AGT/Z2_2

We relate Liouville/Toda CFT correlators on Riemann surfaces with boundaries and cross-cap states to supersymmetric observables in four-dimensional N=2 gauge theories. Our construction naturally involves four-dimensional theories with fields defined on different Z$_2$ quotients of the sphere (hemisphere and projective space) but nevertheless interacting with each other. The six-dimensional origin is a Z$_2$ quotient of the setup giving rise to the usual AGT correspondence. To test the correspondence, we work out the RP$^4$ partition function of four-dimensional N=2 theories by combining a 3d lens space and a 4d hemisphere partition functions. The same technique reproduces known RP$^2$ partition functions in a form that lets us easily check two-dimensional Seiberg-like dualities on this nonorientable space. As a bonus we work out boundary and cross-cap wavefunctions in Toda CFT.Comment: 56 pages. v2: Clarify discrete theta angle. v3: Published in JHEP; extra references. v4: Minor sign fix; extra reference

Modified permittivity observed in bulk Gallium Arsenide and Gallium Phosphide samples at 50 K using the Whispering Gallery mode method

Whispering Gallery modes in bulk cylindrical Gallium Arsenide and Gallium Phosphide samples have been examined both in darkness and under white light at 50 K. In both samples we observed change in permittivity under light and dark conditions. This results from a change in the polarization state of the semiconductor, which is consistent with a free electron-hole creation/recombination process. The permittivity of the semiconductor is modified by free photocarriers in the surface layers of the sample which is the region sampled by Whispering Gallery modes.Comment: 8 pages, 3 figure

Towards achieving strong coupling in 3D-cavity with solid state spin resonance

We investigate the microwave magnetic field confinement in several microwave 3D-cavities, using 3D finite-element analysis to determine the best design and achieve strong coupling between microwave resonant cavity photons and solid state spins. Specifically, we design cavities for achieving strong coupling of electromagnetic modes with an ensemble of nitrogen vacancy (NV) defects in diamond. We report here a novel and practical cavity design with a magnetic filling factor of up to 4 times (2 times higher collective coupling) than previously achieved using 1D superconducting cavities with small mode volume. In addition, we show that by using a double-split resonator cavity, it is possible to achieve up to 200 times better cooperative factor than the currently demonstrated with NV in diamond. These designs open up further opportunities for studying strong and ultra-strong coupling effects on spins in solids using alternative systems with a wider range of design parameters.Comment: 20 pages, 9 figure