RevModPhys.84.671

18d5 c3 2 3 32 9 3 1 2

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Unformatted text preview: . As shown by Nicolis, Rattazzi, and Trincherini (2008), the terms (8.19) are the only polynomial terms in four dimensions with these properties. The Galileon was first discovered in studies of the DGP brane world model (Dvali, Gabadadze, and Porrati, 2000a), for which the cubic Galileon L3 was found to describe the leading interactions of the brane bending mode (Luty, Porrati, and Rattazzi, 2003; Nicolis and Rattazzi, 2004). The rest of the Galileons were then discovered by Nicolis, Rattazzi, and Trincherini (2008), by abstracting the properties of the cubic term away from DGP. They have some other very interesting properties, such as a nonrenormalization theorem [see, e.g., Sec. VI of Hinterbichler, Trodden, and Wesley (2010)], and a connection to the Lovelock invariants through brane embedding (de Rham and Tolley, 2010). Because of these unexpected and interesting properties, they have since taken on a life of their own. They have been generalized in many directions (Deffayet, Deser, and Esposito-Farese, 2009, 2010; Deffayet, Esposito-Farese, and Vikman, 2009; Padilla, Saffin, and Zhou, 2010; Deffayet et al., 2011; Goon, Hinterbichler, and Trodden, 2011; Khoury, Lehners, and Ovrut, 2011) and are the subject of much recent activity [see, for instance, the many papers citing Nicolis, Rattazzi, and Trincherini (2008)]. The fact that the equations are second order ensures that, unlike Eq. (7.10), no extra degrees of freedom propagate. In Rev. Mod. Phys., Vol. 84, No. 2, April–June 2012 699 fact, as pointed out by de Rham and Gabadadze (2010a), the properties (A.17) of the tensors X guarantee that there are no ghosts in the Lagrangian (8.10) of the decoupling limit theory.14 By going through a Hamiltonian analysis similar to that of Sec. II.A, we see that h00 and h0i remain Lagrange multipliers enforcing first class constraints [as they should since the Lagrangian (8.10) is gauge invariant]. In addition, the equations of motion remain second order, so the decoupling limit Lagrangian (8.10) is free of the Boulware-Deser ghost and propagates 3 degrees of freedom around any background. Once the 2 degrees of freedom of the vector A are included, and if there are no ghosts in the vector part or its interactions, the total number of degrees of freedom goes to 5, the same as the linear massive graviton. The vector interactions were shown to be ghost free at cubic order by de Rham and Gabadadze (2010b). de Rham, Gabadadze, and Tolley (2010) showed that the full theory beyond the decoupling limit, including all the fields, is ghost free, up to quartic order in the fields. This guarantees that any ghost must carry a mass scale larger than Ã3 and hence can be consistently excluded from the quantum theory. Finally, Hassan and Rosen (2011a, 2011c) showed, using the Hamiltonian formalism, that the full theory, including all modes and to all orders beyond the decoupling limit, carries 5 degrees of freedom. The Ã3 theory is therefore free of the Boulwar...
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This document was uploaded on 09/28/2013.

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