Thesis title: Quantum Null Energy Condition, Loop Groups and Modular Nuclearity
In this PhD thesis we prove the QNEC for some solitonic states of physical interest on a generic conformal net. The proof relies on explicit computations on the Virasoro nets and on the use of vacuum preserving conditional expectations. The convexity result is not the most general one, but our explicit formulae allow us to achieve other entropy-related results like the Bekenstein Bound.