期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 8, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP08(2010)004
关键词
Field Theories in Lower Dimensions; Conformal and W Symmetry
资金
- Dept. of Science and Technology of the Govt. of India
- STFC [ST/G000522/1] Funding Source: UKRI
- Science and Technology Facilities Council [ST/G000522/1] Funding Source: researchfish
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 2d. 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 2d 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 equation in the simplest case is explicity obtained and checked to be consistent with various requirements.
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