Rotational invariance and Goldstone modes in nematic elastomers and gels

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Abstract
We investigate the symmetries of elastomers and gels cross-linked in a nematic state. The coupling between the local nematic order parameter and an applied deformation leads to a class of uniform deformations which cost no elastic energy, when accompanied by a given rotation of the nematic director; this is a specific realization of a class of soft modes originally proposed, on symmetry arguments, by Golubović and Lubensky [Phys. Rev. Lett. 63 (1989) 1082]. The corresponding elastic theory has a set of Goldstone modes which possesses singular fluctuations. We describe several experimental signatures of these ideas, and elucidate the physical picture of these soft modes

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