"Z k parafermion theory"의 두 판 사이의 차이
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| 5번째 줄: | 5번째 줄: | ||
* the highest-weight modules are parametrized by an integer (Dynkin label) l with <math>0\leq l < k</math> | * the highest-weight modules are parametrized by an integer (Dynkin label) l with <math>0\leq l < k</math> | ||
* <math>\mathbb{Z}_k</math> parafermion theory is known to be equivalent to the coset <math>\hat{\text{su}}(2)_k/\hat{u}(1)</math> | * <math>\mathbb{Z}_k</math> parafermion theory is known to be equivalent to the coset <math>\hat{\text{su}}(2)_k/\hat{u}(1)</math> | ||
| − | * Kac and | + | * Kac and Peterson (1984) obtained expression for the parafermion characters |
* Lepowsky-Primc (1985) expression in fermionic form | * Lepowsky-Primc (1985) expression in fermionic form | ||
* third expression | * third expression | ||
| 32번째 줄: | 32번째 줄: | ||
==related items== | ==related items== | ||
| − | + | * [[String functions and branching functions]] | |
* [[modular invariant partition functions|CFT on torus and modular invariant partition functions]] | * [[modular invariant partition functions|CFT on torus and modular invariant partition functions]] | ||
* [[Ising models]] | * [[Ising models]] | ||
| 48번째 줄: | 48번째 줄: | ||
* Gepner, Doron, and Zongan Qiu. 1987. “Modular Invariant Partition Functions for Parafermionic Field Theories.” Nuclear Physics B 285: 423–453. doi:[http://dx.doi.org/10.1016/0550-3213%2887%2990348-8 10.1016/0550-3213(87)90348-8]. | * Gepner, Doron, and Zongan Qiu. 1987. “Modular Invariant Partition Functions for Parafermionic Field Theories.” Nuclear Physics B 285: 423–453. doi:[http://dx.doi.org/10.1016/0550-3213%2887%2990348-8 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:[http://dx.doi.org/10.1016/0550-3213(87)90176-3 10.1016/0550-3213(87)90176-3]. | * Gepner, Doron. 1987. “New Conformal Field Theories Associated with Lie Algebras and Their Partition Functions.” Nuclear Physics B 290: 10–24. doi:[http://dx.doi.org/10.1016/0550-3213(87)90176-3 10.1016/0550-3213(87)90176-3]. | ||
| − | * [http://dx.doi.org/10.1016/0001-8708%2884%2990032-X | + | * 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:[http://dx.doi.org/10.1016/0001-8708%2884%2990032-X 10.1016/0001-8708(84)90032-X]. |
[[분류:개인노트]] | [[분류:개인노트]] | ||
[[분류:thesis]] | [[분류:thesis]] | ||
[[분류:conformal field theory]] | [[분류:conformal field theory]] | ||
2013년 7월 11일 (목) 05:16 판
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
\(\mathbb{Z}_{n+1}\) theory
- central charge\(\frac{2n}{n+3}\)
history
- String functions and branching functions
- CFT on torus and modular invariant partition functions
- Ising models
- 3-states Potts model
- 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. Mathieu와/과S. O Warnaar. 2006. “Characters of graded parafermion conformal field theory”. hep-th/0602248 (2월 23). [1]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.