High Energy Physics

I will consider simple scalar gauge theories with one scalar field in a low-dimensional representation of a gauge group. The renormalizable action often has accidental symmetries that lead to one or more stable states, providing Dark Matter candidates. The gauge group can confine, or be spontaneously broken by the scalar field: I will discuss the spectrum and symmetries in both cases, focusing in particular on possible dualities between the Higgs and confined phases. I will then discuss the Dark Matter phenomenology in a few illustrative cases, showing that the thermal relic abundance can reproduce the cosmological value for masses around 100 TeV.

The elliptic genus is a powerful deformation invariant of 1+1D SQFTs: if it is nonzero, then it protects the SQFT from admitting a deformation to one with spontaneous supersymmetry breaking. I will describe a "secondary" invariant, defined in terms of mock modularity, that goes beyond the elliptic genus, protecting SQFTs with vanishing elliptic genus. The existence of this invariant supports the hypothesis that the space of minimally supersymmetric 1+1D SQFTs provides a geometric model for universal elliptic cohomology. Based on joint works with D. Gaiotto and E. Witten.