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Nuclear Physics B

Four-point correlation functions and the operator algebra in 2D conformal invariant theories with central charge C≤1

Vl.S. Dotsenko, V.A. Fateev

Published Jan 1, 1985• 782 citations
Publisher
DOI
10.1016/s0550-3213(85)80004-3

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We make a detailed study of the infinite dimensional Galilean Conformal Algebra (GCA) in the case of two spacetime dimensions. Classically, this algebra is precisely obtained from a contraction of the generators of the relativistic conformal symmetry in 2 d . Here we find quantum mechanical realisations of the (centrally extended) GCA by considering scaling limits of certain 2d CFTs. These parent CFTs are non-unitary and have their left and right central charges become large in magnitude and opposite in sign. We therefore develop, in parallel to the usual machinery for 2 d CFT, many of the tools for the analysis of the quantum mechanical GCA. These include the representation theory based on GCA primaries, Ward identities for their correlation functions and a nonrelativistic Kac table. In particular, the null vectors of the GCA lead to differential equations for the four point function. The solution to these equations in the simplest case is explicitly obtained and checked to be consistent with various requirements.