Nima2
One of my favourite young physicists, Nima Arkani-Hamed, was in town today. He gave two talks.
One was about his work on spontaneously-broken diffeomorphism invariance. Specifically, consider a theory in which spatial diffeomorphisms are preserved, but time-translations are spontaneously-broken. There’s a scalar field which, in a really horrible pun, they call the ghostino, whose expectation value satisfies Expanding the field about its VEV,
under an infinitesimal diffeomorphism,
so transforms as a scalar under spatial diffeomorphisms, but transforms inhomogeneously under temporal ones, as befits a Goldstone boson. We also impose a shift symmetry under . The naive time-translation symmetry of a static spacetime is broken in this background, but the combination
is unbroken.
If you write out a general symmetry-breaking effective Lagrangian for (compatible with the shift symmetry and, for simplicity, with ), and expand it about a minimum, you find something like (after rescaling to give it a canonically-normalized kinetic energy)
The dispersion relation is a nonrelativistic one (unsurprising, since the symmetry-breaking has picked out a preferred Lorentz frame) and power-counting is a bit unconventional. should have mass dimension , should have mass dimension and should have mass dimension . The leading interaction term is
and is irrelevant in the infrared, so there’s a good perturbative effective field theory description.
Anyway, if you take eV, the coupling of this theory to gravity modifies gravity at cosmological distance scales, with interesting ramifications for cosmology.
There’s a bit of a swindle here, since the theory just described breaks down above the scale , and requires some ultraviolet completion there. However, if couples only gravitationally, they argue that it doesn’t really matter what the ultraviolet completion is. While there remains a challenge to embed this in a “real” theory, their effective Lagrangian analysis indicates that it’s not completely crazy to try to do so. You might not have expected it, but the long-distance physics makes sense.
Nima’s other talk was about “high energy” supersymmetry, some as yet unpublished work of his with Savas Dimopoulos, in which supersymmetry is broken at a relatively high scale and, of the superpartners, only the gauginos are light.
I’ll talk about that in more detail some other time…Posted by distler at April 28, 2004 1:14 AM