Nonlinear realizations of symmetries and unphysical Goldstone bosons

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.

arXiv comment24 pages; references added

References in corpus (13)

• Spontaneously Broken Spacetime Symmetries and Goldstone's Theorem
• Matter couplings in partially broken extended supersymmetry
• N=1 D=4 supermembrane in the coset approach
• The construction of brane and superbrane actions using non-linear realisations
• Automorphisms, Non-linear Realizations and Branes
• Conformal and Superconformal Mechanics Revisited
• Superbranes and Super Born-Infeld Theories from Nonlinear Realizations
• Superworldvolume dynamics of superbranes from nonlinear realizations
• Partial Supersymmetry Breaking and AdS4 Supermembrane
• Supersymmetric Mechanics in Superspace
• AdS_{d+1} --> AdS_d
• Goldstone multiplet for partially broken superconformal symmetry
• `Conformal Theories - AdS Branes' Transform, or One More Face of AdS/CFT

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