"Z k parafermion theory"의 두 판 사이의 차이

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1번째 줄: 1번째 줄:
 
==introduction==
 
==introduction==
 
* parafermionic Hilbert space
 
* parafermionic Hilbert space
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* 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 $$c=\frac{3k}{k+2}-1=\frac{2(k-1)}{(k+2)}$$
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* 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
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* the highest-weight modules are parametrized by an integer (Dynkin label) $l$ with <math>0\leq l < k</math>
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:<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>
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where <math>\mathfrak{g}=\mathfrak{sl}_2</math> and <math>k=2</math>
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* 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==
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* $k=1$, [[Ising models]]
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* <math>k=1</math>, [[Ising models]]
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* $k=2$, [[3-states Potts model]]
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* <math>k=2</math>, [[3-states Potts model]]
  
  
31번째 줄: 32번째 줄:
 
* [[Graded parafermion theory]]
 
* [[Graded parafermion theory]]
 
   
 
   
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==computational resource==
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* https://docs.google.com/file/d/0B8XXo8Tve1cxZzRnSkZJZ0kyZlE/edit
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==expositions==
 
==expositions==
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* 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
  
  
 
==articles==
 
==articles==
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* Belavin, Alexander A., and Doron R. Gepner. “Generalized Rogers Ramanujan Identities Motivated by AGT Correspondence.” Letters in Mathematical Physics 103, no. 12 (December 1, 2013): 1399–1407. doi:10.1007/s11005-013-0653-2.
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* 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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* Genish, A., and D. Gepner. “Level Two String Functions and Rogers Ramanujan Type Identities.” arXiv:1405.1387 [hep-Th, Physics:math-Ph], May 6, 2014. http://arxiv.org/abs/1405.1387.
 
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* Fendley, Paul. “Parafermionic Edge Zero Modes in Z_n-Invariant Spin Chains.” arXiv:1209.0472 [cond-Mat, Physics:hep-Th], September 3, 2012. http://arxiv.org/abs/1209.0472.
 
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* Keegan, Sinéad, and Werner Nahm. 2011. “Nahm’s conjecture and coset models.” <em>1103.4986</em> (March 25). http://arxiv.org/abs/1103.4986
 
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* 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.
 
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* Schilling, Anne, and S. Ole Warnaar. “Conjugate Bailey Pairs.” arXiv:math/9906092, June 14, 1999. http://arxiv.org/abs/math/9906092.
 
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* 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.
 
* 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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* 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].
 
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* 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].
 
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* 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.
 
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* 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]]
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[[분류:thesis]]
 
 
[[분류:conformal field theory]]
 
[[분류:conformal field theory]]
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[[분류:migrate]]

2020년 11월 16일 (월) 07:09 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


\(\mathbb{Z}_{n+1}\) theory

  • central charge\(\frac{2n}{n+3}\)


history



related items


computational resource


expositions


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.
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