Quantization ofncoupled scalar field theory

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.

Cosmological three-coupled scalar theory for the dS/LCFT correspondence

“…Hence, the only non-zero power spectrum is P 22,0 which is surly non-negative. This could be also proved by using the BRST quantization in the Minkowski spacetime (equivalently, the truncation process in the dS/QFT correspondence in the subhorizon limit) [15,16].…”

“…and 16) which implies that P 23,0 and P 23,0 approach zero when z → 0. In deriving (5.15) and (5.16), ξ was chosen to be a real quantity given by…”

“…We should explain what the BD vacuum is really, since the three-coupled scalar theory is quite different from the three free-scalar theory without µ 2 ϕ 1 ϕ 2 . We mention briefly how to quantize the n-coupled scalar field theory within the Becchi-Rouet-Stora-Tyutin (BRST) quantization scheme in Minkowski space [16]. It has been carried out by introducing the FP ghost action composed of n-FP ghost fields.…”

“…For simplicity, it is natural to consider a sixth-order scalar field theory to cast off the non-unitarity problem. In order to avoid a difficulty in dealing with a single sixth-order theory, we introduce an equivalent three-coupled scalar fields (φ 1 , φ 2 , φ 3 ) with degenerate masses m 2 [15,16]. A bulk version dual to the truncation process to find a unitary CFT in the rank-3 LCFT corresponds to selecting a physical field φ 2 with positive norm propagating on the dS spacetime.…”

“…We consider the three-coupled scalar field theory where three fields (φ 1 , φ 2 , φ 3 ) are coupled minimally to Einstein gravity as [13,16,24] S = S E + S TCS (2.1)…”