Talks

After a quick review of the Higgs and Coulomb branches of 3d N=4 theories, I'll introduce some simple classes of boundary conditions and explain how they lead to (pairs of) modules for certain (pairs of) quantum algebras. I will focus on abelian theories, for which the relevant boundary conditions/modules can be described using the geometry of (pairs of) hyperplane arrangements. From this, the simplest examples of symplectic-dual modules will arise.

I will introduce the unitarity, a parameter quantifying the coherence of a channel and show that it is useful for two reasons. First, it can be efficiently estimated via a variant of randomized benchmarking. Second, it captures useful information about the channel, such as the optimal fidelity achievable with unitary corrections and an improved bound on the diamond distance.

The orbital angular momentum in a chiral superfluid has posed a paradox for several decades. For example, for the $p+ip$-wave superfluid of $N$ fermions, the total orbital angular momentum should be $N/2$ if all the fermions form Cooper pairs. On the other hand, it appears to be substantially suppressed from $N/2$, considering that only the fermions near the Fermi surface would be affected by the pairing interaction. To resolve the long-standing question, we studied chiral superfluids in a two-dimensional circular well, in terms of a conserved charge and spectral flows. We find that the total orbital angular momentum takes the full value $N/2$ in the chiral $p+ip$-wave superfluid, while it is strongly suppressed in higher-order ($d+id$ etc.) chiral superfluids. This surprising difference is elucidated in terms of edge states.