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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.

In order for quantum fluctuations during inflation to be converted to classical stochastic perturbations, they must couple to an environment which produces decoherence. Gravity introduces inevitable nonlinearities or mode couplings. We study their contribution to quantum-to-classical behavior during inflation. Working in the Schrodinger picture, we evolve the wavefunctional for scalar fluctuations, accounting for minimal gravitational nonlinearities.  The reduced density matrix for a given mode is then found by integrating out shorter-scale modes. We find that the nonlinearities produce growing phase oscillations in the wavefunctional, which decohere the single-mode reduced density matrix into a diagonal mixed state. However, the weakness of the coupling delays decoherence until the mode is much longer than the Hubble scale environment modes. In summary, the gravitational coupling of long and short scales is sufficient to produce a mixed state of classical perturbations during inflation.

String theory is starting to provide novel all-loop precision tools for the computation of scattering amplitudes in the high energy (HE) limit of N=4 SYM theory. After a review of some key insights and results for hexagon amplitudes, I will describe ongoing developments addressing higher numbers of external gluons.