Z k parafermion theory

introduction

parafermionic Hilbert space
defined by the algebra of parafermionic fields \(\psi_1\) and \(\psi _1^{\dagger }\) of dimension 1-1/k and central charge 2(k-1)/(k+2)
the highest-weight modules are parametrized by an integer (Dynkin label) l with \(0\leq l < k\)
\(\mathbb{Z}_k\) parafermion theory is known to be equivalent to the coset \(\hat{\text{su}}(2)_k/\hat{u}(1)\)
Kac and Peterson (1984) obtained expression for the parafermion characters
Lepowsky-Primc (1985) expression in fermionic form
third expression

Keegan, Sinéad, and Werner Nahm. 2011. “Nahm’s conjecture and coset models.” 1103.4986 (March 25). http://arxiv.org/abs/1103.4986
Fortin, J.-F., P. Mathieu, and S. O. Warnaar. 2006. “Characters of Graded Parafermion Conformal Field Theory”. ArXiv e-print hep-th/0602248. http://arxiv.org/abs/hep-th/0602248.
Conjugate Bailey pairs. From configuration sums and fractional-level string functions to Bailey's lemma.,Anne Schilling, S. Ole Warnaar, 1999
Cabra, D. C. 1998. “Spinons and Parafermions in Fermion Cosets.” In Supersymmetry and Quantum Field Theory, edited by Julius Wess and Vladimir P. Akulov, 220–229. Lecture Notes in Physics 509. Springer Berlin Heidelberg. http://link.springer.com/chapter/10.1007/BFb0105250.
Bosonization of ZN parafermions and su(2)N Kac -Moody algebra
Gepner, Doron, and Zongan Qiu. 1987. “Modular Invariant Partition Functions for Parafermionic Field Theories.” Nuclear Physics B 285: 423–453. doi:10.1016/0550-3213(87)90348-8.
Gepner, Doron. 1987. “New Conformal Field Theories Associated with Lie Algebras and Their Partition Functions.” Nuclear Physics B 290: 10–24. doi:10.1016/0550-3213(87)90176-3.
Kac, Victor G, and Dale H Peterson. 1984. “Infinite-dimensional Lie Algebras, Theta Functions and Modular Forms.” Advances in Mathematics 53 (2) (August): 125–264. doi:10.1016/0001-8708(84)90032-X.