Yong-Wan Kim, Yun Soo Myung, Young-Jai Park
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 theories. This is helpful to understand the truncation mechanism which is used to obtain the unitary conformal field theory dual to the polycritical gravity. It turns out that the truncation mechanism is nothing but a general quartet mechanism appeared when introducing the FP ghost action.
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http://arxiv.org/abs/1307.6932
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