Modular invariant representations of infinite-dimensional Lie algebras and superalgebras

Kač, Victor G.; Wakimoto, Minoru

doi:10.1073/pnas.85.14.4956

Cited by 279 publications

(462 citation statements)

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“…However, the two models are different, and the appearance of continuous representations in [9] is not replicated here. Finally, we show that the modular invariant partition function written in [17] is compatible with the infinite operator content that we encounter, provided the characters are properly interpreted.…”

Section: Introductionmentioning

confidence: 96%

“…An option for bypassing this obstruction for non-integer level is to consider a non-unitary model as being defined purely algebraically, in terms of an affine Lie algebra at fractional level and its representation theory. 1 The cornerstone of this idea is an observation by Kac and Wakimoto [17] on su(2) k for fractional level k = t/u with t ∈ Z and u ∈ N co-prime, and t + 2u − 2 ≥ 0. They found that there is a finite number of primary fields associated to highest-weight representations that transform linearly among themselves under the modular group.…”

Section: Introductionmentioning

confidence: 99%

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The WZW model and the βγ system

et al. 2002

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The bosonic βγ ghost system has long been used in formal constructions of conformal field theory. It has become important in its own right in the last few years, as a building block of field theory approaches to disordered systems, and as a simple representative -due in part to its underlying su(2) −1/2 structure -of non-unitary conformal field theories. We provide in this paper the first complete, physical, analysis of this βγ system, and uncover a number of striking features. We show in particular that the spectrum involves an infinite number of fields with arbitrarily large negative dimensions. These fields have their origin in a twisted sector of the theory, and have a direct relationship with spectrally flowed representations in the underlying su(2) −1/2 theory. We discuss the spectral flow in the context of the operator algebra and fusion rules, and provide a re-interpretation of the modular invariant consistent with the spectrum.

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Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

The WZW model and the βγ system

et al. 2002

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“…We first note that the branching functions and partition functions can be computed in the same manner as for the N = 2 supersymmetric models [14]. The diagonal modular invariant partition function for the G k,1 model is given by a very similar formula to (2.22):…”

Section: )mentioning

confidence: 99%

“…One can also obtain them from a direct computation of the branching functions [14]. Since the SLOHSS models do not have any fixed points under the field identifications generated by spectral flow, the branching functions can be identified with the characters of the model [ …”

Section: )mentioning

confidence: 99%

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Lattice analogues of N = 2 superconformal models via quantum-group truncation

Maassarani¹,

Nemeschansky²,

Warner³

1993

Nuclear Physics B

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We obtain lattice models whose continuum limits correspond to N = 2 superconformal coset models. This is done by taking the well known vertex model whose continuum limit is the G × G/G conformal field theory, and twisting the transfer matrix and modifying the quantum group truncation. We find that the natural order parameters of the new models are precisely the chiral primary fields. The integrable perturbations of the conformal field theory limit also have natural counterparts in the lattice formulation, and these can be incorporated into an affine quantum group structure. The topological, twisted N = 2 superconformal models also have lattice analogues, and these emerge as an intermediate part of our analysis.

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