Abstract
It is well known that a physical medium that sets a Lorentz frame generates a Lorentz-breaking gap for a graviton. We examine such generated "mass" terms in the presence of a fluid medium whose ground state spontaneously breaks spatial translation invariance in $d = D+1$ spacetime dimensions, and for a solid in $D = 2$ spatial dimensions. By requiring energy positivity and subluminal propagation, certain constraints are placed on the equation of state of the medium. In the case of $D = 2$ spatial dimensions, classical gravity can be recast as a Chern-Simons gauge theory and motivated by this we recast the massive theory of gravity in AdS$_3$ as a massive Chern-Simons gauge theory with an unusual mass term. We find that in the flat space limit the Chern-Simons theory has a novel gauge invariance that mixes the kinetic and mass terms, and enables the massive theory with a non-compact internal group to be free of ghosts and tachyons.
Highlights
AND SUMMARYIt is well known that massless spin 1 bosons can dynamically acquire a mass at low energies
Two long known examples are of a photon acquiring a mass in a neutral plasma [1], where there is a massless remnant, and of the Brout-Englert-Higgs mechanism [2,3,4], where the NG’s are absorbed into the gauge fields while the remaining non-NG massive boson can still be light at weak coupling
Lorentzinvariant models will not be the subject of our work; instead we ask whether gravity can dynamically acquire a gap via coupling to matter that sets a preferred rest frame? A well known example is of the Jeans instability due to a longitudinal graviton acquiring a tachyonic mass within a pressureless matter density distribution
Summary
It is well known that massless spin 1 bosons can dynamically acquire a mass at low energies. When a fluid or solid medium couples to gravity, the low energy dynamics of this theory can be viewed, in the weakly coupled perturbative regime, as the dynamics of a Chern-Simons gauge field with an acquired mass term. We investigate this theory in the special case of gravity in an AdS3 background in which the acquired mass term is none other than the usual FierzPauli mass term. We investigate the dynamics of such a theory and find that it propagates 2 degrees of freedom as we expect from the dual description in terms of the metric Such a system that gives rise to an infrared modification of gravity is of interest for its potential applications in cosmology and condensed matter physics.
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