Talks

We study two-dimensional (4, 4) superconformal field theories of central charge c = 6, corresponding to nonlinear sigma models on K3 surfaces, using the superconformal bootstrap method. This is made possible through a surprising relation between the BPS N = 4 superconformal blocks of c = 6 and bosonic Virasoro conformal blocks of c = 28, and an exact result on the moduli dependence of a certain integrated BPS 4-point function. Nontrivial bounds on the non-BPS spectrum are obtained in the K3 CFT as functions of the CFT moduli, that interpolate between the free orbifold points and singular CFT points. We observe directly from the CFT perspective the signature of a continuous spectrum above a gap at the singular moduli, and find numerically an upper bound on this gap that is saturated by the A1 N = 4 cigar CFT. 

Axions, having a perturbative shift symmetry, can have masses much smaller than other types of particles in a technically natural way. Ultralight axions (ULAs) with m~10^{-22} eV are attractive dark matter candidates with novel properties that distinguish them from cold dark matter (CDM). A single ULA with a GUT scale decay constant provides the correct relic density without fine-tuning. Quantum gravitational effects are expected to break continuous global symmetries, and may spoil the axion potential. However, if the axion global symmetry is an accidental symmetry descending from an exact discrete symmetry, then the problematic higher dimensional operators can be forbidden to very high order. I will discuss the astrophysical and cosmological phenomenology of ULAs that makes them attractive, and methods to distinguish them from CDM observationally. I will also discuss a two-axion model which solves the strong CP problem and in addition possesses a ULA that may be detectable via ~month period nuclear spin precession in an experiment such as CASPEr-Wind. Given time, I may discuss other experimental searches for axion-like particles.