Parafermionic quasi-particle basis and fermionic-type characters

Jacob, P.; Mathieu, Pierre

doi:10.1016/s0550-3213(01)00548-x

Cited by 17 publications

(65 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is the famous Lepowsky-Primc expression [23] which yields the characters as a manifestly positive multiple-series or fermionic (F) form (see also [19]). Specifically, (1.6)χ Yet a third expression for the parafermion characters can be obtained from the so-called su(2) k spinon formula forχ ℓ (q) which was conjectured in [6] and proved in [3,25,26].…”

Section: Introductionmentioning

confidence: 99%

Characters of graded parafermion conformal field theory

Fortin¹,

Mathieu²,

Warnaar³

2007

Advances in Theoretical and Mathematical Physics

View full text Add to dashboard Cite

Abstract. The graded parafermion conformal field theory at level k is a close cousin of the much-studied Z k parafermion model. Three character formulas for the graded parafermion theory are presented, one bosonic, one fermionic (both previously known) and one of spinon type (which is new). The main result of this paper is a proof of the equivalence of these three forms using q-series methods combined with the combinatorics of lattice paths. The pivotal step in our approach is the observation that the graded parafermion theory -which is equivalent to the coset osp(1, 2) k / u(1) -can be factored as ( osp (1, 2) (1)), with the two cosets on the right equivalent to the minimal model M(k + 2, 2k + 3) and the Z k parafermion model, respectively. This factorisation allows for a new combinatorial description of the graded parafermion characters in terms of the one-dimensional configuration sums of the (k + 1)-state Andrews-Baxter-Forrester model.

show abstract

Section: Introductionmentioning

confidence: 99%

Characters of graded parafermion conformal field theory

Fortin¹,

Mathieu²,

Warnaar³

2007

Advances in Theoretical and Mathematical Physics

View full text Add to dashboard Cite

show abstract

“…Based on numerical checks [5,6], these CFTs were earlier identified as the critical behavior of the anyonic chain. The parafermion theory and characters are well known and appear also in the ABF models; we recover the fermionic forms of these characters [16][17][18][19][20]. The fermionic characters we obtain for the coset theory are new to the best of our knowledge.Finally, the fermionic forms of the LHPs of the composite model studied here open an arena of q-identities related to the coset theories su (2)1×su(2)1×su(2)r−4 su(2)r−2.…”

mentioning

confidence: 58%

“…In the equations above, we denoted the fields of the Z r−2 parafermion CFT by Φ l m , and the characters by ch q Φ l m . These characters are given by the following expressions (see, for instance [16][17][18][19][20])…”

Section: (R−2)mentioning

confidence: 99%

Local height probabilities in a composite Andrews–Baxter–Forrester model

Nissinen¹,

Ardonne²

2012

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We study the local height probabilities in a composite height model, derived from the restricted solid-on-solid model introduced by Andrews, Baxter and Forrester, and their connection with conformal field theory characters. The obtained conformal field theories also describe the critical behavior of the model at two different critical points. In addition, at criticality, the model is equivalent to a one-dimensional chain of anyons, subject to competing two-and three-body interactions. The anyonic-chain interpretation provided the original motivation to introduce the composite height model, and by obtaining the critical behaviour of the composite height model, the critical behaviour of the anyonic chains is established as well. Depending on the overall sign of the hamiltonian, this critical behaviour is described by a diagonal coset-model, generalizing the minimal models for one sign, and by Fateev-Zamolodchikov parafermions for the other.

show abstract

“…The basis of parafermionic states in [59,41] is formulated in terms of the modes of a single parafermionic field. However, it is possible to set up a basis that involves the modes of the k−1 non-trivial parafermionic fields [37,43].…”

Section: Parafermionic Bases Of States Paths and Partitions: Their Omentioning

confidence: 99%

Paths and partitions: Combinatorial descriptions of the parafermionic states

Mathieu

2009

Journal of Mathematical Physics

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

Parafermionic quasi-particle basis and fermionic-type characters

Cited by 17 publications

References 54 publications

Characters of graded parafermion conformal field theory

Characters of graded parafermion conformal field theory

Local height probabilities in a composite Andrews–Baxter–Forrester model

Paths and partitions: Combinatorial descriptions of the parafermionic states

Contact Info

Product

Resources

About