BRST quantization of a sixth-order derivative scalar field theory

TL;DR

This paper explores the BRST quantization of a sixth-order derivative scalar field model in Minkowski spacetime, demonstrating consistent quantization and positive norm states despite the lack of explicit gauge symmetry.

Contribution

It introduces a BRST quantization scheme for a higher-derivative scalar field theory, revealing a non-trivial positive norm subspace and potential links to logarithmic conformal field theories.

Findings

Successful BRST quantization of a sixth-order derivative scalar field.

Identification of a positive norm subspace within the theory.

Potential connection to unitary truncation in logarithmic conformal field theory.

Abstract

We study a sixth order derivative scalar field model in Minkowski spacetime as a toy model of higher-derivative critical gravity theories. This model is consistently quantized when using the Becchi-Rouet-Stora-Tyutin (BRST) quantization scheme even though it does not show gauge symmetry manifestly. Imposing a BRST quartet generated by two scalars and ghosts, there remains a non-trivial subspace with positive norm. This might be interpreted as a Minkowskian dual version of the unitary truncation in the logarithmic conformal field theory.