Person:

Georgi, Howard

We present examples of four dimensional, non-supersymmetric field theories in which ultraviolet supersymmetry breaking effects, such as bose-fermi splittings and the vacuum energy, are suppressed by (α/4π) N , where α is a weak coupling factor and N can be made arbitrarily large. The particle content and interactions of these models are conveniently represented by a graph with sites and links, describing the gauge theory space structure. While the theories are supersymmetric “locally” in theory space, supersymmetry can be explicitly broken by topological obstructions.

We introduce a technique for restoring general coordinate invariance into theories where it is explicitly broken. This is the analog for gravity of the Callan-Coleman-WessZumino formalism for gauge theories. We use this to elucidate the properties of interacting massless and massive gravitons. For a single graviton with a Planck scale MPl and a mass mg, we find that there is a sensible effective field theory which is valid up to a high-energy cutoff Λ parametrically above mg. Our methods allow for a transparent understanding of the many peculiarities associated with massive gravitons, among them the need for the Fierz-Pauli form of the Lagrangian, the presence or absence of the van Dam-Veltman-Zakharov discontinuity in general backgrounds, and the onset of non-linear effects and the breakdown of the effective theory at large distances from heavy sources. The natural sizes of all non-linear corrections beyond the Fierz-Pauli term are easily determined. The cutoff scales as Λ ∼ (m4 gMPl) 1/5 for the Fierz-Pauli theory, but can be raised to Λ ∼ (m2 gMPl) 1/3 in certain non-linear extensions. Having established that these models make sense as effective theories, there are a number of new avenues for exploration, including model building with gravity in theory space and constructing gravitational dimensions.

We discuss the form of the chiral anomaly on an S 1/Z2 orbifold with chiral boundary conditions. We find that the 4-divergence of the higher-dimensional current evaluated at a given point in the extra dimension is proportional to the probability of finding the chiral zero mode there. Nevertheless the anomaly, appropriately defined as the five dimensional divergence of the current, lives entirely on the orbifold fixed planes and is independent of the shape of the zero mode. Therefore long distance four dimensional anomaly cancellation ensures the consistency of the higher dimensional orbifold theory.

We propose a new class of four-dimensional theories for natural electroweak symmetry breaking, relying neither on supersymmetry nor on strong dynamics at the TeV scale. The new TeV physics is perturbative, and radiative corrections to the Higgs mass are finite. The softening of this mass occurs because the Higgs is an extended object in theory space, resulting in an accidental symmetry. A novel Higgs potential emerges naturally, requiring a second light SU(2) doublet scalar.

We construct renormalizable, asymptotically free, four dimensional gauge theories that dynamically generate a fifth dimension.