Week 08.03.2024 – 16.03.2024

We propose a correspondence between topological order in 2+1d and Seifert three-manifolds together with a choice of ADE gauge group G. Topological order in 2+1d is known to be characterised in terms of modular tensor categories (MTCs), and we thus propose a relation between MTCs and Seifert three-manifolds. The correspondence defines for every Seifert manifold and choice of G a fusion category, which we conjecture to be modular whenever the Seifert manifold has trivial first homology group with coefficients in the centre of G. The construction determines the spins of anyons and their S-matrix, and provides a constructive way to determine the R- and F-symbols from simple building blocks. We explore the possibility that this correspondence provides an alternative classification of MTCs, which is put to the test by realising all MTCs (unitary or non-unitary) with rank r<=5 in terms of Seifert manifolds and a choice of Lie group G.

CANCELLED due to an unforeseen speaker emergency.

I will describe how to consider the flat space limit of scaterig in AdS relative to a point (where sacttering occurs). The kinematics is related to the Wigner-Inonu contraction. In particular, I will discuss how to take the proper limits of wave functions in AdS (times extra dimensions) to understand a notion of in states and out states and how a scattering amplitude should be conceived. This will make use of the embedding formalism, where the description of these wave functions is simple. I will show how these wave functions are related to other constructions in AdS/CFT and suggest how the Mellin parameters of these other setups arise from integral representations of the wave functions in terms of Schwinger parameters.

I will describe a construction relating the Vertex Operator Algebra (VOA) of a 4d N=2 superconformal field theory (SCFT) to the boundary VOA in 3d N=4 QFT, and to the VOA in 2d QFT. Besides unifying several known constructions, this also draws connections to many other interesting problems, among which are the novel rank-zero 3d N=4 SCFTs emerging in the high-temperature limit of a 4d SCFT "on the second sheet".