We present variational estimates for the low-lying energies of a simple matrix model that approximates SU (3) Yang-Mills theory on a three-sphere of radius R. By fixing the ground state energy, we obtain the (integrated) renormalization group (RG) equation for the Yang-Mills coupling g as a function of R. This RG equation allows to estimate the masses of other glueball states, which we find to be in excellent agreement with lattice simulations. arXiv:1606.08711v3 [hep-th]

When spatial boundaries are inserted, supersymmetry (SUSY) can be broken. We have shown that in an N ¼ 2 supersymmetric theory, all local boundary conditions allowed by self-adjointness of the Hamiltonian break N ¼ 2 SUSY, while only a few of these boundary conditions preserve N ¼ 1 SUSY. We have also shown that for a subset of the boundary conditions compatible with N ¼ 1 SUSY, there exist fermionic ground states which are localized near the boundary. We also show that only very few nonlocal boundary conditions like periodic boundary conditions preserve full N ¼ 2 supersymmetry, but none of them exhibits edge states.

Efficient micro-resonators simultaneously require a large quality factor Q and a small volume V . However, the former is ultimately limited by bending losses, the unavoidable radiation of energy of a wave upon changing direction of propagation. Such bending losses increase exponentially as V decreases and eventually result in a drop of Q. Therefore, circular cavities are generally designed with radii that are much larger than the optical wavelength. The same leakage of energy by radiation limits the sharpness of bends in photonic integrated circuits. In this article, we present a way to reduce bending losses in circular micro-resonators. The proposed scheme consists of one or more external dielectric rings that are concentric with the cavity. These rings alter the field outside the cavity where radial oscillations set in, and thus control the far field radiation. As a result, the Q factor can be increased by several orders of magnitude while keeping a small cavity volume.

Using generalized bosons, we construct the fuzzy sphere S 2 F and monopoles on S 2 F in a reducible representation of SU(2). The corresponding quantum states are naturally obtained using the GNS-construction. We show that there is an emergent nonabelian unitary gauge symmetry which is in the commutant of the algebra of observables. The quantum states are necessarily mixed and have non-vanishing von Neumann entropy, which increases monotonically under a bistochastic Markov map. The maximum value of the entropy has a simple relation to the degeneracy of the irreps that constitute the reducible representation that underlies the fuzzy sphere.