Deformations of Half-Sided Modular Inclusions and Non-local Chiral Field Theories

We construct explicit examples of half-sided modular inclusions ${\mathcal N}\subset{\mathcal M}$ von Neumann algebras with trivial relative commutants. After stating a general criterion for triviality the commutant in terms an algebra localized at infinity, we consider second quantization inclusion large and one-parameter family N}_\kappa\subset{\mathcal M}_\kappa$, $\kappa\geq0$, such that N}_0={\mathcal N}$, M}_0={\mathcal N}_\kappa'\cap{\mathcal M}_\kappa={\mathbb C}1$ $\kappa>0$. The technique use is deformation procedure (warped convolution), explain relation this result to construction chiral conformal quantum field theories on real line circle.