Quantization of n coupled scalar field theory

TL;DR

This paper investigates a model of n coupled scalar fields with degenerate masses, quantized via BRST, revealing a non-trivial structure for odd n and providing insights into the unitarity of dual conformal field theories.

Contribution

It extends the BRST quantization scheme to n coupled scalars, demonstrating the existence of a physical subspace for odd n and clarifying the truncation mechanism for unitarity.

Findings

Positive norm subspace exists for odd n

Only vacuum state for even n

Truncation mechanism explained as a quartet mechanism

Abstract

We study a model of n coupled scalar fields in Minkowski spacetime where all masses degenerate, which is considered as a toy model of polycritical gravity on AdS spacetime. We quantize this model within the Becchi-Rouet-Stora-Tyutin (BRST) scheme by introducing n Faddeev-Popov (FP) ghost fields. Extending a BRST quartet generated by two scalars and two FP ghosts to n scalars and n FP ghosts, there remains a physical subspace with positive norm for odd n, but there exists only the vacuum for even n. This clearly shows a non-triviality of odd-higher order derivative scalar field theories. This is helpful to understand the truncation mechanism which is used to obtain a unitary conformal field theory dual to linearized polycritical gravity. It turns out that the truncation mechanism is nothing but a general quartet mechanism appeared when introducing the FP ghost action.