Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-06-07
Annalen Phys. 10 (2001) 935-964
Physics
High Energy Physics
High Energy Physics - Theory
This work was presented in part at the meeting of the Deutsche Physikalische Gesellschaft held in Bonn, 26-29 March 2001. To a
Scientific paper
10.1002/1521-3889(200111)10:11/1
In this paper, two things are done. (i) Using cohomological techniques, we explore the consistent deformations of linearized conformal gravity in 4 dimensions. We show that the only possibility involving no more than 4 derivatives of the metric (i.e., terms of the form $\partial^4 g_{\mu \nu}$, $\partial^3 g_{\mu \nu} \partial g_{\alpha \beta}$, $\partial^2 g_{\mu \nu} \partial^2g_{\alpha \beta}$, $\partial^2 g_{\mu \nu} \partial g_{\alpha \beta} \partial g_{\rho \sigma}$ or $\partial g_{\mu \nu} \partial g_{\alpha \beta} \partial g_{\rho \sigma} \partial g_{\gamma \delta}$ with coefficients that involve undifferentiated metric components - or terms with less derivatives) is given by the Weyl action $\int d^4x \sqrt{-g} W_{\a\b\g\d} W^{\a\b\g\d}$, in much the same way as the Einstein-Hilbert action describes the only consistent manner to make a Pauli-Fierz massless spin-2 field self-interact with no more than 2 derivatives. No a priori requirement of invariance under diffeomorphisms is imposed: this follows automatically from consistency. (ii) We then turn to "multi-Weyl graviton" theories. We show the impossibility to introduce cross-interactions between the different types of Weyl gravitons if one requests that the action reduces, in the free limit, to a sum of linearized Weyl actions. However, if different free limits are authorized, cross-couplings become possible. An explicit example is given. We discuss also how the results extend to other spacetime dimensions.
Boulanger Nicolas
Henneaux Marc
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