arXiv subjects

Nicolás Abate

Publications and source records attributed to Nicolás Abate.

8 recordsLinked to original sources

arXiv2026

Exact mutual information for free massless fermions in any dimension

We obtain an exact expression for the Rényi mutual information (RMI) between two spherical regions for a free, massless Dirac field in $d$ spacetime dimensions and for a massless Rarita-Schwinger field in $d=4$. We identify each angular momentum mode in the spherical dimensional reduction of the parent theory with a massive Dirac fermion in two dimensional anti-de Sitter space (AdS). The RMI for each mode can be computed analytically for any Rényi index $n$ in terms of solutions of a Painlevé differential equation. We explore the long and short distance asymptotics of the result, where the sum over modes can be computed explicitly. As a result we are able to find subleading contributions to the long distance expansion in $d$ dimensions for arbitrary $n$, as well as to extract the area and logarithmic coefficients for the case $n=1$ in the short distance regime.

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arXiv2026

Irreversibility of quantum field theory in de Sitter: the C, F and A theorems

We prove the C, F and A irreversibility theorems in de Sitter spacetime for quantum field theories that are obtained as renormalization group flows from ultraviolet conformal fixed points. The proof is based on strong subadditivity of the entanglement entropy, de Sitter invariance, and the Markov property of conformal field theory.

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arXiv2026

Entanglement and Renormalization Group Irreversibility of Quantum Field Theory in AdS

We study nonperturbative aspects of quantum field theory (QFT) in rigid anti de Sitter (AdS) spacetime using quantum information theoretic methods. While irreversibility of renormalization group (RG) flows is well established in flat space, it is not obvious whether it persists in AdS, where negative curvature and an asymptotic timelike boundary significantly modify infrared dynamics. Using strong subadditivity and AdS invariance, we derive an entropic second-order differential inequality for the difference between the vacuum entanglement entropy of a QFT and that of its ultraviolet fixed point, evaluated for spherical bulk regions. This inequality allows us to define RG charges that measure the relevant number of degrees of freedom, and we prove the irreversibility of the RG in $2,\,3,$ and $4$ spacetime dimensions. We further analyze free scalar and fermion theories in AdS, developing lattice formulations adapted to the geometry and computing entanglement entropies and RG charges. In AdS$_2$, we obtain analytic results for a massive Dirac fermion and compare them with numerical lattice calculations. These examples illustrate the general irreversibility theorem and clarify the distinction between conformal and massive theories in AdS.

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arXiv2026

Exact Mutual Information Difference: Scalar vs. Maxwell Fields

We compute, for any Rényi index $n$, the exact difference between the mutual Rényi informations of a pair of free massless scalars and that of a Maxwell field in $d=4$ dimensions. Using the standard dimensional reduction method in polar coordinates, the problem is mapped to that of a single scalar field in $d=2$ with Dirichlet boundary conditions, which in turn can be conveniently related to the algebra of a chiral current on the full line. This latter identification, which maps algebras on an interval to two-interval algebras, yields exact results that clarify the structure of the long-distance OPE perturbative expansion of the mutual information. We find that this series has a finite radius of convergence only for integer $n>1$, while it becomes only asymptotical for $n=1$ and general non-integer values of $n$.

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arXiv2024

Entanglement of a chiral scalar on the torus

We compute the entanglement entropy of an interval for a chiral scalar on a circle at an arbitrary temperature. We use the resolvent method, which involves expressing the entropy in terms of the resolvent of a certain operator, and we compute that resolvent by solving a problem that entails finding an analytic function on the complex torus with certain jump conditions at the interval. The resolvent is relevant by itself, since it can be used to compute any function of the reduced density matrix. We illustrate that by also computing all the Rényi entropies for the model.

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arXiv2024

Quantum information and the C-theorem in de Sitter

Information-theoretic methods have led to significant advances in nonperturbative quantum field theory in flat space. In this work, we show that these ideas can be generalized to field theories in a fixed de Sitter space. Focusing on 1+1-dimensional field theories, we derive a boosted strong subadditivity inequality in de Sitter, and show that it implies a C-theorem for renormalization group flows. Additionally, using the relative entropy, we establish a Lorentzian bound on the entanglement and thermal entropies for a field theory inside the static patch. Finally, we discuss possible connections with recent developments using unitarity methods.

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arXiv2023

Modular conjugation for the chiral fermion in multicomponent regions on the torus

We continue the study of the Tomita-Takesaki modular conjugation for a massless Dirac field in a generic multicomponent region in $1+1$ spacetime dimensions. In this paper we focus on the computations for a thermal state on a circle, namely on the euclidean torus. By analytic continuation from the modular flow we arrive at an explicit expression for the modular conjugation in this scenario and derive its relevant limits. In contrast to the case of the vacuum on the line, this new result has a non-local behaviour even for connected regions. It also presents a novel contribution coming from the purification one has to introduce in order to deal with a mixed state: a term that maps the algebra of operators of the region to a copy of the global one, the so called 'second world' algebra.

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arXiv2023

Modular conjugation for multicomponent regions

We consider a massless Dirac field in $1+1$ dimensions, and compute the Tomita-Takesaki modular conjugation corresponding to the vacuum state and a generic multicomponent spacetime region. We do it by analytic continuation from the modular flow, which was computed recently. We use our result to discuss the validity of Haag duality in this model.

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