BRST quantization of a sixth-order derivative scalar field theory

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.