Remarks on BMS3 invariant field theories: Correlation functions and nonunitary CFTs

Thiago Araujo

doi:10.1103/physrevd.98.026014

Abstract

We use the isomorphism between the BMS${}_3$ and the $W(2,2)$ algebras to reconsider some generic aspects of CFTs with the BMS${}_3$ algebra defined as a chiral symmetry. For unitarity theories, it is known that the extended symmetry generator acts trivially, and the resulting theory is equivalent to a CFT with a Virasoro symmetry only. For nonunitary CFTs, we define an operator depending on a nilpotent variable, and we organize the Verma module through the action of this new operator. Finally, we find the conditions imposed by the modified Ward identity.

Highlights

In a harbinger of the AdS=conformal field theories (CFTs) correspondence, Brown and Henneaux [1] showed that the naive asymptotic symmetry SLð2; RÞ × SLð2; RÞ of the AdS3 space is enhanced to two copies of the Virasoro algebra Vir ⊕ Vir
The BMS3 algebra can be obtained from two copies of the Virasoro algebra, with generators ðL; L Þ and central charges ðc; cÞ, respectively, when we define the operators
BMS algebra appears in several physical contexts, integrable models, for example [14,15], but we are interested in the study of some field theories that are invariant under this symmetry algebra

Summary

INTRODUCTION

In a harbinger of the AdS=CFT correspondence, Brown and Henneaux [1] showed that the naive asymptotic symmetry SLð2; RÞ × SLð2; RÞ of the AdS3 space is enhanced to two copies of the Virasoro algebra Vir ⊕ Vir. BMS algebra appears in several physical contexts, integrable models, for example [14,15], but we are interested in the study of some field theories that are invariant under this symmetry algebra. The main motivation in this text is toward the construction of CFTs with extended symmetries defined by another spin field of which the modes satisfy the BMS3 algebra. Under this perspective, we should consider that these (elusive) theories are similar to slðnÞ Toda CFTs, which are endowed with extended Wl algebras l ≥ 3 as chiral symmetries; see, for example, Refs. The βγ system generates a BMS3 algebra with central charges ðc; c2Þ 1⁄4 ð26; 0Þ, and the value of c2 may be changed by a twist

Sugawara construction

Null states

CORRELATION FUNCTIONS

NONUNITARY CFTs

CONCLUSIONS AND FURTHER DIRECTIONS