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2012

Classical Duals, Legendre Transforms and the Vainshtein Mechanism

Padilla, Antonio, Saffin, Paul M.

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We show how to generalize the classical duals found by Gabadadze {\it et al} to a very large class of self-interacting theories.

This enables one to adopt a perturbative description beyond the scale at which classical perturbation theory breaks down in the original theory.
This is particularly relevant if we want to test modified gravity scenarios that exhibit Vainshtein screening on solar system scales.
We recognise the duals as being related to the Legendre transform of the original Lagrangian, and present a practical method for finding the dual in general; our methods can also be applied to self-interacting theories with a hierarchy of strong coupling scales, and with multiple fields.

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C. Burrage and D. Seery, JCAP 1008
Original
1927
Earlier work this paper cites.
N. Arkani-Hamed, S. Dimopoulos, G. Dvali and G. Gabadadze, hep-th/0209227. S. M. Carroll and M. M. Guica, hep-th/0302067. C. Charmousis, E. J. Copeland, A. Padilla and P. M. Saffin, Phys. Rev. Lett. 108
Original
2000
Earlier work this paper cites.
G. R. Dvali, G. Gabadadze and M. Porrati, Phys. Lett. B 485
2000
Earlier work this paper cites.
A. I. Vainshtein, Phys. Lett. B39
2002
Earlier work this paper cites.
M. A. Luty, M. Porrati and R. Rattazzi, JHEP 0309
2003
Earlier work this paper cites.

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Then

A. Nicolis, R. Rattazzi and E. Trincherini, Phys. Rev. D 79
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S. M. Carroll, V. Duvvuri, M. Trodden and M. S. Turner, Phys. Rev. D 70
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C. de Rham and G. Gabadadze, Phys. Rev. D 82
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