arXiv subjects

Lorenzo Panebianco

Publications and source records attributed to Lorenzo Panebianco.

5 recordsLinked to original sources

arXiv2026

Entanglement Entropy in CFT and Modular Nuclearity

In the framework of Algebraic Quantum Field Theory, several operator algebraic notions of entanglement entropy can be associated with any pair of causally disjoint spacetime regions $\mathcal{S}_A$ and $\mathcal{S}_B$ with positive relative distance. Among them, the canonical entanglement entropy is defined as the von Neumann entropy of a canonical intermediate type I factor. In this work, we show that the canonical entanglement entropy of the vacuum state is finite for a broad class of conformal nets including the $U(1)$-current model and the $SU(n)$-loop group models. Since previous studies suggest that this finiteness property is related to nuclearity properties of the system, we show that the mutual information is finite in any local QFT satisfying a modular $p$-nuclearity condition for some $0 < p < 1$. A similar finiteness result is established for another notion of entanglement entropy introduced in this paper. We conclude with remarks for future work in this direction.

quant-ph↗

arXiv2026

An Italian Gender Equality Index

Composite indices like the Gender Equality Index (GEI) are widely used to monitor gender disparities and guide evidence-based policy. However, their original design is often limited when applied to subnational contexts. Building on the GEI framework and the WeWorld Index Italia, this study proposes a composite indicator tailored to measure gender disparities across Italian regions. The methodology, based on a variation of the Mazziotta-Pareto Index, introduces a novel aggregation approach that penalizes uneven performances across domains. Indicators cover employment, economic resources, education, use of time, political participation, and health, reflecting multidimensional gender inequality. Using open regional data for 2024, the proposed Italian Gender Equality Index (IGEI) provides a comparable and robust measure across regions, highlighting both high-performing and lagging areas. The approach addresses compensatory limitations of traditional aggregation and offers a practical tool for regional monitoring and targeted interventions, benefiting from the fact that the IGEI is specifically tailored on the GEI framework.

stat.AP↗

arXiv2022

Modular Nuclearity and Entanglement measures

In the framework of Algebraic Quantum Field Theory, several operator algebraic notions of entanglement entropy can be associated to a couple of causally disjoint and distant spacetime regions $\mathcal{S}_A$ and $\mathcal{S}_B$. In this work, 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 recently studied entanglement measure. Furthermore, if we assume conformal covariance then by comparison with other entanglement measures we can state that the mutual information satisfies lower bounds of area law type when the distance between $\mathcal{S}_A$ and $\mathcal{S}_B$ approaches to zero. As an application, in $1+1$-dimensional integrable models with factorizing S-matrices, we study the asymptotic behaviour of different entanglement measures as the distance between two causally disjoint wedges diverges.

math-ph↗

arXiv2020

Loop Groups and QNEC

We investigate some analytical properties of loop group models, showing that a Positive Energy Representation (PER) of a loop group $LG$ can be extended to a PER of $H^{3/2}(S^1,G)$ for any compact, simple and simply connected Lie group $G$. We then explicitly compute the adjoint action of $H^{5/2}(S^1,G)$ on the stress energy tensor and we use these results to prove the Quantum Null Energy Condition (QNEC) and the Bekenstein Bound for states obtained by applying a Sobolev loop to the vacuum. We also give a simpler proof of these last results in the case $G=SU(n)$. Finally, we construct and study solitonic representations of the loop group conformal nets induced by the conjugation by a loop with a discontinuity in $-1$.

math-ph↗

arXiv2020

A formula for the relative entropy in chiral CFT

We give a general formula for the relative entropy between the vacuum state and a coherent state, that is a state obtained by applying an exponentiated stress energy tensor to the vacuum of a chiral conformal field theory on the lightray. As an application of this result, we verify the QNEC and the Bekenstein Bound.

math-ph↗