θ-Vacua and Particle Spectrum beyond Perturbative Electroweak Theory and General Relativity

I will argue that in theories with a θ-vacuum structure and spectral asymmetry of the Dirac operator, the anomalous symmetry is realized non-linearly. Applying this to General Relativity, we conclude that: (i) the Einstein’s theory requires an expanded gauge structure based on local supersymmetry; (ii) even in the simplest such theory, N=1 supergravity, supersymmetry is spontaneously broken by the gravitino condensate, leading to a (pseudo)Goldstone supermultiplet consisting of the dilaton, R-symmetry axion, and goldstino. Similarly, the electroweak sector of the Standard Model must exhibit non-linearly realized anomalous B+L invariance, accompanied by the (pseudo)Goldstone particle, the electroweak ηw, which can be viewed as the electroweak counterpart of the QCD η meson.