Unitarity of rationalN = 2 superconformal theories

Eholzer, Wolfgang; Gaberdiel, Matthias R.

doi:10.1007/bf02885672

Cited by 36 publications

(56 citation statements)

References 32 publications

(74 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This formalism, has the advantage that the Virasoro modes are still represented as linear differential operators, and that it is compact and elegant allowing for arbitrary rank Jordan cell structures. Moreover, the connection between LCFTs and supersymmetric CFTs, which one could glimpse here and there [16,33,105,106] (see also [22]), seems to be a quite fundamental one.…”

Section: Logarithmic Null Vectorsmentioning

confidence: 96%

Bits and Pieces in Logarithmic Conformal Field Theory

Flohr

2003

Int. J. Mod. Phys. A

227

341

View full text Add to dashboard Cite

These notes cover only selected parts of the by now quite extensive knowledge on logarithmic conformal field theories. In particular, I discuss the proper generalization of null vectors towards the logarithmic case, and how these can be used to compute correlation functions. My other main topic is modular invariance, where I discuss the problem of the generalization of characters in the case of indecomposable representations, a proposal for a Verlinde formula for fusion rules and identities relating the partition functions of logarithmic conformal field theories to such of well known ordinary conformal field theories. These two main topics are complemented by some remarks on ghost systems, the Haldane-Rezayi fractional quantum Hall state, and the relation of these two to the logarithmic c = −2 theory.

show abstract

Section: Logarithmic Null Vectorsmentioning

confidence: 96%

Bits and Pieces in Logarithmic Conformal Field Theory

Flohr

2003

Int. J. Mod. Phys. A

227

341

View full text Add to dashboard Cite

show abstract

“…This formalism, which we introduce in section two, has the advantage that the Virasoro modes are still represented as linear differential operators, and that it is compact and elegant allowing for arbitrary rank Jordan cell structures. Moreover, the connection between LCFTs and supersymmetric CFTs, which one could glimpse here and there [15,6,36,37] (see also [9]), seems to be a quite fundamental one. The second half of section two is then devoted to apply our formalism to the definition of logarithmic null vectors.…”

Section: Introductionmentioning

confidence: 94%

Singular vectors in logarithmic conformal field theories

Flohr

1998

Nuclear Physics B

View full text Add to dashboard Cite

Null vectors are generalized to the case of indecomposable representations which are one of the main features of logarithmic conformal field theories. This is done by developing a compact formalism with the particular advantage that the stress energy tensor acting on Jordan cells of primary fields and their logarithmic partners can still be represented in form of linear differential operators. Since the existence of singular vectors is subject to much stronger constraints than in regular conformal field theory, they also provide a powerful tool for the classification of logarithmic conformal field theories. *

show abstract

“…By modular data we mean here unitary matrices S, T such that T is diagonal and of finite order, S is symmetric, (ST ) 3 = S 2 =: C is an order-2 (or order-1) permutation matrix, C0 = 0, and the fusion coefficients N c ab given by (2) are all nonnegative integers…”

Section: Definitionmentioning

confidence: 99%

“…Indeed, some of the better known RCFTs are nonunitary, such as the Yang-Lee model (c = −22 /5). Presumably (but see [2]! ), most RCFTs will be nonunitary -for example the Virasoro minimal model (p, p ), with central charge c = 1 − 6 (p − p ) 2 /pp , is unitary iff |p − p | = 1.…”

Section: Introductionmentioning

confidence: 99%

Comments on nonunitary conformal field theories

Gannon¹

2003

Nuclear Physics B

View full text Add to dashboard Cite

As is well-known, nonunitary RCFTs are distinguished from unitary ones in a number of ways, two of which are that the vacuum 0 doesn't have minimal conformal weight, and that the vacuum column of the modular S matrix isn't positive. However there is another primary field, call it o, which has minimal weight and has positive S column. We find that often there is a precise and useful relationship, which we call the Galois shuffle, between primary o and the vacuum; among other things this can explain why (like the vacuum) its multiplicity in the full RCFT should be 1. As examples we consider the minimal WSU(N) models. We conclude with some comments on fractional level admissible representations of affine algebras. As an immediate consequence of our analysis, we get the classification of an infinite family of nonunitary W 3 minimal models in the bulk.

show abstract

Unitarity of rationalN = 2 superconformal theories

Cited by 36 publications

References 32 publications

Bits and Pieces in Logarithmic Conformal Field Theory

Bits and Pieces in Logarithmic Conformal Field Theory

Singular vectors in logarithmic conformal field theories

Comments on nonunitary conformal field theories

Contact Info

Product

Resources

About