International Journal of Theoretical Physics, Vol. 44, No. 10, October 2005 ( C  2005) DOI: 10.1007/s10773-005-8892-0 Deconstruction of Gravity C. Deffayet 1,2,4 and J. Mourad 1,3 We review how one can construct a deconstructed gravity by a transverse latticification of 5D General Relativity. The obtained theory is a multigravity theory, with link fields that are explicitly constructed out of the metric. We also discuss the spectrum of the theory at the level of the linearized theory. KEY WORDS: gravity; deconstruction; extra-dimensions; massive gravity. 1. INTRODUCTION An interesting procedure has recently been proposed to obtain from a five- dimensional Yang–Mills theory a four-dimensional theory which approaches the five-dimensional one in the infrared and which has a finite number of modes (Arkani-Hamed et al., 2001; Hill et al., 2001). The key point in the approach is to replace the extra component of the vector field by bifundamental scalars which can be viewed as arising from the latticized Wilson line along the fifth dimension. A similar construction for gravity would be highly desirable, for many obvious reasons. If one follows the same path as for Yang–Mills theories (Arkani-Hamed et al., 2003; Arkani-Hamed and Schwartz, 2003; Schwartz, 2003,?), the sought for deconstructed gravity would be likely to look like some type of multigravity the- ory, and indeed those type of theories are known to suffer from various pathologies related to those of the Pauli–Fierz theory for a single massive graviton (Fierz and Pauli, 1939; Boulware and Deser, 1972; Isham et al., 1971; Aragone and Chela- Flores, 1972; Salam and Strathdee, 1977; Isham and Storey, 1978; Chamseddine, 2003; Cutler and Wald, 1987; Wald, 1987; Boulanger et al., 2001; Damour and Kogan, 2002; Damour et al., 2002, 2003; Dolan and Duff, 1984; Aulakh and 1 APC, UMR 7164 (CNRS, Universit´ e Paris 7, CEA, Observatoire de Paris), Paris Cedex 05, France. 2 GReCO/IAP, UMR 7095 (CNRS, Universit´ e Paris 6), Paris, France. 3 Laboratoire de Physique Th´ eorique, UMR 8627 (CNRS, Universit´ e Paris 11), Universit´ e Paris XI, Orsay Cedex, France. 4 To whom correspondence should be addressed at APC, UMR 7164 (CNRS, Universit´ e Paris 7, CEA, Observatoire de Paris), 11 place Marcelin Berthelot, F-75231 Paris Cedex 05, France; e-mail: deffayet@iap.fr. 1743 0020-7748/05/1000-1743/0 C  2005 Springer Science+Business Media, Inc.