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Nonlinear completion of massive gravity of the Fierz-Pauli type.pdf

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Nonlinear completion of massive gravity of the Fierz-Pauli type

a r X i v : 0 7 1 0 .3 6 2 0 v 1 [ h e p - t h ] 1 9 O c t 2 0 0 7 Nonlinear completion of massive gravity of the Fierz-Pauli type Shinji Hamamoto Department of Physics, University of Toyama, Toyama 930-8555, Japan E-mail: hamamoto@sci.u-toyama.ac.jp Abstract. A possible nonlinear completion of massive gravity of the Fierz-Pauli type is proposed. The theory describes a system consisting of a massive tensor field of the Fierz-Pauli type and an additional massive vector field. Massless limit as well as flat-spacetime limit can be taken smoothly. Constructing a nonlinear version of the physical-state condition which drives an extra scalar ghost from physical states is still unsettled. PACS numbers: 04.50.Kd, 04.60.-m, 11.15.-q Submitted to: JPhysA Special Issue-QTS5 Nonlinear completion of massive gravity of the Fierz-Pauli type 2 1. Introduction In a series of papers [1, 2, 3, 4, 5], attempts to construct the theory of massive gravity with smooth massless limit were made. We studied infrared regularization of linearized massive tensor fields in [1, 2, 3, 4]. Two model theories were considered: one is of the pure-tensor (PT) type, which describes an ordinary massive tensor field of five degrees of freedom; the other is of the additional-scalar-ghost (ASG) type, which contains a scalar ghost in addition to the pure tensor. The ASG model shows second-order massless singularities in two- point functions, whereas the PT model contains fourth-order singularities. It turns out that two procedures, the BRS one and the Nakanishi one, are effective in regularizing such singularities. The BRS procedure produces transparent structures to the resulting theories, as compared with the Nakanishi one. So we studied the former in detail. In order to drive away the second-order infrared singularities in the ASG model, we introduce an auxiliary vector-like field, and promote the original theory to the one that is invariant under the vector BRS transformation. On the other hand, t