Main advances concern in particular the Minkowskian description and model constructions of Boundary Conformal QFT, the first construction QFT models with minimal length, conditions to construct a Vertex Algebra from a Local Conformal Net and back, the description of the localized states associated with infinite spin particles, showing that states localized in a bounded spacetime regions do not exist.
The important recent advances concerns quantum information for infinite systems, in particular rigorous derivations of entropy bounds in QFT.
Conclusion of the action
The project has been very successful in different respects.
Previous line of research has been brought to completion, in particular the algebraic structure of Conformal Quantum Field Theory has been analyzed and carried to a higher level of comprehension, the relation with Vertex Algebras has understood within a wide general framework.
A new line of research has been opened, it concerns Entropy and Quantum Energy Inequalities. Intense research activity has been performed in this direction during the second part of the project and is still successfully going on.
General derivations of Landauer and Bekenstein inequality have been provided, a new, operator algebraic approach to the Quantum Null Energy Inequality has been set up with model analysis.
A formula for the local massive Modular Hamiltonian has been given, solving a long standing open problem.