Z k parafermion theory
imported>Pythagoras0님의 2014년 10월 12일 (일) 00:22 판 (→articles)
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 $$c=\frac{3k}{k+2}-1=\frac{2(k-1)}{(k+2)}$$
- 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 \(\hat{\text{su}}(2)_k/\hat{u}(1)_k\)
- Kac and Peterson (1984) obtained expression for the parafermion characters
- Lepowsky-Primc (1985) expression in fermionic form
- third expression
examples
- $k=1$, Ising models
- $k=2$, 3-states Potts model
\(\mathbb{Z}_{n+1}\) theory
- central charge\(\frac{2n}{n+3}\)
history
- String functions and branching functions
- CFT on torus and modular invariant partition functions
- Graded parafermion theory
articles
- 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.
- Schilling, Anne, and S. Ole Warnaar. “Conjugate Bailey Pairs.” arXiv:math/9906092, June 14, 1999. http://arxiv.org/abs/math/9906092.
- 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.
- Fateev, V. A., and Al. B. Zamolodchikov. “Integrable Perturbations of ZN Parafermion Models and the O(3) Sigma Model.” Physics Letters B 271, no. 1–2 (November 14, 1991): 91–100. doi:10.1016/0370-2693(91)91283-2.
- Bilal, Adel. “Bosonization of ZN Parafermions and su(2)N KAČ-Moody Algebra.” Physics Letters B 226, no. 3–4 (August 10, 1989): 272–78. doi:10.1016/0370-2693(89)91194-5.
- 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.
- Lepowsky, James, and Mirko Primc. 1985. Structure of the Standard Modules for the Affine Lie Algebra $A^{(1)}_1$. Vol. 46. Contemporary Mathematics. American Mathematical Society, Providence, RI. http://www.ams.org/mathscinet-getitem?mr=814303.
- 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.