Papers:

• L. Panebianco, B. Wegener, Modular Nuclearity and Entanglement Measures, 2021
  Abstract: In the framework of Algebraic Quantum Field Theory, several operator algebraic notions of entanglement entropy can be associated to any couple of causally disjoint and distant spacetime regions SA and SB . One of them, known as canonical entanglement entropy, is defined as the von Neumann entropy on some canonical intermediate type I factor. In this work  we show the canonical entanglement entropy of the vacuum state to be finite on a wide family of conformal nets including the U(1)-current model and the SU(n)-loop group models.  More in general, such a finiteness property is expected to  rely on some nuclearity condition of the system.  To support this conjecture, we show that the mutual information is finite in any local QFT verifying a  modular p-nuclearity condition for some 0<p<1. A similar result is proved for another entanglement entropy introduced in this work.  We conclude with some personal considerations on 1+1-dimensional integrable models with factorizing S-matrices and remarks for future works in this direction.  

• L. Panebianco, Loop Groups and QNEC, Communications in Mathematical Physics, 2021
  Abstract: We construct and study solitonic representations of the conformal net associated to some vacuum Positive Energy Representation (PER) of a loop group LG. For the corresponding solitonic states, we  prove the Quantum Null Energy Condition (QNEC) and the Bekenstein Bound. As an intermediate result, we show that a Positive Energy Representation of a loop group LG can be extended to a PER of Hs(S1,G) for s>3/2, where G is  any compact, simple and simply connected Lie group. We also show the existence of the exponential map of the semidirect product LG⋊R, with R a one-parameter subgroup of Diff, and we compute the adjoint action of Hs(S1,G) on the stress energy tensor. 

• L. Panebianco, A formula for the relative entropy in chiral CFT, Letters in Mathematical Physics, 2020
  Abstract: We prove the QNEC on the Virasoro nets for a class of unitary states extending the coherent states, that is states obtained by applying an exponentiated stress energy tensor to the vacuum. We also verify the Bekenstein Bound by computing the relative entropy on a bounded interval.