Quantization ofncoupled scalar field theory

Abstract

We study a model of $n$ coupled scalar fields in Minkowski spacetime in which all masses degenerate, which is considered as a toy model of polycritical gravity on anti-de Sitter spacetime. We quantize this model within the Becchi--Rouet--Stora--Tyutin scheme by introducing $n$ Faddeev--Popov (FP) ghost fields. Extending a Becchi--Rouet--Stora--Tyutin 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 nontriviality 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 that appears when introducing the FP ghost action.