High Energy Physics

We perform an exact localization calculation for the expectation value of Wilson-'t Hooft line operators in N=2 gauge theories on S^1 x R^3. The expectation values form a quantum mechanically deformed algebra of functions on the Hitchin moduli space by Moyal multiplication. We demonstrate that these expectation values are the Weyl transform of the Verlinde operators, which acts on conformal blocks as difference operators. Our results are also in exact match with the predictions from wall-crossing in the IR effective theory.

The world's most ambitious scientific experiment is buried 100 meters underground, straddling Switzerland and France. A billion times every minute, the Large Hadron Collider (LHC) slams together protons, while four giant detectors watch closely. - So how does the Large Hadron Collider work? - Why can slamming tiny particles into each other provide clues about the nature of all space and time? - What mysteries are physicists trying to solve with data from the LHC? - How does the cutting edge of particle physics relate to the world around us, from the patterns of stars in the sky to the fact that they shine at all? Natalia Toro, PI Faculty, works at the intersection of theories and hard data. She will explain how complex collision data from the LHC is being digested and examined right now, and how it may set the course for the science of the future.

In recent years there has been a lot of interest in F-Theory GUTs, mostly considering local models. In this talk I first consider an SU(5) GUT locally at the "point of E_8". The requirements of proton stability and reasonable flavour structure single out exactly two models. However, both models cannot be embedded in a semilocal construction (via the spectral cover approach). This casts doubts on the predictivity of local models.

I will first summarize recent exact localization computations of supersymmetric gauge theories, and then discuss curious connections between SUSY/non-SUSY theories coming from 6d (2,0) theories. I particular, I will focus on our recent proposal relating 3d N=2 theories and 3d SL(2,R) Chern-Simons theories (or more mathematically, geometry of 3-manifolds).

The hierarchy of the Yukawa couplings is an outstanding problem of the standard model. We present a class of models in which the first and second generation fermions are SUSY partners of pseudo-Nambu-Goldstone bosons that parameterize an E_7/SO(10) Kahler manifold, explaining the small values of these fermion masses relative to those of the third generation. We consider experimental constraints on this scenario, and find that the simplest model with universal gaugino masses is already ruled out by the LHC. However, models with non-universal gaugino masses will likely be excluded only by direct dark matter searches.