Characters of graded parafermion conformal field theory

In this paper we apply the previously derived formalism of permutation orbifold conformal field theories to N = 2 supersymmetric minimal models. By interchanging extensions and permutations of the factors we find a very interesting structure relating various conformal field theories that seems not to be known in literature. Moreover, unexpected exceptional simple currents arise in the extended permuted models, coming from off-diagonal fields. In a few situations they admit fixed points that must be resolved. We determine the complete CFT data with all fixed point resolution matrices for all simple currents of all Z 2 -permutations orbifolds of all minimal N = 2 models with k = 2 mod 4. is the following. Start with a field f which has l-label equal to k 2 and apply J ± on f , recalling that J 4 ± = 1 and J 2 ± = T F for NS-type currents, f

show abstract

“…Our formula is the standard one, given in[37]. It also agrees with[40,41] For equivalent, but different-looking, expressions, see[42,43].…”

supporting

confidence: 81%

Permutation orbifolds of supersymmetric minimal models

Maio

Schellekens

2011

Nuclear Physics B

View full text Add to dashboard Cite

show abstract

“…As before, the chiral algebra A 1 for the (A 1 , A 2n+1 ) model is generated by the upper triangular SU(2n + 1) currents at level 1. Moreover, according to Fortin et al [60] this is given by the character of Sp(2n) at level 1.…”

Section: Jhep11(2017)013mentioning

confidence: 99%

Superconformal index, BPS monodromy and chiral algebras

Cecotti

Song

Vafa

et al. 2017

J. High Energ. Phys.

View full text Add to dashboard Cite

We show that specializations of the 4d N = 2 superconformal index labeled by an integer N is given by Tr M N where M is the Kontsevich-Soibelman monodromy operator for BPS states on the Coulomb branch. We provide evidence that the states enumerated by these limits of the index lead to a family of 2d chiral algebras A N . This generalizes the recent results for the N = −1 case which corresponds to the Schur limit of the superconformal index. We show that this specialization of the index leads to the same integrand as that of the elliptic genus of compactification of the superconformal theory on S 2 × T 2 where we turn on 1 2 N units of U(1) r flux on S 2 .

show abstract

“…Consider thus its associated multiple partition and use the exchange relation to move the cluster n (j) m j to the far right in order to reach its lowest allowed weight. It is thus displaced through all clusters of larger charge by means of the exchange relation (36). This reduces its weight to n (j) m j − 2j(m j+1 + · · · + m k−1 ).…”

Section: From Paths To Multiple Partitionsmentioning

confidence: 99%

“…1 · · · n (j) ℓ · · · n (k−1) m k−1 . Each cluster is then inserted successively (starting with n (2) 1 up to n (k−1) m k−1 ) within the partition, using the interchange rule (36), treating again each part as a cluster of charge 1. Once inserted within the partition (at a position subject to criteria to be specified), a cluster is unfolded into the number of parts given by its charge, with parts as equal as possible.…”

Section: From Multiple Partitions To Restricted Partitionsmentioning

confidence: 99%

See 1 more Smart Citation

Paths and partitions: Combinatorial descriptions of the parafermionic states

Mathieu

2009

Journal of Mathematical Physics

Self Cite

View full text Add to dashboard Cite

The Z k parafermionic conformal field theories, despite the relative complexity of their modes algebra, offer the simplest context for the study of the bases of states and their different combinatorial representations. Three bases are known. The classic one is given by strings of the fundamental parafermionic operators whose sequences of modes are in correspondence with restricted partitions with parts at distance k − 1 differing at least by 2. Another basis is expressed in terms of the ordered modes of the k − 1 different parafermionic fields, which are in correspondence with the so-called multiple partitions. Both types of partitions have a natural (Bressoud) path representation. Finally, a third basis, formulated in terms of different paths, is inherited from the solution of the restricted solid-on-solid model of Andrews-Baxter-Forrester. The aim of this work is to review, in a unified and pedagogical exposition, these four different combinatorial representations of the states of the Z k parafermionic models.The first part of this article presents the different paths and partitions and their bijective relations; it is purely combinatorial, self-contained and elementary; it can be read independently of the conformal-field-theory applications. The second part links this combinatorial analysis with the bases of states of the Z k parafermionic theories. With the prototypical example of the parafermionic models worked out in detail, this analysis contributes to fix some foundations for the combinatorial study of more complicated theories. Indeed, as we briefly indicate in ending, generalized versions of both the Bressoud and the Andrews-Baxter-Forrester paths emerge naturally in the description of the minimal models.

show abstract

Characters of graded parafermion conformal field theory

Cited by 6 publications

References 30 publications

Permutation orbifolds of supersymmetric minimal models

Permutation orbifolds of supersymmetric minimal models

Superconformal index, BPS monodromy and chiral algebras

Paths and partitions: Combinatorial descriptions of the parafermionic states

Contact Info

Product

Resources

About