Fermionic characters of Virasoro minimal models

introduction

• unitary case
• non-unitary case
• bosonic charaters of minimal models
• Rogers-Ramanujan identities for the minimal models \(M(p,p')\) perturbed by the operators \(\phi_{1,3},\phi_{2,1},\phi_{1,5}\) and \(\phi_{1,2}\)

unitary case

• minimal models
• Cartan matrices A_n

examples

• integrable perturbations of Ising model
• Integrable perturbation of Yang-Lee model

related items

• Massive integrable perturbations of CFT and quasi-particles
• sources of Bailey pairs
• coset characters and Fermionic character formula

books

• Trevor Alan Welsh Fermionic expressions for minimal model Virasoro characters
  • http://arxiv.org/abs/math/0212154

expositions

• Warnaar, Review of Welsh's book
• Kedem, Rinat, Barry M. McCoy, and Ezer Melzer. 1995. “The Sums of Rogers, Schur and Ramanujan and the Bose-Fermi Correspondence in \((1+1)\)-Dimensional Quantum Field Theory.” In Recent Progress in Statistical Mechanics and Quantum Field Theory (Los Angeles, CA, 1994), 195–219. World Sci. Publ., River Edge, NJ. http://xxx.lanl.gov/abs/hep-th/9304056

articles

• Berkovich, Alexander, Barry M. McCoy, and Anne Schilling. 1998. “Rogers-Schur-Ramanujan Type Identities for the \(M(p,p’)\) Minimal Models of Conformal Field Theory.” Communications in Mathematical Physics 191 (2): 325–395. doi:10.1007/s002200050271.
• Berkovich, Alexander, and Barry M. McCoy. 1996. “Continued Fractions and Fermionic Representations for Characters of \(M(p,p’)\) Minimal Models.” Letters in Mathematical Physics. A Journal for the Rapid Dissemination of Short Contributions in the Field of Mathematical Physics 37 (1): 49–66. doi:10.1007/BF00400138.
• Foda, Omar, and Yas-Hiro Quano. 1997. “Virasoro Character Identities from the Andrews-Bailey Construction.” International Journal of Modern Physics A. Particles and Fields. Gravitation. Cosmology. Nuclear Physics 12 (9): 1651–1675. doi:10.1142/S0217751X97001110.
• Berkovich, Alexander. 1994. “Fermionic Counting of RSOS States and Virasoro Character Formulas for the Unitary Minimal Series \(M(\nu,\nu+1)\): Exact Results.” Nuclear Physics. B 431 (1-2): 315–348. doi:10.1016/0550-3213(94)90108-2.
• Melzer, Ezer. 1994. “Fermionic Character Sums and the Corner Transfer Matrix.” International Journal of Modern Physics A. Particles and Fields. Gravitation. Cosmology 9 (7): 1115–1136. doi:10.1142/S0217751X94000510.
• Kedem, R., T. R. Klassen, B. M. McCoy, and E. Melzer. 1993. “Fermionic Sum Representations for Conformal Field Theory Characters.” Physics Letters. B 307 (1-2): 68–76. doi:10.1016/0370-2693(93)90194-M.
• Kedem, R., T. R. Klassen, B. M. McCoy, and E. Melzer. 1993. “Fermionic Quasi-Particle Representations for Characters of \((G^{(1)})_1\times (G^{(1)})_1/(G^{(1)})_2\).” Physics Letters. B 304 (3-4): 263–270. doi:10.1016/0370-2693(93)90292-P.
• Feigin, Boris L., Tomoki Nakanishi, and Hirosi Ooguri. 1992. “The Annihilating Ideals of Minimal Models.” In Infinite Analysis, Part A, B (Kyoto, 1991), 16:217–238. Adv. Ser. Math. Phys. World Sci. Publ., River Edge, NJ.