to construct models of rational supersymmetric conformal field theories. Among those modules, the classification of irreducible ones is conjectured by [BFK86], and its mathematically rigorous proof is given by [Ioh10] for the untwisted sector. In its proof the N = 2 supersymmetric coset construction [DVPYZ86] (and [KS89] for general affine Lie algebras) plays an important role to construct some specific unitarizable modules, the so-called minimal unitary series of the N = 2 SCA.…”

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confidence: 99%

Equivalences between weight modules via $\mathcal{N}=2$ coset constructions

Sato¹

2016

Preprint

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In this paper we introduce a variant of weight modules for certain conformal vertex superalgebras as an appropriate framework of the N = 2 supersymmetric coset construction. We call them weight-wise admissible modules. Motivated by the work of Feigin-Semikhatov-Tipunin, we give (blockwise) categorical equivalences between the categories of weight-wise admissible modules over sl 2 and the N = 2 superconformal algebra, induced by the coset construction.As an application, we obtain some character formulas of modules over the N = 2 superconformal algebra.

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“…We begin by noting that throughout this paper linear spaces V and W are considered of arbitrary dimensions and over an arbitrary base field F, and also the increasing interest in the study of modules over different classes of algebras, and so over linear spaces, specially motivated by their relation with mathematical physics (see [6], [7], [8], [9], [11], [12], [13]). Definition 1.…”

Section: Introduction and Previous Definitionsmentioning

confidence: 99%

Modules over linear spaces admitting a multiplicative basis

Martín

Izquierdo

Sánchez

2016

Linear and Multilinear Algebra

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We study the structure of certain modules V over linear spaces W with restrictions neither on the dimensions nor on the base field F. A basis B = {vi}i∈I of V is called multiplicative respect to the basis B = {wj}j∈J of W if for any i ∈ I, j ∈ J we have either viwj = 0 or 0 = viwj ∈ Fv k for some k ∈ I. We show that if V admits a multiplicative basis then it decomposes as the direct sum V = k V k of well-described submodules admitting each one a multiplicative basis. Also the minimality of V is characterized in terms of the multiplicative basis and it is shown that the above direct sum is by means of the family of its minimal submodules, admitting each one a multiplicative basis.

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Unitarizable Highest Weight Modules of the N = 2 Super Virasoro Algebras: Untwisted Sectors

Cited by 9 publications

References 12 publications

N =2 Superconformal Nets

N =2 Superconformal Nets

Equivalences between weight modules via $\mathcal{N}=2$ coset constructions

Modules over linear spaces admitting a multiplicative basis

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