# Models in Boundary Quantum Field Theory Associated with Lattices and Loop Group Models

August 24, 2011

In this article we give new examples of models in boundary quantum field
theory, i.e. local time-translation covariant nets of von Neumann algebras,
using a recent construction of Longo and Witten, which uses a local conformal
net A on the real line together with an element of a unitary semigroup
associated with A. Namely, we compute elements of this semigroup coming from
HÃ¶lder continuous symmetric inner functions for a family of (completely
rational) conformal nets which can be obtained by starting with nets of real
subspaces, passing to its second quantization nets and taking local extensions
of the former. This family is precisely the family of conformal nets associated
with lattices, which as we show contains as a special case the level 1 loop
group nets of simply connected, simply laced groups. Further examples come from
the loop group net of Spin(n) at level 2 using the orbifold construction.

Keywords:

Boundary QFT, conformal qft