arXiv subjects

Goffredo Chirco

Publications and source records attributed to Goffredo Chirco.

At least 19 recordsLinked to original sources

arXiv2026

Dimensional reduction of AdS3 Chern-Simons gravity: Schwarzian and affine boundary theories

We study a symmetry-reduced sector of $AdS_3$ gravity formulated as an $SO(2,2)$ Chern--Simons theory on a three-dimensional manifold with toroidal boundary. The reduction is implemented by requiring a global symmetry and restricting to the sector where the gauge connection is invariant along the symmetry flow. The resulting theory reduces to a two-dimensional BF-like model together with an induced one-dimensional boundary action, whose form is fixed by the three-dimensional Chern--Simons origin. On the boundary subspace selected by suitable mixed boundary conditions, the one-dimensional action reproduces the standard Drinfel'd--Sokolov restriction to coadjoint orbits of the Virasoro group, among them the Schwarzian dynamics associated with JT gravity. Moreover, the $\mathfrak{so}(2,2)$ algebra of the three-dimensional Chern--Simons model naturally generates current-dressed Kac--Moody extensions of the one-dimensional boundary dynamics. The full one dimensional boundary dynamics of the reduced theory is then shown to be compatible SYK-like tensor models with global symmetries.

hep-th↗

arXiv2026

Hamiltonian formulation of a gravity model from (A)dS Yang-Mills theory

We study the Hamiltonian formulation of a gravity model obtained from a Yang--Mills theory for a one-parameter family of (A)dS Lie algebras parametrized by $α$, when the family of algebras is contracted to the Poincaré algebra in the limit $α\to 0$. We derive the canonical structure and first-class constraints and analyze the resulting algebra in the contraction limit. In this limit, the constraints generate the residual Lorentz gauge invariance, and the components of the AdS potential transform as tetrads and Lorentz connection. Finally, we determine the number of physical degrees of freedom, showing that in the non-propagating torsion sector - selected by a Lorentz-covariant gauge condition preserved under dynamical evolution - the theory exhibits only two propagating degrees of freedom.

gr-qc↗

arXiv2026

Bias in Local Spin Measurements from Deformed Symmetries

We study local spin measurements on bipartite singlet states when rotational symmetry is described by a quantum group rather than an ordinary Lie group. Although the fundamental spin-1/2 representation has the usual one-particle action on states, the non-trivial coproduct selects a deformed analogue of the Bell singlet state. We show that conventional tensor-factor measurements on this invariant singlet lead to deformation-dependent one-site outcome statistics. We then compare this standard-local prescription with a braided-local one, obtained by dressing local observables with the R-matrix and using the corresponding braided inner product. The braided observables are covariant under the Hopf adjoint action, but define a distinct measurement structure and lead to the reciprocal bias on the deformed singlet state.

quant-ph↗

arXiv2025

Operator Entanglement from Non-Commutative Symmetries

We argue that Hopf-algebra deformations of symmetries -- as encountered in non-commutative models of quantum spacetime -- carry an intrinsic content of $operator$ $entanglement$ that is enforced by the coproduct-defined notion of composite generators. As a minimal and exactly solvable example, we analyze the $U_q(\mathfrak{su}(2))$ quantum group and a two-qubit realization obtained from the coproduct of a $q$-deformed single-spin Hamiltonian. Although the deformation is invisible on a single qubit, it resurfaces in the two-qubit sector through the non-cocommutative coproduct, yielding a family of intrinsically nonlocal unitaries. We compute their operator entanglement in closed form and show that, for Haar-uniform product inputs, their entangling power is fully determined by the latter. This provides a concrete mechanism by which non-commutative symmetries enforce a baseline of entanglement at the algebraic level, with implications for information dynamics in quantum-spacetime settings and quantum information processing.

quant-ph↗

arXiv2025

Gravity model from (A)dS Yang-Mills theory

We investigate the relationship between a one-parameter family of (anti-)de Sitter Yang-Mills models and a model of Einstein-Palatini gravity with matter, realized through Inönu-Wigner contraction of the (A)dS algebra. By setting the group parameter $α$ to zero, the gauge transformation of the potential becomes consistent with the transformation properties of the tetrad form and spin connection. We show that a sector of the Yang-Mills dynamics exists in which the equations decouple. Moreover, a subset of the gauge transformations can be related to diffeomorphisms, leading to the identification of the tetrad field. Finally, the resulting dynamics is consistent with a gravitational dynamics in the first-order formalism.

gr-qc↗

arXiv2025

A so(2,2) extension of JT gravity via the Virasoro-Kac-Moody semidirect product

We consider a bulk plus boundary extension of Jackiw-Teitelboim Gravity (JT) coupled with non-abelian gauge fields. The generalization is performed in the Poisson Sigma Model formulation and it is derived as a dimensional reduction of the AdS3 Chern-Simons theory with WZW boundary terms. We discuss the role of boundary conditions in relation to the symmetries of the boundary dynamics and we show that the boundary action can be written in terms of coadjoint orbits of an appropriate Virasoro Kac-Moody group. We obtain a Schwarzian action and interaction terms with additional edge modes that match the effective low energy action of recent SYK-like tensor models.

hep-th↗

arXiv2024

Dually affine Information Geometry modeled on a Banach space

In this chapter, we study Information Geometry from a particular non-parametric or functional point of view. The basic model is a probabilities subset usually specified by regularity conditions. For example, probability measures mutually absolutely continuous or probability densities with a given degree of smoothness. We construct a manifold structure by giving an atlas of charts as mappings from probabilities to a Banach space. The charts we use are quite peculiar in that we consider only instances where the transition mappings are affine. We chose a particular expression of the tangent and cotangent bundles in this affine setting.

math.ST↗

arXiv2024

Stabilizer entropy of quantum tetrahedra

How complex is the structure of quantum geometry? In several approaches, the spacetime atoms are obtained by the SU(2) intertwiner called quantum tetrahedron. The complexity of this construction has a concrete consequence in recent efforts to simulate such models and toward experimental demonstrations of quantum gravity effects. There are, therefore, both a computational and an experimental complexity inherent to this class of models. In this paper, we study this complexity under the lens of stabilizer entropy (SE). We calculate the SE of the gauge-invariant basis states and its average in the SU(2) gauge invariant subspace. We find that the states of definite volume are singled out by the (near) maximal SE and give precise bounds to the verification protocols for experimental demonstrations on available quantum computers.

hep-th↗

arXiv2023

Curvature from multipartite entanglement in quantum gravity states

We investigate the multipartite entanglement of a uniformly curved quantum 3D space region with boundary, realised in terms of spin networks defined on a graph with non trivial SU(2) holonomies, in the framework of loop quantum gravity. The presence of intrinsic curvature in the region is encoded in closure (topological) defects associated with tag-spins attached to the vertices of the graph. For such states, we generalise the bulk-to-boundary mapping as to include the space of tags in an extended boundary space: bulk information is shared among generically entangled boundary surfaces and intrinsic curvature degrees of freedom. We model the quantum region on a tripartite system composed by two (complementary) boundary subregions and the set of bulk tags. Via replica techniques, we can compute the typical value of the logarithmic negativity of the reduced boundary, described as an open quantum system, in a large spin regime. We find three entanglement regimes, depending on the ratio between the number of tags (curvature) and the area of the dual surface at the boundary. These are well described by the generalised Page curve of a tripartite random state. In particular, we find area scaling behaviour for negativity in case of small curvature, while for large curvature the negativity vanishes, suggesting an effective thermalization of the boundary. Remarkably, the PPT character of the mixed boundary state corresponds to a change in the effective topology of the network, with the two boundary subregions becoming disconnected.

hep-th↗

arXiv2022

Entanglement Negativity on Random Spin Networks

We investigate multipartite entanglement for quantum states of 3d space geometry, described via generalised random spin networks with fixed areas, in the context of background independent approaches to quantum gravity. We focus on entanglement negativity as a well defined witness of quantum correlations for mixed states, in our setting describing generic subregions of the boundary of a quantum 3d region of space. In particular, we consider a generic tripartition of the boundary of an open spin network state and we compute the typical Rényi negativity of two boundary subregions A and B immersed in the environment C, explicitly for a set of simple open random spin network states. We use the random character of the spin network to exploit replica and random average techniques to derive the typical Rényi negativty via a classical generalised Ising model correspondence, generally used for random tensor networks in the large bond regime. For trivially correlated random spin network states, with only local entanglement between spins located on the network edges, we find that typical log negativity displays a holographic character, in agreement with the results for random tensor networks, in large spin limit. When non-local bulk entanglement between intertwiners at the vertices is considered the negativity increases, while at the same time the holographic scaling is generally perturbed by the bulk contribution.

hep-th↗

arXiv2022

Lagrangian and Hamiltonian Mechanics for Probabilities on the Statistical Manifold

We provide an Information-Geometric formulation of Classical Mechanics on the Riemannian manifold of probability distributions, which is an affine manifold endowed with a dually-flat connection. In a non-parametric formalism, we consider the full set of positive probability functions on a finite sample space, and we provide a specific expression for the tangent and cotangent spaces over the statistical manifold, in terms of a Hilbert bundle structure that we call the Statistical Bundle. In this setting, we compute velocities and accelerations of a one-dimensional statistical model using the canonical dual pair of parallel transports and define a coherent formalism for Lagrangian and Hamiltonian mechanics on the bundle. Finally, in a series of examples, we show how our formalism provides a consistent framework for accelerated natural gradient dynamics on the probability simplex, paving the way for direct applications in optimization, game theory and neural networks.

math.ST↗

arXiv2021

Bulk area law for boundary entanglement in spin network states: entropy corrections and horizon-like regions from volume correlations

For quantum gravity states associated to open spin network graphs, we study how the entanglement entropy of the boundary degrees of freedom (spins on open edges) is affected by the bulk data, specifically by its combinatorial structure and by the quantum correlations among intertwiner degrees of freedom. For a specific assignment of bulk edge spins and slightly entangled intertwiners, we recover the Ryu-Takayanagi formula (with a properly (discrete) geometric notion of area, thanks to the underlying quantum gravity formalism) and its corrections due to the entanglement entropy of the bulk state. We also show that the presence of a region with highly entangled intertwiners deforms the minimal-area surface, which is then prevented from entering that region when the entanglement entropy of the latter exceeds a certain bound. This entanglement-based mechanism leads thus to the formation of a black hole-like region in the bulk.

hep-th↗

arXiv2021

Holographic maps from quantum gravity states as tensor networks

We define bulk/boundary maps corresponding to quantum gravity states in the tensorial group field theory formalism, for quantum geometric models sharing the same type of quantum states of loop quantum gravity. The maps are defined in terms of a partition of the quantum geometric data associated to an open graph into bulk and boundary ones, in the spin representation. We determine the general condition on the entanglement structure of the state that makes the bulk/boundary map isometric (a necessary condition for holographic behaviour), and we analyse different types of quantum states, identifying those that define isometric bulk/boundary maps.

hep-th↗

arXiv2020

Covariant Momentum Map Thermodynamics for Parametrized Field Theories

A general-covariant statistical framework capable of describing classical fluctuations of the gravitational field is a thorny open problem in theoretical physics, yet ultimately necessary to understand the nature of the gravitational interaction and a key to quantum gravity. Inspired by Souriau's symplectic generalization of the Maxwell-Boltzmann-Gibbs equilibrium in Lie group thermodynamics, we investigate a spacetime-covariant formulation of statistical mechanics for parametrized first-order field theories, as a simplified model sharing essential general covariant features with canonical general relativity. Starting from a covariant multi-symplectic phase space formulation, we define a general-covariant notion of Gibbs state in terms of the covariant momentum map associated with the lifted action of the diffeomorphisms group on the extended phase space. We show how such a covariant notion of equilibrium encodes the whole information about symmetry, gauge and dynamics carried by the theory, associated to a canonical spacetime foliation, where the covariant choice of a reference frame reflects in a Lie algebra-valued notion of local temperature. We investigate how physical equilibrium, hence time evolution, emerges from such a state and the role of the gauge symmetry in the thermodynamic description.

math-ph↗

arXiv2019

Generalized Gibbs Ensembles in Discrete Quantum Gravity

Maximum entropy principle and Souriau's symplectic generalization of Gibbs states have provided crucial insights leading to extensions of standard equilibrium statistical mechanics and thermodynamics. In this brief contribution, we show how such extensions are instrumental in the setting of discrete quantum gravity, towards providing a covariant statistical framework for the emergence of continuum spacetime. We discuss the significant role played by information-theoretic characterizations of equilibrium. We present the Gibbs state description of the geometry of a tetrahedron and its quantization, thereby providing a statistical description of the characterizing quanta of space in quantum gravity. We use field coherent states for a generalized Gibbs state to write an effective statistical field theory that perturbatively generates 2-complexes, which are discrete spacetime histories in several quantum gravity approaches.

gr-qc↗

arXiv2019

Statistical equilibrium of tetrahedra from maximum entropy principle

Discrete formulations of (quantum) gravity in four spacetime dimensions build space out of tetrahedra. We investigate a statistical mechanical system of tetrahedra from a many-body point of view based on non-local, combinatorial gluing constraints that are modelled as multi-particle interactions. We focus on Gibbs equilibrium states, constructed using Jaynes' principle of constrained maximisation of entropy, which has been shown recently to play an important role in characterising equilibrium in background independent systems. We apply this principle first to classical systems of many tetrahedra using different examples of geometrically motivated constraints. Then for a system of quantum tetrahedra, we show that the quantum statistical partition function of a Gibbs state with respect to some constraint operator can be reinterpreted as a partition function for a quantum field theory of tetrahedra, taking the form of a group field theory.

gr-qc↗

arXiv2019

Group Field Theory and Holographic Tensor Networks: Dynamical Corrections to the Ryu-Takayanagi formula

We introduce group field theory networks as a generalization of spin networks and of (symmetric) random tensor networks and provide a statistical computation of the Rényi entropy for a bipartite network state using the partition function of a simple interacting group field theory. The expectation value of the entanglement entropy is calculated by an expansion into stranded Feynman graphs and is shown to be captured by a Ryu- Takayanagi formula. For a simple interacting group field theory, we can prove the linear corrections, given by a polynomial perturbation of the Gaussian measure, to be negligible for a broad class of networks.

hep-th↗

arXiv2018

Fisher Metric, Geometric Entanglement and Spin Networks

Starting from recent results on the geometric formulation of quantum mechanics, we propose a new information geometric characterization of entanglement for spin network states in the context of quantum gravity. For the simple case of a single-link fixed graph (Wilson line), we detail the construction of a Riemannian Fisher metric tensor and a symplectic structure on the graph Hilbert space, showing how these encode the whole information about separability and entanglement. In particular, the Fisher metric defines an entanglement monotone which provides a notion of distance among states in the Hilbert space. In the maximally entangled gauge-invariant case, the entanglement monotone is proportional to a power of the area of the surface dual to the link thus supporting a connection between entanglement and the (simplicial) geometric properties of spin network states. We further extend such analysis to the study of non-local correlations between two non-adjacent regions of a generic spin network graph characterized by the bipartite unfolding of an Intertwiner state. Our analysis confirms the interpretation of spin network bonds as a result of entanglement and to regard the same spin network graph as an information graph, whose connectivity encodes, both at the local and non-local level, the quantum correlations among its parts. This gives a further connection between entanglement and geometry.

gr-qc↗