Path-integral quantization of tensionless (super) string

Abstract

In this work, we study the tensionless (super)string in the formalism of path-integral quantization. We introduce BMS $bc$ and $\beta \gamma$ ghosts intrinsically by accounting for the Faddeev-Popov determinants appeared in fixing the gauges. We then do canonical quantization and obtain the critical dimensions for different tensionless strings. We find that among four kinds of tensionless superstrings, the $\mathcal{N}=2$ homogeneous and inhomogeneous doublet tensionless superstrings have the same critical dimension as the usual superstrings. Taking the BMS $bc$ and $\beta \gamma$ ghosts as new types of BMS free field theories, we find that their enhanced underlying symmetries are generated by BMS-Kac-Moody algebras, with the Kac-Moody subalgebras being built from a three-dimensional non-abelian and non-semi-simple Lie algebra.

49 pages, 3 tables; v2: typos corrected; v3: discussion of the enlarged BMS symmetry completed, references added; v4: matches JHEP version