GCA in 2d

被引：151

作者：

Bagchi, Arjun ^{[1
]}

Gopakumar, Rajesh ^{[1
]}

Mandal, Ipsita ^{[1
,2
]}

Miwa, Akitsugu ^{[1
]}

机构：

[1] Harish Chandra Res Inst, Allahabad 211019, Uttar Pradesh, India

[2] Univ Paris 06, LPTHE, F-75252 Paris 05, France

来源：

JOURNAL OF HIGH ENERGY PHYSICS | 2010年 / 08期

关键词：

Field Theories in Lower Dimensions; Conformal and W Symmetry; INVARIANCE; SCALE;

D O I：

10.1007/JHEP08(2010)004

中图分类号：

O412 [相对论、场论]; O572.2 [粒子物理学];

学科分类号：

摘要：

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.

引用

页数：40