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Journal articles on the topic 'Conformal representations'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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1

MATSUDA, SATOSHI. "REPRESENTATION BLOCKS OF CONFORMAL FIELDS FOR THE N=4SU(2)k SUPERCONFORMAL ALGEBRAS." International Journal of Modern Physics A 10, no. 11 (April 30, 1995): 1671–91. http://dx.doi.org/10.1142/s0217751x95000802.

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The representation theories of the SU(2)k-extended N=4 superconformal algebras (SCA’s) with arbitrary level k are developed, based on their Feigin-Fuchs representations found recently by the present author. A basic unit of the representation blocks consisting of eight “boson-like” and eight “fermion-like” conformal fields is found to describe arbitrary representations of the N=4 SU(2)k SCA’s, including unitary and nonunitary representations. The transformation properties of the fundamental sets of the conformal fields under the N=4 SU(2)k superconformal symmetries are given. Then, the whole sets of the charge screening operators of the N=4 SU(2)k SCA’s are identified out of the 16 conformal fields in the basic unit of the representation blocks. The conditions for the eligible charge screening operators are analyzed in terms of the continuous parameters which enter in our vertex operator forms for the fundamental conformal fields of the representation blocks.

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2

EHOLZER, W. "FUSION ALGEBRAS INDUCED BY REPRESENTATIONS OF THE MODULAR GROUP." International Journal of Modern Physics A 08, no. 20 (August 10, 1993): 3495–507. http://dx.doi.org/10.1142/s0217751x93001405.

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Using the representation theory of the subgroups SL 2(ℤp) of the modular group we investigate the induced fusion algebras in some simple examples. Only some of these representations lead to "good" fusion algebras. Furthermore, the conformal dimensions and the central charge of the corresponding rational conformal field theories are calculated. Two series of representations which can be realized by unitary theories are presented. We show that most of the fusion algebras induced by admissible representations are realized in well-known rational models.

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3

LLEDÓ, FERNANDO. "CONFORMAL COVARIANCE OF MASSLESS FREE NETS." Reviews in Mathematical Physics 13, no. 09 (September 2001): 1135–61. http://dx.doi.org/10.1142/s0129055x01000958.

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In the present paper we review in a fiber bundle context the covariant and massless canonical representations of the Poincaré group as well as certain unitary representations of the conformal group (in 4-dimensions). We give a simplified proof of the well-known fact that massless canonical representations with discrete helicity extend to unitary and irreducible representations of the conformal group mentioned before. Further we give a simple new proof that massless free nets for any helicity value are covariant under the conformal group. Free nets are the result of a direct (i.e. independent of any explicit use of quantum fields) and natural way of constructing nets of abstract C *-algebras indexed by open and bounded regions in Minkowski space that satisfy standard axioms of local quantum physics. We also give a group theoretical interpretation of the embedding ℐ. that completely characterizes the free net: it reduces the (algebraically) reducible covariant representation in terms of the unitary canonical ones. Finally, we also mention some of the expected algebraic properties of these models that are a direct consequence of the conformal covariance (essential duality, PCT-symmetry etc.).

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4

Kolesnikov, P. S. "Universal enveloping Poisson conformal algebras." International Journal of Algebra and Computation 30, no. 05 (March 20, 2020): 1015–34. http://dx.doi.org/10.1142/s0218196720500289.

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Lie conformal algebras are useful tools for studying vertex operator algebras and their representations. In this paper, we establish close relations between Poisson conformal algebras and representations of Lie conformal algebras. We also calculate explicitly Poisson conformal brackets on the associated graded conformal algebras of universal associative conformal envelopes of the Virasoro conformal algebra and the Neveu–Schwartz conformal superalgebra.

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5

RYTTOV, THOMAS A., and FRANCESCO SANNINO. "CONFORMAL HOUSE." International Journal of Modern Physics A 25, no. 24 (September 30, 2010): 4603–21. http://dx.doi.org/10.1142/s0217751x10050391.

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We investigate the gauge dynamics of nonsupersymmetric SU (N) gauge theories featuring the simultaneous presence of fermionic matter transforming according to two distinct representations of the underlying gauge group. We bound the regions of flavors and colors which can yield a physical infrared fixed point. As a consistency check we recover the previously investigated bounds of the conformal windows when restricting to a single matter representation. The earlier conformal windows can be imagined to be part now of the new conformal house. We predict the nonperturbative anomalous dimensions at the infrared fixed points. We further investigate the effects of adding mass terms to the condensates on the conformal house chiral dynamics and construct the simplest instanton induced effective Lagrangian terms.

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6

Kolesnikov, P. S. "Conformal representations of Leibniz algebras." Siberian Mathematical Journal 49, no. 3 (May 2008): 429–35. http://dx.doi.org/10.1007/s11202-008-0043-7.

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7

Carpi, Sebastiano, and Robin Hillier. "Loop groups and noncommutative geometry." Reviews in Mathematical Physics 29, no. 09 (September 7, 2017): 1750029. http://dx.doi.org/10.1142/s0129055x17500295.

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We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level [Formula: see text] projective unitary positive-energy representations of any given loop group [Formula: see text]. The construction is based on certain supersymmetric conformal field theory models associated with [Formula: see text] in the setting of conformal nets. We then generalize the construction to many other rational chiral conformal field theory models including coset models and the moonshine conformal net.

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8

Wu, Henan. "Finite irreducible representations of map Lie conformal algebras." International Journal of Mathematics 28, no. 01 (January 2017): 1750002. http://dx.doi.org/10.1142/s0129167x17500021.

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In this paper, we study the finite representation theory of the map Lie conformal algebra [Formula: see text], where G is a finite simple Lie conformal algebra and A is a commutative associative algebra with unity over [Formula: see text]. In particular, we give a complete classification of nontrivial finite irreducible conformal modules of [Formula: see text] provided A is finite-dimensional.

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9

ALTSCHÜLER, D. "THE CRITICAL REPRESENTATIONS OF AFFINE LIE ALGEBRAS." Modern Physics Letters A 01, no. 10 (November 1986): 557–64. http://dx.doi.org/10.1142/s0217732386000701.

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A critical representation of an affine algebra Ĝ is a representation with central charge k=−g, g being the dual Coxeter number of the underlying simple Lie algebra G. These representations arise naturally in the study of conformal current algebras and BRS cohomology. The author shows how to construct them explicitly in a number of cases, and some intriguing open problems are mentioned.

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10

Morel, B., A. Sciarrino, and P. Sorba. "Unitary massless representations of conformal superalgebras." Physics Letters B 166, no. 1 (January 1986): 69–74. http://dx.doi.org/10.1016/0370-2693(86)91157-3.

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11

Furlan, P., V. B. Petkova, G. M. Sotkov, and I. T. Todorov. "Conformal quantum electrodynamics and nondecomposable representations." La Rivista Del Nuovo Cimento Series 3 8, no. 3 (March 1985): 1–50. http://dx.doi.org/10.1007/bf02724350.

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12

Kolesnikov, Pavel. "On finite representations of conformal algebras." Journal of Algebra 331, no. 1 (April 2011): 169–93. http://dx.doi.org/10.1016/j.jalgebra.2010.12.014.

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13

FERRARA, SERGIO, and EMERY SOKATCHEV. "CONFORMAL SUPERFIELDS AND BPS STATES IN AdS4/7 GEOMETRIES." International Journal of Modern Physics B 14, no. 22n23 (September 20, 2000): 2315–33. http://dx.doi.org/10.1142/s0217979200001837.

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We carry out a general analysis of the representations of the superconformal algebras OSp(8/4, ℝ) and OSp(8*/2N) in terms of harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different types of massless conformal superfields ("supersingletons"). Particular attention is paid to the so-called "short multiplets". Representations undergoing shortening have "protected dimension" and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.

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14

Dasmahapatra, S., R. Dedem, T. R. Klassen, B. M. McCoy, and E. Melzer. "Quasi-Particles, Conformal Field Theory, and q-Series." International Journal of Modern Physics B 07, no. 20n21 (September 30, 1993): 3617–48. http://dx.doi.org/10.1142/s0217979293003437.

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We review recent results concerning the representation of conformal field theory characters in terms of fermionic quasi-particle excitations, and describe in detail their construction in the case of the integrable three-state Potts chain. These fermionic representations are q-series which are generalizations of the sums occurring in the Rogers-Ramanujan identities.

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15

PEREIRA, J. G., A. C. SAMPSON, and L. L. SAVI. "DE SITTER TRANSITIVITY, CONFORMAL TRANSFORMATIONS AND CONSERVATION LAWS." International Journal of Modern Physics D 23, no. 04 (March 18, 2014): 1450035. http://dx.doi.org/10.1142/s0218271814500357.

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Minkowski spacetime is transitive under ordinary translations, a transformation that do not have matrix representations. The de Sitter spacetime, on the other hand, is transitive under a combination of translations and proper conformal transformations, which do have a matrix representation. Such matrix, however, is not by itself a de Sitter generator: it gives rise to a conformal re-scaling of the metric, a transformation not belonging to the de Sitter group, and in general not associated with diffeomorphisms in spacetime. When dealing with variational principles and Noether's theorem in de Sitter spacetime, it is necessary to regularize the transformations in order to eliminate the conformal re-scaling of the metric.

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16

LARSSON, T. A. "CONFORMAL FIELDS: A CLASS OF REPRESENTATIONS OF Vect(N)." International Journal of Modern Physics A 07, no. 26 (October 20, 1992): 6493–508. http://dx.doi.org/10.1142/s0217751x92002970.

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Vect (N), the algebra of vector fields in N dimensions, is studied. Some aspects of local differential geometry are formulated as Vect(N) representation theory. There is a new class of modules, conformal fields, whose restrictions to the subalgebra sl(N+1)⊂ Vect (N) are finite-dimensional sl (N+1) representations. In this regard they are simpler than tensor fields. Fock modules are also constructed. Infinities, which are unremovable even by normal ordering, arise unless bosonic and fermionic degrees of freedom match.

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17

Kincaid, Joshua, and Tevian Dray. "Division algebra representations of SO(4, 2)." Modern Physics Letters A 29, no. 25 (August 20, 2014): 1450128. http://dx.doi.org/10.1142/s0217732314501284.

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Representations of SO (4, 2) are constructed using 4×4 and 2×2 matrices with elements in ℍ' ⊗ ℂ and the known isomorphism between the conformal group and SO (4, 2) is written explicitly in terms of the 4×4 representation. The Clifford algebra structure of SO (4, 2) is briefly discussed in this language, as is its relationship to other groups of physical interest.

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18

Xu, Xiaoping. "Conformal oscillator representations of orthosymplectic Lie superalgebras." Journal of Pure and Applied Algebra 225, no. 3 (March 2021): 106530. http://dx.doi.org/10.1016/j.jpaa.2020.106530.

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19

Kolesnikov, Pavel. "Universally defined representations of Lie conformal superalgebras." Journal of Symbolic Computation 43, no. 6-7 (June 2008): 406–21. http://dx.doi.org/10.1016/j.jsc.2007.02.004.

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20

Binegar, B. "Conformal superalgebras, massless representations, and hidden symmetries." Physical Review D 34, no. 2 (July 15, 1986): 525–32. http://dx.doi.org/10.1103/physrevd.34.525.

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21

SIEGEL, W. "ALL FREE CONFORMAL REPRESENTATIONS IN ALL DIMENSIONS." International Journal of Modern Physics A 04, no. 08 (May 10, 1989): 2015–20. http://dx.doi.org/10.1142/s0217751x89000819.

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We find all free, massless, finite-dimensional, irreducible representations of the conformal group SO(D, 2) in all space-time dimensions D. In odd D they are only the scalar and spinor, but in even D they are all those which are (anti-)self-dual (chiral) on all vector indices. These are exactly the ones described by the mechanics of the extended spinning particle.

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22

Goulian, Mark D., and Oscar F. Hernández. "Constraints on representations of conformal field theories." Physics Letters B 215, no. 3 (December 1988): 511–16. http://dx.doi.org/10.1016/0370-2693(88)91351-2.

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23

Xu, XiaoPing. "Conformal oscillator representations of orthogonal Lie algebras." Science China Mathematics 59, no. 1 (August 14, 2015): 37–48. http://dx.doi.org/10.1007/s11425-015-5058-5.

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24

Friedrich, Roland, and Wendelin Werner. "Conformal Restriction, Highest-Weight Representations and SLE." Communications in Mathematical Physics 243, no. 1 (November 1, 2003): 105–22. http://dx.doi.org/10.1007/s00220-003-0956-8.

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25

Gervais, J. L., and A. Neveu. "Oscillator representations of the 2D-conformal algebra." Communications in Mathematical Physics 100, no. 1 (March 1985): 15–21. http://dx.doi.org/10.1007/bf01212685.

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26

Branson, Thomas P. "Group representations arising from Lorentz conformal geometry." Journal of Functional Analysis 74, no. 2 (October 1987): 199–291. http://dx.doi.org/10.1016/0022-1236(87)90025-5.

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27

Dolan, L., P. Goddard, and P. Montague. "Conformal field theories, representations and lattice constructions." Communications in Mathematical Physics 179, no. 1 (July 1996): 61–120. http://dx.doi.org/10.1007/bf02103716.

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28

Xia, Chunguang. "Representations of twisted infinite Lie conformal superalgebras." Journal of Algebra 596 (April 2022): 155–76. http://dx.doi.org/10.1016/j.jalgebra.2021.12.038.

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29

Gao, Dongfang, and Yun Gao. "Representations of the Planar Galilean Conformal Algebra." Communications in Mathematical Physics 391, no. 1 (January 30, 2022): 199–221. http://dx.doi.org/10.1007/s00220-021-04302-9.

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30

ODAKE, SATORU. "c=3d CONFORMAL ALGEBRA WITH EXTENDED SUPERSYMMETRY." Modern Physics Letters A 05, no. 08 (March 30, 1990): 561–80. http://dx.doi.org/10.1142/s0217732390000640.

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We define a superconformal algebra with the central charge c=3d, which is the symmetry of the non-linear σ model on a complex d dimensional Calabi-Yau manifold. The c=3d algebra is an extended superconformal algebra obtained by adding the spectral flow generators to the N=2 superconformal algebra. We study the representation theory and show that its representations are invariant under the integer-shift spectral flow. We present the character formulas and their modular transformation properties. We also discuss the relation to the N=4 superconformal algebra.

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31

FERRARA, SERGIO, and EMERY SOKATCHEV. "REPRESENTATIONS OF SUPERCONFORMAL ALGEBRAS IN THE AdS7/4/CFT6/3 CORRESPONDENCE." International Journal of Modern Physics A 16, no. 05 (February 20, 2001): 976–89. http://dx.doi.org/10.1142/s0217751x01004050.

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We perform a general analysis of representations of the superconformal algebras OSp (8/4, ℝ) and OSp (8*/2N) in harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different types of massless conformal superfields ("supersingletons"). In particular, all "short multiplets" are classified. Representations undergoing shortening have "protected dimension" and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.

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32

MIZOGUCHI, SHUN'YA. "LOCALIZED MODES IN SINGULAR CALABI-YAU CONFORMAL FIELD THEORIES." International Journal of Modern Physics A 23, no. 14n15 (June 20, 2008): 2184–86. http://dx.doi.org/10.1142/s0217751x08040779.

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We construct spacetime supersymmetric, modular invariant partition functions for type II and heterotic strings on the conifold-type singularities such that they include contributions coming from the discrete-series representations of SL(2, R). In particular for the E8 × E8 heterotic case, they are in the 27 representation of E6 and localized on a four-dimensional "brane" at the tip of the cigar geometry.

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33

Ohya, Satoshi. "Intertwining operator in thermal CFTd." International Journal of Modern Physics A 32, no. 02n03 (January 25, 2017): 1750006. http://dx.doi.org/10.1142/s0217751x17500063.

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It has long been known that two-point functions of conformal field theory (CFT) are nothing but the integral kernels of intertwining operators for two equivalent representations of conformal algebra. Such intertwining operators are known to fulfill some operator identities — the intertwining relations — in the representation space of conformal algebra. Meanwhile, it has been known that the S-matrix operator in scattering theory is nothing but the intertwining operator between the Hilbert spaces of in- and out-particles. Inspired by this algebraic resemblance, in this paper, we develop a simple Lie-algebraic approach to momentum-space two-point functions of thermal CFT living on the hyperbolic space–time [Formula: see text] by exploiting the idea of Kerimov’s intertwining operator approach to exact S-matrix. We show that in thermal CFT on [Formula: see text], the intertwining relations reduce to certain linear recurrence relations for two-point functions in the complex momentum space. By solving these recurrence relations, we obtain the momentum-space representations of advanced and retarded two-point functions as well as positive- and negative-frequency two-point Wightman functions for a scalar primary operator in arbitrary space–time dimension [Formula: see text].

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34

HOSOMICHI, KAZUO, and YUJI SATOH. "OPERATOR PRODUCT EXPANSION IN SL(2) CONFORMAL FIELD THEORY." Modern Physics Letters A 17, no. 11 (April 10, 2002): 683–93. http://dx.doi.org/10.1142/s021773230200703x.

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In the conformal field theories having affine SL(2) symmetry, we study the operator product expansion (OPE) involving primary fields in highest weight representations. For this purpose, we analyze properties of primary fields with definite SL(2) weights, and calculate their two- and three-point functions. Using these correlators, we show that the correct OPE is obtained when one of the primary fields belongs to the degenerate highest weight representation. We briefly comment on the OPE in the SL (2,R) WZNW model.

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35

Friedrich, Roland, and Wendelin Werner. "Conformal fields, restriction properties, degenerate representations and SLE." Comptes Rendus Mathematique 335, no. 11 (December 2002): 947–52. http://dx.doi.org/10.1016/s1631-073x(02)02581-5.

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36

Mathieu, P., and M. A. Walton. "On principal admissible representations and conformal field theory." Nuclear Physics B 553, no. 3 (August 1999): 533–58. http://dx.doi.org/10.1016/s0550-3213(99)00252-7.

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37

Gannon, Terry. "Boundary conformal field theory and fusion ring representations." Nuclear Physics B 627, no. 3 (April 2002): 506–64. http://dx.doi.org/10.1016/s0550-3213(01)00632-0.

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38

Dobrev, V. K., and R. Floreanini. "The massless representations of the conformal quantum algebra." Journal of Physics A: Mathematical and General 27, no. 14 (July 21, 1994): 4831–40. http://dx.doi.org/10.1088/0305-4470/27/14/012.

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39

Lagomasino, Guillermo López, Domingo Pestana, José M. Rodríguez, and Dmitry Yakubovich. "Computation of conformal representations of compact Riemann surfaces." Mathematics of Computation 79, no. 269 (January 1, 2010): 365. http://dx.doi.org/10.1090/s0025-5718-09-02265-0.

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40

Avakyan, R. M., E. V. Chubaryan, G. H. Harutyunyan, A. V. Hovsepyan, and A. S. Kotanjyan. "Cosmological models in conformal representations of Jordan theory." Journal of Physics: Conference Series 496 (March 25, 2014): 012020. http://dx.doi.org/10.1088/1742-6596/496/1/012020.

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41

Boyallian, Carina, Victor G. Kac, and Jose I. Liberati. "Finite growth representations of infinite Lie conformal algebras." Journal of Mathematical Physics 44, no. 2 (2003): 754. http://dx.doi.org/10.1063/1.1534890.

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42

Nojima, Ryo. "On Induction for Twisted Representations of Conformal Nets." Annales Henri Poincaré 21, no. 10 (September 11, 2020): 3217–51. http://dx.doi.org/10.1007/s00023-020-00952-y.

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43

Kedem, R., T. R. Klassen, B. M. McCoy, and E. Melzer. "Fermionic sum representations for conformal field theory characters." Physics Letters B 307, no. 1-2 (June 1993): 68–76. http://dx.doi.org/10.1016/0370-2693(93)90194-m.

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44

Da̧browski, L., V. K. Dobrev, R. Floreanini, and V. Husain. "Positive energy representations of the conformal quantum algebra." Physics Letters B 302, no. 2-3 (March 1993): 215–22. http://dx.doi.org/10.1016/0370-2693(93)90387-w.

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45

PIUNIKHIN, SERGEY. "RESHETIKHIN-TURAEV AND CRANE-KOHNO-KONTSEVICH 3-MANIFOLD INVARIANTS COINCIDE." Journal of Knot Theory and Its Ramifications 02, no. 01 (March 1993): 65–95. http://dx.doi.org/10.1142/s0218216593000052.

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The coincidence of two different presentations of Witten 3-manifold invariants is proved. One of them, invented by Reshetikhin and Turaev, is based on the surgery presentation a of 3-manifold and the representation theory of quantum groups; another one, invented by Kohno and Crane and, in slightly different language by Kontsevich, is based on a Heegaard decomposition of a 3-manifold and representations of the Teichmuller group, arising in conformal field theory. The explicit formula for the matrix elements of generators of the Teichmuller group in the space of conformal blocks in the SU(2) k, WZNW-model is given,using the Jones polynomial of certain links.

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46

Coman, Ioana, Elli Pomoni, and Jörg Teschner. "Toda Conformal Blocks, Quantum Groups, and Flat Connections." Communications in Mathematical Physics 375, no. 2 (November 7, 2019): 1117–58. http://dx.doi.org/10.1007/s00220-019-03617-y.

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Abstract This paper investigates the relations between the Toda conformal field theories, quantum group theory and the quantisation of moduli spaces of flat connections. We use the free field representation of the $${{\mathcal {W}}}$$W-algebras to define natural bases for spaces of conformal blocks of the Toda conformal field theory associated to the Lie algebra $${\mathfrak {s}}{\mathfrak {l}}_3$$sl3 on the three-punctured sphere with representations of generic type associated to the three punctures. The operator-valued monodromies of degenerate fields can be used to describe the quantisation of the moduli spaces of flat $$\mathrm {SL}(3)$$SL(3)-connections. It is shown that the matrix elements of the monodromies can be expressed as Laurent polynomials of more elementary operators which have a simple definition in the free field representation. These operators are identified as quantised counterparts of natural higher rank analogs of the Fenchel–Nielsen coordinates from Teichmüller theory. Possible applications to the study of the non-Lagrangian SUSY field theories are briefly outlined.

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47

GIERES, FRANÇOIS. "CONFORMALLY COVARIANT OPERATORS ON RIEMANN SURFACES (WITH APPLICATIONS TO CONFORMAL AND INTEGRABLE MODELS)." International Journal of Modern Physics A 08, no. 01 (January 10, 1993): 1–58. http://dx.doi.org/10.1142/s0217751x93000023.

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Following the standard procedure for gauging in Yang-Mills and gravitational theories, we introduce projective connections to covariantize differential operators on Riemann surfaces. We present applications in integrable models (Lax pairs, Poisson operators) and conformal models (conformal Ward identity, diffeomorphism anomaly, Krichever-Novikov algebra, Virasoro algebra and its representations, Kac-Moody algebras, W-algebras, WZW model, twistor theory). The generalization to higher dimensions is indicated and the whole discussion is generalized to the supersymmetric case (both in superspace and in component field formalism).

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48

Pevzner, M. "Analyse conforme sur les algèbres de Jordan." Journal of the Australian Mathematical Society 73, no. 2 (October 2002): 279–300. http://dx.doi.org/10.1017/s1446788700008831.

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AbstractWe construct the Weil representation of the Kantor-Koecher-Tits Lie algebra g associated to a simple real Jordan algebra V. Later we introduce a family of integral operators intertwining the Weil representation with the infinitesimal representations of the degenerate principal series of the conformal group G of the Jordan algebra V. The decomposition of L2(V) in the case of Jordan algebra of real square matrices is given using this construction.

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49

METSAEV, R. R. "ALL CONFORMAL INVARIANT REPRESENTATIONS OF d-DIMENSIONAL ANTI-DE SITTER GROUP." Modern Physics Letters A 10, no. 23 (July 30, 1995): 1719–31. http://dx.doi.org/10.1142/s0217732395001848.

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All the irreducible representations of the anti-de Sitter group which are relevant for elementary particles and which can be realized as irreducible representations of the conformal group are found. It is shown that all these representations correspond to massless representations which arise from considerations of gauge invariance. The problem is studied for arbitrary d>2 dimensional anti-de Sitter group.

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50

ZAMOLODCHIKOV, A. B. "EXACT SOLUTIONS OF CONFORMAL FIELD THEORY IN TWO DIMENSIONS AND CRITICAL PHENOMENA." Reviews in Mathematical Physics 01, no. 02n03 (January 1989): 197–234. http://dx.doi.org/10.1142/s0129055x89000110.

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Abstract:

Modern development of conformal field theory in two dimensions and its applications to critical phenomena are briefly reviewed. The specific properties of the renormalization group in two dimensions and the fundamentals of 2-dimensional conformal field theory are presented. The properties of degenerate representations of the Virasoro algebra and other infinite dimensional algebras, "minimal" models of conformal and superconformal field theory, "parafermionic" and other symmetries are discussed. We also investigate a perturbation theory around conformal solutions of field theory.

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