Abstract: In Algebraic Quantum Field Theory, Haag duality violations give rise to the existence of non-local operators. These non-local operators become very useful for understanding different aspects of quantum field theory from first principles. In this talk, I will comment on two topics we are working on in Bariloche. The first concerns order parameters, where we study how the expectation values of non-local operators are related. I will briefly comment on recent work in which we found a way to maximize the expectation value of certain non-local operators. The second topic is the quantum version of Noether’s theorem. I will discuss why there are difficulties with Noether’s theorem in quantum field theory and comment on some recent progress in this area.

Abstract: Perturbative gauge theories can be conveniently formulated within the BV-BRST formalism. In a non-perturbative construction some new view points have to be taken into account, in particular the preservation of locality. Moreover, anomalies induce an L_infty structure which results in an extended group of inner symmetries.

Abstract: As an analogue to the density matrix in quantum mechanics, the Tomita-Takesaki modular operator characterizes mixed states in quantum field theory. Hence it is of fundamental conceptual importance; but its explicit form, beyond a small class of special cases, is notoriously hard to determine. It is however amenable to a numerical, approximate description. Here we present results on free massive Majorana fermions in the vacuum state on a 1+1-dimensional cylinder space-time, with respect to the observables in one double cone and in the union of two of these.

Abstract: The S-matrix bootstrap program was devised in the late 70s and mid 80s as a possible path for a fully explicit construction of numerous massive integrable quantum field theories in 1+1 dimensions. On technical grounds, the bootstrap program refers to a coupled system of Riemann–Hilbert problems whose solution allows one to explicitly realise the quantum fields of the theory as generalised integral operators on suitable spaces of functions. Among other things, this construction allows one to produce explicit expressions for the correlation functions, i.e. the central objects in those theories. These are given in terms of series of multiple integrals and allow to establish the compatibility of the bootstrap construction with the Wightman axiomatic formulation of a quantum field theory. This talk, will review the various developments of the theory up to discussing the most recent results and the numerous open questions. For illustrative purposes, I shall focus on the simplest non-trivial massive integrable quantum field theory in 1+1 dimensions: the Sinh-Gordon model.

Abstract: The Renyi quantum null energy condition conjectures that the second null shape variation of the sandwiched Renyi divergence (SRD) of an excited state relative to the vacuum is non-negative in local Poincare-invariant quantum field theory, giving a one-parameter generalization of the quantum null energy condition (QNEC). I will describe our proof of Renyi QNEC for all integer Renyi parameters n greater than 1 for von Neumann algebras carrying a half-sided modular inclusion structure. Concretely, for any sigma-finite von Neumann algebra with such an inclusion, I will sketch a proof of log-convexity, under the associated null-translation semigroup, of the Kosaki L^n norm of any normal positive functional with finite L^n norm. If time permits, i will end with some comments on Renyi quantum focusing in quantum gravity. Based on work with Tanay Kibe in arXiv:2605.15272.