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Patrizia Vitale

Publications and source records attributed to Patrizia Vitale.

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 $\alpha$, when the family of algebras is contracted to the Poincar\'e algebra in the limit $\alpha \to 0$. 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↗
arXiv2025

The electromagnetic field in Poisson gauge theory: the groupoidal approach

We consider the problem of defining the field strength of abelian potentials when the spacetime is a Poisson manifold, within the groupoidal approach. The natural definition in terms of gauge invariant momenta is proved to be equivalent to covariant and invariant tensors of a local symplectic groupoid representing a symplectic realization of the Poisson manifold. A Poisson Chern-Simons model is then proposed and its equations of motion are shortly discussed.

hep-th↗
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 In\"o\"nu-Wigner contraction of the (A)dS algebra. By setting the group parameter $\alpha$ 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↗
arXiv2024

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

Jacobi Sigma Models and Twisted Jacobi Structures

Jacobi sigma models are two-dimensional topological non-linear field theories which are associated with Jacobi structures. The latter can be considered as a generalization of Poisson structures. After reviewing the main properties and peculiarities of these models, we focus on the twisted version in which a Wess-Zumino term is included. This modification allows for the target space to be a twisted Jacobi manifold. We discuss in particular the model on the sphere $S^5$.

hep-th↗
arXiv2024

Symplectic realizations and Lie groupoids in Poisson Electrodynamics

We define the gauge potentials of Poisson electrodynamics as sections of a symplectic realization of the spacetime manifold and infinitesimal gauge transformations as a representation of the associated Lie algebroid acting on the symplectic realization. Finite gauge transformations are obtained by integrating the sections of the Lie algebroid to bisections of a symplectic groupoid, which form a one-parameter group of transformations, whose action on the fields of the theory is realized in terms of an action groupoid. A covariant electromagnetic two-form is obtained, together with a dual two-form, invariant under gauge transformations. The duality appearing in the picture originates from the existence of a pair of orthogonal foliations of the symplectic realization, which produce dual quotient manifolds, one related with space-time, the other with momenta.

hep-th↗
arXiv2023

Introduction to noncommutative field and gauge theory

These are lecture notes for an introductory course on noncommutative field and gauge theory. We begin by reviewing quantum mechanics as the prototypical noncommutative theory, as well as the geometrical language of standard gauge theory. Then, we review a specific approach to noncommutative field and gauge theory, which relies on the introduction of a derivations-based differential calculus. We focus on the cases of constant and linear noncommutativity, e.g., the Moyal spacetime and the so-called $\mathbb{R}^3_λ$, respectively. In particular, we review the $gφ^4$ scalar field theory and the $U(1)$ gauge theory on such noncommutative spaces. Finally, we discuss noncommutative spacetime symmetries from both the observer and particle point of view. In this context, the twist approach is reviewed and the $λ$-Minkowski $gφ^4$ model is discussed.

hep-th↗
arXiv2023

Monotone metric tensors in Quantum Information Geometry

We review some geometrical aspects pertaining to the world of monotone quantum metrics in finite dimensions. Particular emphasis is given to an unfolded perspective for quantum states that is built out of the spectral theorem and is naturally suited to investigate the comparison with the classical case of probability distributions.

quant-ph↗
arXiv2023

Double Quantization

In a quantum gravity theory, it is expected that the classical notion of spacetime disappears, leading to a quantum structure with new properties. A possible way to take into account these quantum effects is through a noncommutativity of spacetime coordinates. In the literature, there is not a clear way to describe at the same time a noncommutativity of spacetime and the phase-space noncommutativity of quantum mechanics. In this paper we address this issue by constructing a Drinfel'd twist in phase space which deals with both quantizations. This method can be applied to a noncommutativity which involves only space, leaving time aside. We apply our construction to the so-called $λ$-Minkwoski and $\mathbb{R}^3_λ$ noncommutative spaces.

hep-th↗
arXiv2022

Localization and observers in $\varrho$-Minkowski spacetime

We consider the $\varrho$-Minkowski spacetime, a model with linear noncommutativity involving the time and the azimuthal angle. We study its quantum symmetries, the $\varrho$-Poincaré quantum group, and analyse the concepts of localizability and quantum observers.

hep-th↗
arXiv2022

On the classical Integrability of Poisson-Lie T-dual WZW models

We consider the integrability of a two-parameter deformation of the Wess-Zumino-Witten model, previously introduced in relation with Poisson-Lie T-duality. The resulting family of Poisson-Lie dual models is shown to be integrable by using the Maillet r/s formalism.

hep-th↗
arXiv2022

The Mass Hyperboloid as a Poisson-Lie Group

The light cone formalism of a massive scalar field has been shown by Dirac to have many advantages. But it is not manifestly Lorentz invariant. We will show that this is a feature not a bug: Lorentz invariance is indeed a symmetry, but in a different sense defined by Drinfel'd. The key idea is that the mass shell (mass hyperboloid) is a Poisson-Lie group: there is a non-abelian group multiplication and non-zero Poisson brackets between components of four-momentum. Rotations form the dual group of the hyperboloid in the sense of Drinfel'd. Infinitesimal Lorentz transformations form a Lie bi-algebra.

hep-th↗
arXiv2021

Four-dimensional noncommutative deformations of $U(1)$ gauge theory and $L_{\infty}$ bootstrap

We construct a family of four-dimensional noncommutative deformations of $U(1)$ gauge theory following a general scheme, recently proposed in JHEP 08 (2020) 041 for a class of coordinate-dependent noncommutative algebras. This class includes the $\mathfrak{su}(2)$, the $\mathfrak{su}(1,1)$ and the angular (or $λ$-Minkowski) noncommutative structures. We find that the presence of a fourth, commutative coordinate $x^0$ leads to substantial novelties in the expression for the deformed field strength with respect to the corresponding three-dimensional case. The constructed field theoretical models are Poisson gauge theories, which correspond to the semi-classical limit of fully noncommutative gauge theories. Our expressions for the deformed gauge transformations, the deformed field strength and the deformed classical action exhibit flat commutative limits and they are exact in the sense that all orders in the deformation parameter are present. We review the connection of the formalism with the $L_{\infty}$ bootstrap and with symplectic embeddings, and derive the $L_{\infty}$-algebra, which underlies our model.

hep-th↗
arXiv2021

Gribov horizon in Noncommutative QED

It is known that Noncommutative QED (NCQED) exhibits Gribov ambiguities in the Landau gauge. These ambiguities are related to zero modes of the Faddeev-Popov operator and arise in the ghost propagator when it has a pole. In this work, we establish a positive Faddeev-Popov operator for NCQED and the condition for the ghost propagator not to have poles, the so-called Gribov no-pole condition. This condition is implemented in the path integral, and allows for the calculation of the photon propagator in momentum space, which is dependent on the squared non-commutativity parameter. In the commutative limit standard QED is recovered.

hep-th↗
arXiv2021

Topological and dynamical aspects of Jacobi sigma models

The geometric properties of sigma models with target space a Jacobi manifold are investigated. In their basic formulation, these are topological field theories - recently introduced by the authors - which share and generalise relevant features of Poisson sigma models, such as gauge invariance under diffeomorphisms and finite dimension of the reduced phase space. After reviewing the main novelties and peculiarities of these models, we perform a detailed analysis of constraints and ensuing gauge symmetries in the Hamiltonian approach. Contact manifolds as well as locally conformal symplectic manifolds are discussed, as main instances of Jacobi manifolds.

hep-th↗
arXiv2021

Towards a Geometrization of Quantum Complexity and Chaos

In this paper, we show how the restriction of the Quantum Geometric Tensor to manifolds of states that can be generated through local interactions provides a new tool to understand the consequences of locality in physics. After a review of a first result in this context, consisting in a geometric out-of-equilibrium extension of the quantum phase transitions, we argue the opportunity and the usefulness to exploit the Quantum Geometric Tensor to geometrize quantum chaos and complexity.

quant-ph↗