GCA in 2d

Arjun Bagchi, Rajesh Gopakumar, Ipsita Mandal, Akitsugu Miwa

Research output: Contribution to journalArticlepeer-review


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 equations in the simplest case is explicitly obtained and checked to be consistent with various requirements.
Original languageEnglish
Pages (from-to)-
Number of pages38
JournalJournal of High Energy Physics
Issue number4
Publication statusPublished - 6 Dec 2009


  • hep-th
  • cond-mat.stat-mech
  • math-ph
  • math.MP
  • Field Theories in Lower Dimensions
  • Conformal and W Symmetry


Dive into the research topics of 'GCA in 2d'. Together they form a unique fingerprint.

Cite this