Week 23.05.2022 – 29.05.2022

The string landscape, together with the mechanism of eternal inflation for populating vacua, leads to the seemingly inescapable conclusion that we are part of a vast multiverse. As an inhabitant of the multiverse, how should we reason probabilistically about the expected physical properties of our observable universe? Probabilities in eternal inflation are usually defined in terms of frequencies, but this approach has failed to yield a unique answer. In this talk, I will present a different approach to the problem, based on Bayesian reasoning. By adopting the least informative priors on the model parameters, we will be led to well-defined, time-reparametrization invariant (and non-anthropic) probabilities for occupying different vacua. Remarkably, these probabilities favor vacua whose surrounding landscape topography is that of a deep valley or funnel, akin to folding funnels of naturally-occurring proteins. Furthermore, by modeling the landscape of vacua as a random network, I will show that our probabilities favor regions that are close to the directed percolation phase transition. As usual, the predictive power of criticality lies in scale invariant observables characterized by critical exponents. As an example, I will show that the probability distribution for the cosmological constant is power-law, with a particular critical exponent, and favors a naturally small and positive vacuum energy. Tantalizingly, this hints at a deep connection between non-equilibrium critical phenomena on the landscape and the near-criticality of our universe.

The moduli space of Supersymmetric gauge theories with 8 supercharges has a rich structure of symplectic singularities associated with degenerations in which additional massless states arise. These are neatly arranged into phase diagrams that encode the different sets of massless states, with information on the moduli that are needed to be tuned in order to move from one phase to another. We will present results from studies of families of quivers, including those on the affine grassmanian of finite dimensional Lie algebras. ; part of the London TQFT Journal Club (please register at https://london-tqft.vercel.app)

For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions, and determine the fusion rule. We give an explicit realization of this duality defect in the free Maxwell theory. The duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides. [for zoom link please contact h(dot)jiang(at)qmul(dot)ac(dot)uk]