# Deformations of half-sided modular inclusions and non-local chiral field theories

November 04, 2021

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

Keywords:

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