Path-integral quantization of tensionless (super) string

TL;DR

This paper develops a path-integral quantization framework for tensionless (super)strings, introduces BMS ghosts, and identifies critical dimensions and underlying symmetries, revealing connections to BMS-Kac-Moody algebras.

Contribution

It provides a novel path-integral quantization approach for tensionless superstrings, including ghost fields and symmetry analysis, extending understanding of their critical dimensions and algebraic structures.

Findings

Critical dimensions match those of usual superstrings for certain tensionless superstrings.

BMS ghosts form free field theories with BMS-Kac-Moody symmetries.

Underlying symmetries involve non-abelian, non-semi-simple Lie algebras.

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.