Talks

Concepts of information theory are increasingly used to characterize collective phenomena in condensed matter systems, such as the use of entanglement entropies to identify emergent topological order in interacting quantum many-body systems. Here we employ classical variants of these concepts, in particular Renyi entropies and their associated mutual information, to identify topological order in classical systems.

Like for their quantum counterparts, the presence of topological order can be identified in such classical systems via a universal, subleading contribution to the prevalent volume and boundary laws of the classical Renyi entropies. We demonstrate that an additional subleading O(1) contribution generically arises for all Renyi entropies S(n) with n ≥ 2 when driving the system towards a phase transition, e.g. into a conventionally ordered phase. This additional subleading term, which we dub connectivity contribution, tracks back to partial subsystem ordering and is proportional to the number of connected parts in a given bipartition. Notably, the Levin-Wen summation scheme – typically used to extract the topological contribution to the Renyi entropies – does not fully eliminate this additional connectivity contribution in this classical context. This indicates that the distillation of topological order from Renyi entropies requires an additional level of scrutiny to distinguish topological from non-topological O(1) contributions. This is also the case for quantum systems, for which we discuss which entropies are sensitive to these connectivity contributions. We showcase these findings by extensive numerical simulations of a classical variant of the toric code model, for which we study the stability of topological order in the presence of a magnetic field and at finite temperatures from a Renyi entropy perspective.

We consider 4d N=1 superconformal theories on a cylinder. The partition function on this geometry computes the superconformal index, and can be obtained via the path integral with time direction compactified on a circle and periodic conditions for fermions. We will describe universal formulas for the asymptotics of such partition functions in the limit of very large circle and of very small circle. These limits are completely fixed in terms of coefficients of the Weyl anomaly (a,c). We will explain why supersymmetry is a necessary condition in 4d to establish these higher dimensional analogues of classic results in 2d CFTs. Finally we will discuss some applications and the extension to 6d.

We argue that solutions to the strong CP problem motivate different searches for TeV scale physics at the LHC than are currently being emphasized. We present two solutions to the strong CP problem that require the existence of new colored particles with masses below 10 TeV. New motivated searches at the LHC would provide a strong constraint on these solutions to the strong CP problem.

The next hope to constrain cosmological parameters observationally is in surveys of the large scale structure (LSS) of the universe. LSS has the potential to rival the CMB in cosmological constraints because the number of modes scales like the volume, but the nonlinear clustering due to gravity makes it more difficult to extract primordial parameters. In order to take full advantage of the constraining power of LSS, we must understand it in the quasi-nonlinear regime. The effective field theory (EFT) of LSS provides a consistent way to perturbatively predict the clustering of matter at large distances. In this talk, I will discuss the status of the EFT of LSS and present recent work describing the inclusion of baryons in the EFT approach, including comparisons to N-body simulations.