Extended multiplet structure in Logarithmic Conformal Field Theories

Abstract

We use the process of quantum hamiltonian reduction of SU(2)_k, at rational level k, to study explicitly the correlators of the h_{1,s} fields in the c_{p,q} models. We find from direct calculation of the correlators that we have the possibility of extra, chiral and non-chiral, multiplet structure in the h_{1,s} operators beyond the `minimal' sector. At the level of the vacuum null vector h_{1,2p-1}=(p-1)(q-1) we find that there can be two extra non-chiral fermionic fields. The extra indicial structure present here permeates throughout the entire theory. In particular we find we have a chiral triplet of fields at h_{1,4p-1}=(2p-1)(2q-1). We conjecture that this triplet algebra may produce a rational extended c_{p,q} model. We also find a doublet of fields at h_{1,3p-1}=(\f{3p}{2}-1)(\f{3q}{2}-1). These are chiral fermionic operators if p and q are not both odd and otherwise parafermionic.

24 pages LATEX. Minor corrections and extra references

References in corpus (15)

• Fusion rules and logarithmic representations of a WZW model at fractional level
• Logarithmic Conformal Field Theories via Logarithmic Deformations
• The su(2)_{-1/2} WZW model and the beta-gamma system
• A c=-2 boundary changing operator for the Abelian sandpile
• Solution of the multi-reggeon compound state problem in multi-colour QCD
• Modular transformation and boundary states in logarithmic conformal field theory
• Operator Product Expansion in Logarithmic Conformal Field Theory
• Boundary States in c=-2 Logarithmic Conformal Field Theory
• PP-waves and logarithmic conformal field theories
• Boundary states in boundary logarithmic CFT
• SU(2)_0 and OSp(2|2)_{-2} WZNW models : Two current algebras, one Logarithmic CFT
• Prelogarithmic operators and Jordan blocks in SL(2)_k affine algebra
• On the AdS/CFT Correspondence and Logarithmic Operator
• Extended chiral algebras in the SU(2)_0 WZNW model
• Calculation of Four Point Correlation Function of Logarithmic Conformal Field Theory Using AdS/CFT Correspondence

Cited by in corpus (5)

• The Neveu-Schwarz and Ramond Algebras of Logarithmic Superconformal Field Theory
• Toward logarithmic extensions of ^sl(2)_k conformal field models
• The O(n) Model in the $n\to 0$ Limit (self-avoiding-walks) and Logarithmic Conformal Field Theory
• Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas
• The origin of multiplets of chiral fields in SU(2)_k WZNW at rational level