Nonlinear realizations of symmetries and unphysical Goldstone bosons

TL;DR

This work analyzes why certain Goldstone bosons arising from nonlinearly realized spacetime symmetries are unphysical and can be removed via the inverse Higgs constraint or equations of motion. It argues that these unphysical modes are gauge degrees of freedom associated with an enlarged isotropy group, a perspective supported by coset constructions and several prototypical examples, including p-branes and conformally invariant dilaton actions. The paper demonstrates that the inverse Higgs constraint and EOM elimination are often equivalent for actions built from Cartan forms (Nambu-type brane actions) and explores how a coset parametrization that exhibits a right action by the enlarged isotropy group can yield formulations where the unphysical Goldstones drop out explicitly. It also discusses conformally invariant dilaton actions, showing how an IH-free covariant form can be obtained, and relates these structures to AdS bases, thereby providing a unifying interpretation of gauge-like unphysical Goldstones across multiple theories.

Abstract

The embedding of a $p$-brane into higher dimensional spacetime breaks not only translational symmetries transverse to the worldvolume, but also Lorentz symmetries. There exist formulations for $p$-brane actions which associate Goldstone bosons with the generators of the broken Lorentz symmetries. These Goldstone bosons are unphysical, in that they can be eliminated in favour of other Goldstone bosons either via their equations of motion or via the imposition of an inverse Higgs constraint. In this paper, we examine the inter-relationship between the coset parameterization necessary to implement the inverse Higgs constraint, the equivalence of the inverse Higgs constraint to equations of motion, and the ability to find versions of the action with no explicit dependence on the unphysical Goldstone bosons. This is evidence that the unphysical Goldstone bosons are gauge degrees of freedom associated with an enlarged isotropy group. In addition to $p$-brane actions, a number of other cases, including conformally invariant dilaton actions, are shown to exhibit the same structure.