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Franco Pezzella

Publications and source records attributed to Franco Pezzella.

At least 19 recordsLinked to original sources
arXiv2025

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↗
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 Effective Theory of Quantum Black Holes

We explore the quantum nature of black holes by introducing an effective framework that takes into account deviations from the classical results. The approach is based on introducing quantum corrections to the classical Schwarzschild geometry in a way that is consistent with the physical scales of the black hole and its classical symmetries. This is achieved by organizing the quantum corrections in inverse powers of a physical distance. By solving the system in a self-consistent way we show that the derived physical quantities, such as event horizons, temperature and entropy can be expressed in a well defined expansion in the inverse powers of the black hole mass. The approach captures the general form of the quantum corrections to black hole physics without requiring to commit to a specific model of quantum gravity.

gr-qc↗
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

Jacobi sigma models

We introduce a two-dimensional sigma model associated with a Jacobi manifold. The model is a generalisation of a Poisson sigma model providing a topological open string theory. In the Hamiltonian approach first class constraints are derived, which generate gauge invariance of the model under diffeomorphisms. The reduced phase space is finite-dimensional. By introducing a metric tensor on the target, a non-topological sigma model is obtained, yielding a Polyakov action with metric and B-field, whose target space is a Jacobi manifold.

hep-th↗
arXiv2020

Poisson-Lie T-Duality of WZW Model via Current Algebra Deformation

Poisson-Lie T-duality of the Wess-Zumino-Witten (WZW) model having the group manifold of $SU(2)$ as target space is investigated. The whole construction relies on the deformation of the affine current algebra of the model, the semi-direct sum $\mathfrak{su}(2)(\mathbb{R}) \, \dot{\oplus} \, \mathfrak{a}$, to the fully semisimple Kac-Moody algebra $\mathfrak{sl}(2,\mathbb{C})(\mathbb{R})$. A two-parameter family of models with $SL(2,\mathbb{C})$ as target phase space is obtained so that Poisson-Lie T-duality is realised as an $O(3,3)$ rotation in the phase space. The dual family shares the same phase space but its configuration space is $SB(2,\mathbb{C})$, the Poisson-Lie dual of the group $SU(2)$. A parent action with doubled degrees of freedom on $SL(2,\mathbb{C})$ is defined, together with its Hamiltonian description.

hep-th↗
arXiv2020

More Stringy Effects in Target Space from Double Field Theory

In Double Field Theory, the mass-squared of doubled fields associated with bosonic closed string states is proportional to $N_L+N_R-2$. Massless states are therefore not only the graviton, anti-symmetric, and dilaton fields with $(N_L=1, N_R=1)$ such theory is focused on, but also the symmetric traceless tensor and the vector field relative to the states $(N_L=2, N_R=0)$ and $(N_L=0, N_R=2)$ which are massive in the lower-dimensional non-compactified space. While they are not even physical in the absence of compact dimensions, they provide a sample of states for which both momenta and winding numbers are non-vanishing, differently from the states $(N_L=1, N_R=1)$. A quadratic action is therefore here built for the corresponding doubled fields. It results that its gauge invariance under the linearized double diffeomorphisms is based on a generalization of the usual weak constraint, giving rise to an extra mass term for the symmetric traceless tensor field, not otherwise detectable: this can be interpreted as a mere stringy effect in target space due to the simultaneous presence of momenta and windings. Furthermore, in the context of the generalized metric formulation, a non-linear extension of the gauge transformations is defined involving the constraint extended from the weak constraint that can be uniquely defined in triple products of fields. Finally, we show that the above mentioned stringy effect does not appear in the case of only one compact doubled space dimension.

hep-th↗
arXiv2020

Principal Chiral Model without and with WZ term: Symmetries and Poisson-Lie T-Duality

Duality properties of the $SU(2)$ Principal Chiral Model are investigated starting from a one-parameter family of its equivalent Hamiltonian descriptions generated by a non-Abelian deformation of the cotangent space $T^*SU(2) \simeq SU(2) \ltimes \mathbb{R}^3$. The corresponding dual models are obtained through $O(3,3)$ duality transformations and result to be defined on the group $SB(2,\mathbb{C})$, which is the Poisson-Lie dual of $SU(2)$ in the Iwasawa decomposition of the Drinfel'd double $SL(2,\mathbb{C})=SU(2) \bowtie SB(2,\mathbb{C})$.These dual models provide an explicit realization of Poisson-Lie T-duality. A doubled generalized parent action is then built on the tangent space $TSL(2,\mathbb{C})$. Furthermore, a generalization of the $SU(2)$ PCM with a WZ term is shortly discussed.

hep-th↗
arXiv2019

T-Dualities and Doubled Geometry of the Principal Chiral Model

The Principal Chiral Model (PCM) defined on the group manifold of SU(2) is here investigated with the aim of getting a further deepening of its relation with Generalized and Doubled Geometry. A one-parameter family of equivalent Hamiltonian descriptions is introduced, and cast into the form of Born geometries. Then O(3,3) duality transformations of the target phase space are performed and we show that the resulting dual models are defined on the group SB(2,C) which is the Poisson-Lie dual of SU(2) in the Iwasawa decomposition of the Drinfel'd double SL(2, C). Moreover, starting from the Lagrangian approach, a new kind of duality is found between the SU(2) PCM and the natural one defined on SB(2,C) which is not an isometry of the target phase space. A parent action with doubled degrees of freedom and configuration space SL(2, C) is then defined that reduces to either one of the dually related models, once suitable constraints are implemented.

hep-th↗
arXiv2019

T-Duality and Doubling of the Isotropic Rigid Rotator

After reviewing some of the fundamental aspects of Drinfel'd doubles and Poisson-Lie T-duality, we describe the three-dimensional isotropic rigid rotator on $SL(2,\mathbb{C})$ starting from a non-Abelian deformation of the natural carrier space of its Hamiltonian description on $T^*SU(2) \simeq SU(2) \ltimes \mathbb{R}^3$. A new model is then introduced on the dual group $SB(2,\mathbb{C})$, within the Drinfel'd double description of $SL(2,\mathbb{C})=SU(2) \bowtie SB(2,\mathbb{C})$. The two models are analyzed from the Poisson-Lie duality point of view, and a doubled generalized action is built with $TSL(2,\mathbb{C})$ as carrier space. The aim is to explore within a simple case the relations between Poisson-Lie symmetry, Doubled Geometry and Generalized Geometry. In fact, all the mentioned structures are discussed, such as a Poisson realization of the $C$-brackets for the generalized bundle $T \oplus T^*$ over $SU(2)$ from the Poisson algebra of the generalized model. The two dual models exhibit many features of Poisson-Lie duals and from the generalized action both of them can be respectively recovered by gauging one of its symmetries.

hep-th↗
arXiv2018

Doubling, T-Duality and Generalized Geometry: a Simple Model

A simple mechanical system, the three-dimensional isotropic rigid rotator, is here investigated as a 0+1 field theory, aiming at further investigating the relation between Generalized/Double Geometry on the one hand and Doubled World-Sheet Formalism/Double Field Theory, on the other hand. The model is defined over the group manifold of SU(2) and a dual model is introduced having the Poisson-Lie dual of SU(2) as configuration space. A generalized action with configuration space SL(2,C), i.e. the Drinfel'd double of the group SU(2), is then defined: it reduces to the original action of the rotator or to its dual, once constraints are implemented. The new action contains twice as many variables as the original. Moreover, its geometric structures can be understood in terms of Generalized Geometry. keywords: Generalized Geometry, Double Field Theory, T-Duality, Poisson-Lie symmetry.

hep-th↗
arXiv2017

Geometric Low-Energy Effective Action in a Doubled Spacetime

The ten-dimensional supergravity theory is a geometric low-energy effective theory and the equations of motion for its fields can be obtained from string theory by computing $β$ functions. With $d$ compact dimensions, we can add to it an $O(d, d;\mathbb{Z})$ geometric structure and construct the supergravity theory inspired by double field theory through the use of a suitable commutative star product. The latter implements the weak constraint of the double field theory on its fields and gauge parameters in order to have a closed gauge symmetry algebra. The consistency of the action here proposed is based on the orthogonality of the momenta associated with fields in their triple star products in the cubic terms defined for $d\ge1$. This orthogonality holds also for an arbitrary number of star products of fields for $d=1$. Finally, we extend our analysis to the double sigma model, non-commutative geometry and open string theory.

hep-th↗
arXiv2016

Supergravity with Doubled Spacetime Structure

Double Field Theory (DFT) is a low-energy effective theory of a manifestly $O(D,D)$ invariant formulation of the closed string theory when toroidally compactified dimensions are present. The theory is based on a doubled spacetime structure and, in order to preserve the gauge symmetry provided by the invariance under generalized diffeomorphisms, a constraint has to be imposed on fields and gauge parameters. In this paper, we propose a DFT-inspired Supergravity by using a suitable {\em star product} that implements such constraint and the corresponding algebraic structure is explored. We get a consistent DFT in which also an orthogonality condition of momenta is necessary for having a closed gauge algebra. In constructing this theory, we start from the simplest case of doubling one spatial dimension where the action is uniquely determined, without ambiguities, by the gauge symmetry. Then, the extension to the generic $O(D, D)$ case is presented. The result is consistent with the closed string field theory.

hep-th↗
arXiv2016

Some Aspects of the T-Duality Symmetric String Sigma Model

A manifestly T-dual invariant formulation of bosonic string theory is discussed here. It can be obtained by making both the usual string compact coordinates and their duals explicitly appear, on the same footing, in the world-sheet action. A peculiarity of such a model is the loss of the local Lorentz invariance which is required to be recovered on-shell. This dictates a constraint on the backgrounds which characterizes the double geometry of the target space. Constant and non-constant backgrounds are considered. In the former case, the local Lorentz constraint implies the geometry of a double torus with an $O(D,D)$ invariance. In the latter, it is shown how and when the $O(D,D)$ invariance still holds and when deformations from it can be implied. Results of the quantization of the free theory are also briefly exhibited.

hep-th↗
arXiv2015

Two Double String Theory Actions: Non-Covariance vs. Covariance

The aim of this work is to achieve a formulation of the bosonic string theory in which T-duality appears as a manifest symmetry. Two models exhibiting this property are discussed. The first is based on the stringy extension of the Floreanini-Jackiw Lagrangians for chiral fields and is characterized by the loss of manifest covariance on the world-sheet, recovered on mass-shell. The second model exhibits two-dimensional covariance while doubling a priori the string coordinates in the target space. They are shown to be equivalent.

hep-th↗
arXiv2014

Comparing Double String Theory Actions

Aimed to a deeper comprehension of a manifestly T-dual invariant formulation of string theory, in this paper a detailed comparison between the non-covariant action proposed by Tseytlin and the covariant one proposed by Hull is done. These are obtained by making both the string coordinates and their duals explicitly appear, on the same foot, in the world-sheet action, so "doubling" the string coordinates along the compact dimensions. After a discussion of the nature of the constraints in both the models and the relative quantization, it results that the string coordinates and their duals behave like "non-commuting" phase space type coordinates but their expressions in terms of Fourier modes generate the oscillator algebra of the standard bosonic string formulation. A proof of the equivalence of the two formulations is given. Furthermore, open-string solutions are also discussed.

hep-th↗
arXiv2014

On the Number of Cosmic Strings

The number of cosmic strings in the observable universe is relevant in determining the probability of detecting such cosmic defects through their gravitational signatures. In particular, we refer to the observation of gravitational lensing events and anisotropy in the CMB radiation induced by cosmic strings. In this paper, a simple method is adopted to obtain an approximate estimate of the number of segments of cosmic strings, crossing the particle horizon, which fall inside the observed part of the universe. We show that there is an appreciable difference in the expected number of segments which differentiates cosmic strings arising in Abelian Higgs and Nambu-Goto models, and that a different choice of setting for the cosmological model can lead to significant differences in the expected number of cosmic string segments. Of this number, the fraction realistically detectable may be considerably smaller.

astro-ph.CO↗