Classical and quantum conformal field theory

Categories for the Working Mathematician

Lane, S. M. (1971) · Graduate texts in mathematics · doi:10.1007/978-1-4612-9839-7 · Cited by 9,077 · see citing works

Infinite conformal symmetry in two-dimensional quantum field theory

Belavin, A. A., Polyakov, A., & Zamolodchikov, A. B. (1984) · Nuclear Physics B · doi:10.1016/0550-3213(84)90052-x · Cited by 4,862 · see citing works

Elementary Theory of Angular Momentum

Rose, M. E., & Feld, B. T. (1957) · Physics Today · doi:10.1063/1.3060162 · Cited by 3,625 · see citing works

Cohomology of Groups

Brown, K. S. (1976) · Graduate texts in mathematics · doi:10.1007/978-1-4684-9327-6 · Cited by 3,166 · see citing works

Elementary Theory of Angular Momentum

Pincherle, L. (1958) · Physics Bulletin · doi:10.1088/0031-9112/9/2/013 · Cited by 2,795 · see citing works

Non-abelian bosonization in two dimensions

Witten, E. (1984) · Communications in Mathematical Physics · doi:10.1007/bf01215276 · Cited by 2,307 · see citing works

Strings on orbifolds

Dixon, L. J., Harvey, J. A., Vafa, C., et al. (1985) · Nuclear Physics B · doi:10.1016/0550-3213(85)90593-0 · Cited by 1,851 · see citing works

Current algebra and Wess-Zumino model in two dimensions

Knizhnik, V. G., & Zamolodchikov, A. B. (1984) · Nuclear Physics B · doi:10.1016/0550-3213(84)90374-2 · Cited by 1,838 · see citing works

Braids, Links, and Mapping Class Groups

Birman, J. S. (1974) · International Linear Collider · Cited by 1,652 · see citing works

Fusion rules and modular transformations in 2D conformal field theory

Verlinde, E. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90603-7 · Cited by 1,537 · see citing works

Index for subfactors

Jones, V. F. R. (1983) · Inventiones mathematicae · doi:10.1007/bf01389127 · Cited by 1,495 · see citing works

Elements of the Theory of Representations

Kirillov, A. A. (1976) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-3-642-66243-0 · Cited by 1,493 · see citing works

Vertex algebras, Kac-Moody algebras, and the Monster

Borcherds, R. E. (1986) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.83.10.3068 · Cited by 1,367 · see citing works

Unitary representations of the Virasoro and super-Virasoro algebras

Goddard, P., Kent, A., & Olive, D. (1986) · Communications in Mathematical Physics · doi:10.1007/bf01464283 · Cited by 979 · see citing works

Introduction to number theory

(2009) · Choice Reviews Online · doi:10.5860/choice.46-6857 · Cited by 947 · see citing works

Infinite additional symmetries in two-dimensional conformal quantum field theory

Zamolodchikov, A. B. (1985) · Theoretical and Mathematical Physics · doi:10.1007/bf01036128 · Cited by 858 · see citing works

Natural Associativity and Commutativity

Lane, S. M. (1979) · Springer eBooks · doi:10.1007/978-1-4615-7831-4_19 · Cited by 561 · see citing works

Introduction to Number Theory

Keng, H. L. (1982) · Springer eBooks · doi:10.1007/978-3-642-68130-1 · Cited by 531 · see citing works

The Yang-Baxter equation and invariants of links

Тураев, В. Г. (1988) · Inventiones mathematicae · doi:10.1007/bf01393746 · Cited by 495 · see citing works

Polynomial equations for rational conformal field theories

Moore, G., & Nathan Seiberg, B. (1988) · Physics Letters B · doi:10.1016/0370-2693(88)91796-0 · Cited by 477 · see citing works

The analytic geometry of two-dimensional conformal field theory

Friedan, D. H., & Shenker, S. H. (1987) · Nuclear Physics B · doi:10.1016/0550-3213(87)90418-4 · Cited by 441 · see citing works

Hodge Cycles, Motives, and Shimura Varieties

Deligne, P., Milne, J. S., Ogus, A., et al. (1982) · Lecture notes in mathematics · doi:10.1007/978-3-540-38955-2 · Cited by 439 · see citing works

The second homology group of the mapping class group of an orientable surface

Harer, J. (1983) · Inventiones mathematicae · doi:10.1007/bf01389321 · Cited by 339 · see citing works

Extensions of the Virasoro algebra constructed from Kac-Moody algebras using higher order Casimir invariants

Bais, F. A., Bouwknegt, P., Surridge, M., & Schoutens, K. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90631-1 · Cited by 332 · see citing works

Cohomology Theory in Abstract Groups. I

Eilenberg, S., & MacLane, S. (1947) · Annals of Mathematics · doi:10.2307/1969215 · Cited by 324 · see citing works

Vertex Operators in Conformal Field Theory on $\mathbb{P}^{1}$ and Monodromy Representations of Braid Group

Tsuchiya, A., & Kanie, Y. (2018) · Advanced studies in pure mathematics · doi:10.2969/aspm/01610297 · Cited by 278 · see citing works

Naturality in conformal field theory

Moore, G. M., & Nathan Seiberg, B. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90511-7 · Cited by 272 · see citing works

String field theory on the conformal plane (I).

LeClair, A., Peskin, M. E., & Preitschopf, C. R. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90075-8 · Cited by 240 · see citing works

Strings in the operator formalism

Gaumé, L. Á., Gómez, C., Moore, G. M., et al. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90391-4 · Cited by 237 · see citing works

Toward classification of conformal theories

Vafa, C. (1988) · Physics Letters B · doi:10.1016/0370-2693(88)91603-6 · Cited by 207 · see citing works

Determinant bundles and Virasoro algebras

Beilinson, A., & Schechtman, V. V. (1988) · Communications in Mathematical Physics · doi:10.1007/bf01221114 · Cited by 188 · see citing works

A simple presentation for the mapping class group of an orientable surface

Wajnryb, B. (1983) · Israel Journal of Mathematics · doi:10.1007/bf02774014 · Cited by 185 · see citing works

On braid groups

Birman, J. S. (1969) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160220104 · Cited by 184 · see citing works

Three-Cocycle in Mathematics and Physics

Jackiw, R. (1985) · Physical Review Letters · doi:10.1103/physrevlett.54.159 · Cited by 181 · see citing works

Operator formulation on Riemann surfaces

Vafa, C. (1987) · Physics Letters B · doi:10.1016/0370-2693(87)90838-0 · Cited by 171 · see citing works

Operator content of the ADE lattice models

Pasquier, V. (1987) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/20/16/043 · Cited by 160 · see citing works

Vertex operators in the conformal field theory on P 1 and monodromy representations of the braid group

Tsuchiya, A., & Kanie, Y. (1987) · Letters in Mathematical Physics · doi:10.1007/bf00401159 · Cited by 159 · see citing works

Critical Ising correlation functions in the plane and on the torus

Francesco, P. D., Saleur, H., & Zuber, J.-B. (1987) · Nuclear Physics B · doi:10.1016/0550-3213(87)90202-1 · Cited by 155 · see citing works

Virasoro algebras with central chargec>1

Bagger, J., Nemeschansky, D., & Yankielowicz, S. (1988) · Physical Review Letters · doi:10.1103/physrevlett.60.389 · Cited by 136 · see citing works

Current algebra and conformal discrete series

Kastor, D. A., Martinec, E. J., & Qiu, Z. (1988) · Physics Letters B · doi:10.1016/0370-2693(88)90148-7 · Cited by 135 · see citing works

Loop groups, grassmanians and string theory

Álvarez-Gaumé, L., Gómez, C., & Reina, C. (1987) · Physics Letters B · doi:10.1016/0370-2693(87)90839-2 · Cited by 135 · see citing works

Modular invariance and the fusion algebra

Dijkgraaf, R., & Verlinde, E. (1988) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/0920-5632(88)90371-4 · Cited by 134 · see citing works

Rationality in conformal field theory

Anderson, G., & Moore, G. (1988) · Communications in Mathematical Physics · doi:10.1007/bf01223375 · Cited by 130 · see citing works

Sewing conformal field theories II

Sonoda, H. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90067-3 · Cited by 117 · see citing works

Conformal theories and punctured surfaces

Vafa, C. (1987) · Physics Letters B · doi:10.1016/0370-2693(87)91358-x · Cited by 104 · see citing works

SOLITON EQUATIONS AND FREE FERMIONS ON RIEMANN SURFACES

Ishibashi, N., Matsuo, Y., & Ooguri, H. (1987) · Modern Physics Letters A · doi:10.1142/s0217732387000161 · Cited by 102 · see citing works

Parafermionic Currents in the Two-Dimensional Conformal Quantum Field Theory and Selfdual Critical Points in Z(n) Invariant Statistical Systems

Fateev, V. A., & Zamolodchikov, A. B. (1985) · Cited by 102 · see citing works

Unitary construction of extended conformal algebras

Goddard, P., & Schwimmer, A. (1988) · Physics Letters B · doi:10.1016/0370-2693(88)91263-4 · Cited by 101 · see citing works

Einstein causality and Artin braids

Rehren, K.-H., & Schroer, B. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90580-4 · Cited by 98 · see citing works

AN INFINITE CLASS OF NEW CONFORMAL FIELD THEORIES WITH EXTENDED ALGEBRAS

Ravanini, F. (1988) · Modern Physics Letters A · doi:10.1142/s0217732388000490 · Cited by 76 · see citing works

A 3-cocycle in quantum mechanics

Grossman, B. (1985) · Physics Letters B · doi:10.1016/0370-2693(85)91146-3 · Cited by 72 · see citing works

Differential equations for correlators and characters in arbitrary rational conformal field theories

Mathur, S. D., Mukhi, S., & Sen, A. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90022-9 · Cited by 59 · see citing works

Quasicrystalline compactification

Harvey, J. A., Moore, G. M., & Vafa, C. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90627-x · Cited by 45 · see citing works

Factorization and selection rules of operator product algebras in conformal field theories

Brustein, R., Shimon Yankielowicz, B., & Zuber, J.-B. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90322-2 · Cited by 44 · see citing works

The spectrum of Wess-Zumino-Witten models

Felder, G., Gawędzki, K., & Kupiainen, A. J. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90288-x · Cited by 40 · see citing works

Elastic and inelastic scattering of 14.1 MeV neutrons on 28Si nuclei in a wide angular range, and the spin-orbit interaction

KLICZEWSKI, S., & Lewandowski, Z. (1978) · Nuclear Physics A · doi:10.1016/0375-9474(78)90237-3 · Cited by 31 · see citing works

Quasiprimary fields: An approach to positivity of 2D conformal quantum field theory

Rehren, K.-H., & Schroer, B. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90254-4 · Cited by 21 · see citing works

Operator approach to conformal invariant quantum field theories and related problems

Schroer, B. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90537-8 · Cited by 18 · see citing works

A New Formulation of String Theory

Friedan, D. (1987) · Physica Scripta · doi:10.1088/0031-8949/1987/t15/009 · Cited by 15 · see citing works

Structure constants for rational conformal field theories

Francesco, P. D. (1988) · Physics Letters B · doi:10.1016/0370-2693(88)91082-9 · Cited by 12 · see citing works

Extended current algebras and the coset construction of conformal field theories

Blok, B., & Yankielowicz, S. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90447-1 · Cited by 7 · see citing works

Relativistic spin networks and quantum gravity

Barrett, J. W., & Crane, L. (1998) · Journal of Mathematical Physics · doi:10.1063/1.532254 · Cited by 404 · see citing works

Linking topological quantum field theory and nonperturbative quantum gravity

Smolin, L. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531251 · Cited by 234 · see citing works

Holographic entanglement entropy from 2d CFT: heavy states and local quenches

Asplund, C. T., Bernamonti, A., Galli, F., & Hartman, T. (2015) · Journal of High Energy Physics · doi:10.1007/jhep02(2015)171 · Cited by 280 · see citing works

State sum invariants of 4-manifolds

Crane, L., Kauffman, L. H., & Yetter, D. N. (1997) · Journal of Knot Theory and Its Ramifications · doi:10.1142/s0218216597000145 · Cited by 139 · see citing works

A universal Schwarzian sector in two-dimensional conformal field theories

Ghosh, A., Maxfield, H., & Turiaci, G. J. (2020) · Journal of High Energy Physics · doi:10.1007/jhep05(2020)104 · Cited by 135 · see citing works

Clock and category: Is quantum gravity algebraic?

Crane, L. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531240 · Cited by 102 · see citing works

Quantum geometry with intrinsic local causality

Markopoulou, F., & Smolin, L. (1998) · Physical Review D · doi:10.1103/physrevd.58.084032 · Cited by 95 · see citing works

The geometry of quantum spin networks

Borissov, R., Major, S., & Smolin, L. (1996) · Classical and Quantum Gravity · doi:10.1088/0264-9381/13/12/009 · Cited by 68 · see citing works

Boundary conformal invariants and the conformal anomaly in five dimensions

Astaneh, A. F., & Solodukhin, S. N. (2021) · Physics Letters B · doi:10.1016/j.physletb.2021.136282 · Cited by 14 · see citing works

Springer Tracts in Modern Physics

Ferrara, S., Gatto, P., & Grilla, A. F. (1973) · Springer eBooks · doi:10.1007/bfb0111103 · Cited by 579 · see citing works

Conformal Symmetry in Statistical Mechanics

Eckle, H.-P. (2019) · doi:10.1093/oso/9780199678839.003.0007

Conformal field theories and critical phenomena

Xu, B.-W. (1993) · Foundations of Physics · doi:10.1007/bf01883633

Quantum conformal algebras and closed conformal field theoryPreprint

Anselmi, D. (2013) · Cited by 17 · see citing works