1304.3051 (Borut Bajc et al.)

On the matching method and the Goldstone theorem in holography    [PDF]

Borut Bajc, Adrian R. Lugo

We study the transition of a scalar field in a fixed $AdS_{d+1}$ background between an extremum and a minimum of a potential. We first prove that the potential involved cannot be generic, i.e. that a fine-tuning of their parameters is mandatory for the solution to exist. We compute analytically the solution to the perturbation equation by generalizing the usual matching method to higher orders and find the propagator of the boundary theory operator defined through the AdS-CFT correspondence. We show that it always presents a simple pole at $q^2=0$ in accordance with the Goldstone theorem applied to a spontaneously broken dilatation invariance. The result is supported also by a WKB calculation.

View original: http://arxiv.org/abs/1304.3051