"Z k parafermion theory"의 두 판 사이의 차이
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==introduction== | ==introduction== | ||
* parafermionic Hilbert space | * parafermionic Hilbert space | ||
| − | * defined by the algebra of parafermionic fields <math>\psi_1</math> and <math>\psi _1^{\dagger }</math> of dimension 1-1/k and central charge | + | * defined by the algebra of parafermionic fields <math>\psi_1</math> and <math>\psi _1^{\dagger }</math> of dimension 1-1/k and central charge |
| − | * the highest-weight modules are parametrized by an integer (Dynkin label) | + | :<math>c=\frac{k \dim \mathfrak{g}}{k+h^{\vee}}-\operatorname{rank}\mathfrak{g}=\frac{3k}{k+2}-1=\frac{2(k-1)}{(k+2)}</math> |
| + | where <math>\mathfrak{g}=\mathfrak{sl}_2</math> and <math>k=2</math> | ||
| + | * the highest-weight modules are parametrized by an integer (Dynkin label) <math>l</math> 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)_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)_k</math> | ||
* Kac and Peterson (1984) obtained expression for the parafermion characters | * 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 | ||
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==examples== | ==examples== | ||
| − | * | + | * <math>k=1</math>, [[Ising models]] |
| − | * | + | * <math>k=2</math>, [[3-states Potts model]] |
| 31번째 줄: | 32번째 줄: | ||
* [[Graded parafermion theory]] | * [[Graded parafermion theory]] | ||
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| + | ==computational resource== | ||
| + | * https://docs.google.com/file/d/0B8XXo8Tve1cxZzRnSkZJZ0kyZlE/edit | ||
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==expositions== | ==expositions== | ||
* Gepner, [http://www.integrable-qft.uni-wuppertal.de/program/Gepner.pdf Level Two String Functions and Rogers Ramanujan Type Identities] | * Gepner, [http://www.integrable-qft.uni-wuppertal.de/program/Gepner.pdf Level Two String Functions and Rogers Ramanujan Type Identities] | ||
* http://physics.stackexchange.com/questions/76617/what-is-parafermion-in-condensed-matter-physics | * http://physics.stackexchange.com/questions/76617/what-is-parafermion-in-condensed-matter-physics | ||
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==articles== | ==articles== | ||
| − | * | + | * Bianchini, Davide, Elisa Ercolessi, Paul A. Pearce, and Francesco Ravanini. ‘RSOS Quantum Chains Associated with Off-Critical Minimal Models and <math>\mathbb{Z}_n</math> Parafermions’. arXiv:1412.4942 [cond-Mat, Physics:hep-Th, Physics:math-Ph], 16 December 2014. http://arxiv.org/abs/1412.4942. |
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* 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. | * 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:[http://dx.doi.org/10.1016/0370-2693%2889%2991194-5 10.1016/0370-2693(89)91194-5]. | * 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:[http://dx.doi.org/10.1016/0370-2693%2889%2991194-5 10.1016/0370-2693(89)91194-5]. | ||
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[[분류:개인노트]] | [[분류:개인노트]] | ||
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[[분류:conformal field theory]] | [[분류:conformal field theory]] | ||
| + | [[분류:migrate]] | ||
2020년 11월 16일 (월) 06:09 기준 최신판
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
\[c=\frac{k \dim \mathfrak{g}}{k+h^{\vee}}-\operatorname{rank}\mathfrak{g}=\frac{3k}{k+2}-1=\frac{2(k-1)}{(k+2)}\] where \(\mathfrak{g}=\mathfrak{sl}_2\) and \(k=2\)
- 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
computational resource
expositions
- Gepner, Level Two String Functions and Rogers Ramanujan Type Identities
- http://physics.stackexchange.com/questions/76617/what-is-parafermion-in-condensed-matter-physics
articles
- Bianchini, Davide, Elisa Ercolessi, Paul A. Pearce, and Francesco Ravanini. ‘RSOS Quantum Chains Associated with Off-Critical Minimal Models and \(\mathbb{Z}_n\) Parafermions’. arXiv:1412.4942 [cond-Mat, Physics:hep-Th, Physics:math-Ph], 16 December 2014. http://arxiv.org/abs/1412.4942.
- 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.