arXiv subjects

Daniele Pranzetti

Publications and source records attributed to Daniele Pranzetti.

At least 19 recordsLinked to original sources

arXiv2026

Higher-spin charges and the $L_Λ w_{1 + \infty}$ algebra in (A)dS$_4$

We consider $(3+1)$-dimensional asymptotically locally (anti-)de Sitter ((A)dS$_4$) spacetimes with boundary conditions allowing for gravitational flux. We construct an infinite tower of higher-spin charges as perturbative solutions in the cosmological constant $Λ$ to a hierarchy of evolution equations resulting from an asymptotic expansion of the Einstein equations. We show that these charges canonically realize the $Λ$-deformed $w_{1+\infty}$ algebra ($L_Λ w_{1+\infty}$) on a restricted gravitational phase space, thereby extending the higher-spin symmetry structure of asymptotically flat spacetimes to asymptotically (A)dS spacetimes. We further construct the curved-space counterparts of conformally soft gravitons directly in terms of spacetime data. We show that they are primaries with respect to an $\mathfrak{sl}(2,\mathbb{R})$ subalgebra of the (A)dS$_4$ isometry algebra and that their Poisson brackets with the quadratic higher-spin charges reproduce the $Λ$-deformed celestial operator product expansion proposed by Taylor and Zhu. Our results establish the bulk gravitational origin of the $L_Λw_{1+\infty}$ symmetry and extend the celestial bulk-boundary dictionary to asymptotically (A)dS$_4$ gravity.

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arXiv2026

Mixed-helicity bracket of celestial symmetries

Celestial symmetries of gravity and gauge theory can be enhanced to a $w_{1+\infty}$ algebra and an $S$-algebra respectively, when restricting to a single graviton/gluon helicity sector. Difficulties in combining both sectors in the full theory have been pointed out in the previous literature. In this work, we face this problem from the covariant phase space perspective and analyze in detail the structure of the mixed-helicity bracket of the higher-spin charges for both gravity and Yang--Mills theory. We show that, when restricting one of the two helicities to the wedge sector, a closed algebra can be obtained for all spins in terms of a notion of shadow charge we introduce. Furthermore, when focusing on the lower spin subalgebra sectors, in the case of gravity, we show that a dual mass extension of the BMS algebra can be consistently constructed; in the case of Maxwell theory, inclusion of magnetic charges allows us to recover a non-vanishing expression for the electromagnetic central charge previously obtained through different methods.

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arXiv2026

Double-soft limit and celestial shadow OPE from charge bracket

The dual formulations of an infinite tower of tree-level soft theorems in asymptotically flat spacetimes for scattering amplitudes in the standard energy-momentum basis and for correlators of a 2D celestial conformal field theory imply a correspondence between the celestial operator product expansion (OPE) and the higher spin charge bracket. We apply such correspondence to provide first a prescription to solve the double-soft limit ambiguity in the mixed-helicity sector of celestial OPEs. Furthermore, demanding the charge OPE/bracket correspondence to remain valid when operators are shadow transformed, we construct an algorithm to compute shadow celestial OPEs. We first test the algorithm by recovering results in the previous literature involving the celestial energy-momentum tensor; we then apply it to both gravity and Yang-Mills theory and generalize the OPE derivation to arbitrary spins.

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arXiv2024

On the Definition of the Spin Charge in Asymptotically-Flat Spacetimes

We propose a solution to a classic problem in gravitational physics consisting of defining the spin associated with asymptotically-flat spacetimes. We advocate that the correct asymptotic symmetry algebra to approach this problem is the generalized-BMS algebra $\textsf{gbms}$ instead of the BMS algebra used hitherto in the literature for which a notion of spin is generically unavailable. We approach the problem of defining the spin charges from the perspective of coadjoint orbits of $\textsf{gbms}$ and construct the complete set of Casimir invariants that determine $\textsf{gbms}$ coadjoint orbits, using the notion of vorticity for $\textsf{gbms}$. This allows us to introduce spin charges for $\textsf{gbms}$ as the generators of area-preserving diffeomorphisms forming its isotropy subalgebra. To elucidate the parallelism between our analysis and the Poincaré case, we clarify several features of the Poincaré embedding in $\textsf{gbms}$ and reveal the presence of condensate fields associated with the symmetry breaking from $\textsf{gbms}$ to Poincaré. We also introduce the notion of a rest frame available only for this extended algebra. This allows us to construct, from the spin generator, the gravitational analog of the Pauli--Lubański pseudo-vector. Finally, we obtain the $\textsf{gbms}$ moment map, which we use to construct the gravitational spin charges and gravitational Casimirs from their dual algebra counterparts.

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arXiv2024

A discrete basis for celestial holography

Celestial holography provides a reformulation of scattering amplitudes in four dimensional asymptotically flat spacetimes in terms of conformal correlators of operators on the two dimensional celestial sphere in a basis of boost eigenstates. A basis of {massless particle} states has previously been identified in terms of conformal primary wavefunctions labeled by a boost weight $Δ= 1 + iλ$ with $λ\in \mathbb{R}$. Here we show that a {\it discrete} orthogonal and complete basis exists for $Δ\in \mathbb{Z}$. This new basis consists of a tower of discrete memory and Goldstone observables, which are conjugate to each other and allow to reconstruct gravitational signals belonging to the Schwartz space. We show how generalized dressed states involving the whole tower of Goldstone operators can be constructed and evaluate the higher spin Goldstone 2-point functions. Finally, we recast the tower of higher spin charges providing a representation of the $w_{1+\infty}$ loop algebra (in the same helicity sector) in terms of the new discrete basis.

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arXiv2023

On infinite symmetry algebras in Yang-Mills theory

Similar to gravity, an infinite tower of symmetries generated by higher-spin charges has been identified in Yang-Mills theory by studying collinear limits or celestial operator products of gluons. This work aims to recover this loop symmetry in terms of charge aspects constructed on the gluonic Fock space. We propose an explicit construction for these higher spin charge aspects as operators which are polynomial in the gluonic annihilation and creation operators. The core of the paper consists of a proof that the charges we propose form a closed loop algebra to quadratic order. This closure involves using the commutator of the cubic order expansion of the charges with the linear (soft) charge. Quite remarkably, this shows that this infinite-dimensional symmetry constrains the non-linear structure of Yang-Mills theory. We provide a similar all spin proof in gravity for the so-called global quadratic (hard) charges which form the loop wedge subalgebra of $w_{1+\infty}$.

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arXiv2022

Black Hole Entropy in Loop Quantum Gravity

We give an account of the state of the art about black hole entropy in Loop Quantum Gravity. This chapter contains a historical summary and explains how black hole entropy is described by relying on the concept of isolated horizon, with an emphasis on different representations of its associated symmetry group. It continues with a review of the combinatorial methods necessary to understand the behavior of the entropy as a function of the area and concludes with a discussion of the nature of the quantum horizon degrees of freedom that account for the black hole entropy and the related issue of the fixing of the Immirzi parameter.

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arXiv2022

Gravity from symmetry: Duality and impulsive waves

We show that we can derive the asymptotic Einstein's equations that arises at order $1/r$ in asymptotically flat gravity purely from symmetry considerations. This is achieved by studying the transformation properties of functionals of the metric and the stress-energy tensor under the action of the Weyl BMS group, a recently introduced asymptotic symmetry group that includes arbitrary diffeomorphisms and local conformal transformations of the metric on the 2-sphere. Our derivation, which encompasses the inclusion of matter sources, leads to the identification of covariant observables that provide a definition of conserved charges parametrizing the non-radiative corner phase space. These observables, related to the Weyl scalars, reveal a duality symmetry and a spin-2 generator which allow us to recast the asymptotic evolution equations in a simple and elegant form as conservation equations for a null fluid living at null infinity. Finally we identify non-linear gravitational impulse waves that describe transitions among gravitational vacua and are non-perturbative solutions of the asymptotic Einstein's equations. This provides a new picture of quantization of the asymptotic phase space, where gravitational vacua are representations of the asymptotic symmetry group and impulsive waves are encoded in their couplings.

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arXiv2022

Higher spin dynamics in gravity and $w_{1 + \infty}$ celestial symmetries

In this paper we extract from a large-$r$ expansion of the vacuum Einstein's equations a dynamical system governing the time evolution of an infinity of higher-spin charges. Upon integration, we evaluate the canonical action of these charges on the gravity phase space. The truncation of this action to quadratic order and the associated charge conservation laws yield an infinite tower of soft theorems. We show that the canonical action of the higher spin charges on gravitons in a conformal primary basis, as well as conformally soft gravitons reproduces the higher spin celestial symmetries derived from the operator product expansion. Finally, we give direct evidence that these charges form a canonical representation of a $w_{1+\infty}$ loop algebra on the gravitational phase space.

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arXiv2022

Sub-subleading Soft Graviton Theorem from Asymptotic Einstein's Equations

We identify in Einstein gravity an asymptotic spin-$2$ charge aspect whose conservation equation gives rise, after quantization, to the sub-subleading soft theorem. Our treatment reveals that this spin-$2$ charge generates a non-local spacetime symmetry represented at null infinity by pseudo-vector fields. Moreover, we demonstrate that the non-linear nature of Einstein's equations is reflected in the Ward identity through collinear corrections to the sub-subleading soft theorem. Our analysis also provides a unified treatment of the universal soft theorems as conservation equations for the spin-0,-1,-2 canonical generators, while highlighting the important role played by the dual mass.

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arXiv2021

Extended corner symmetry, charge bracket and Einstein's equations

We develop the covariant phase space formalism allowing for non-vanishing flux, anomalies and field dependence in the vector field generators. We construct a charge bracket that generalizes the one introduced by Barnich and Troessaert and includes contributions from the Lagrangian and its anomaly. This bracket is uniquely determined by the choice of Lagrangian representative of the theory. We then extend the notion of corner symmetry algebra to include the surface translation symmetries and prove that the charge bracket provides a canonical representation of the extended corner symmetry algebra. This representation property is shown to be equivalent to the projection of the gravitational equations of motion on the corner, providing us with an encoding of the bulk dynamics in a locally holographic manner.

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arXiv2021

The Weyl BMS group and Einstein's equations

We propose an extension of the BMS group, which we refer to as Weyl BMS or BMSW for short, that includes, besides super-translations, local Weyl rescalings and arbitrary diffeomorphisms of the 2d sphere metric. After generalizing the Barnich-Troessaert bracket, we show that the Noether charges of the BMSW group provide a centerless representation of the BMSW Lie algebra at every cross section of null infinity. This result is tantamount to proving that the flux-balance laws for the Noether charges imply the validity of the asymptotic Einstein's equations at null infinity. The extension requires a holographic renormalization procedure, which we construct without any dependence on background fields. The renormalized phase space of null infinity reveals new pairs of conjugate variables. Finally, we show that BMSW group elements label the gravitational vacua.

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arXiv2021

Electromagnetic duality and central charge from first order formulation

In the context of the infrared triangle there have been recent discussions on the existence and the role of dual charges. We present a new viewpoint on dual magnetic charges in $p$-form theories, and argue that they can be inherited from the charges of a first order formulation as a topological BF theory with potential. This happens because, depending on the spacetime dimension and on the form degree, the so-called translational gauge symmetries of BF theory become reducible and therefore admit zero-modes. Although such zero-modes lead to trivial symmetries of the $p$-form theory, they are associated with non-trivial charges. These turn out to be precisely the dual magnetic charges. The centrally-extended current algebra of electric and magnetic charges in the $p$-form theory then descends naturally from that of BF theory. This is an effort towards finding an existence criterion for dual charges.

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arXiv2021

Edge modes of gravity. Part III. Corner simplicity constraints

In the tetrad formulation of gravity, the so-called simplicity constraints play a central role. They appear in the Hamiltonian analysis of the theory, and in the Lagrangian path integral when constructing the gravity partition function from topological BF theory. We develop here a systematic analysis of the corner symplectic structure encoding the symmetry algebra of gravity, and perform a thorough analysis of the simplicity constraints. Starting from a precursor phase space with Poincaré and Heisenberg symmetry, we obtain the corner phase space of BF theory by imposing kinematical constraints. This amounts to fixing the Heisenberg frame with a choice of position and spin operators. The simplicity constraints then further reduce the Poincaré symmetry of the BF phase space to a Lorentz subalgebra. This picture provides a particle-like description of (quantum) geometry: The internal normal plays the role of the four-momentum, the Barbero-Immirzi parameter that of the mass, the flux that of a relativistic position, and the frame that of a spin harmonic oscillator. Moreover, we show that the corner area element corresponds to the Poincaré spin Casimir. We achieve this central result by properly splitting, in the continuum, the corner simplicity constraints into first and second class parts. We construct the complete set of Dirac observables, which includes the generators of the local $\mathfrak{sl}(2,\mathbb{C})$ subalgebra of Poincaré, and the components of the tangential corner metric satisfying an $\mathfrak{sl}(2,\mathbb{R})$ algebra. We then present a preliminary analysis of the covariant and continuous irreducible representations of the infinite-dimensional corner algebra. Moreover, as an alternative path to quantization, we also introduce a regularization of the corner algebra and interpret this discrete setting in terms of an extended notion of twisted geometries.

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arXiv2020

Edge modes of gravity -- I: Corner potentials and charges

This is the first paper in a series devoted to understanding the classical and quantum nature of edge modes and symmetries in gravitational systems. The goal of this analysis is to: i) achieve a clear understanding of how different formulations of gravity provide non-trivial representations of different sectors of the corner symmetry algebra, and ii) set the foundations of a new proposal for states of quantum geometry as representation states of this corner symmetry algebra. In this first paper we explain how different formulations of gravity, in both metric and tetrad variables, share the same bulk symplectic structure but differ at the corner, and in turn lead to inequivalent representations of the corner symmetry algebra. This provides an organizing criterion for formulations of gravity depending on how big the physical symmetry group that is non-trivially represented at the corner is. This principle can be used as a "treasure map" revealing new clues and routes in the quest for quantum gravity. Building up on these results, we perform a detailed analysis of the corner symplectic potential and symmetries of Einstein-Cartan-Holst gravity in [1], use this to provide a new look at the simplicity constraints in [2], and tackle the quantization in [3].

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arXiv2020

Asymptotically de Sitter Universe inside a Schwarzschild black hole

Extending our previous analysis, we study the interior of a Schwarzschild black hole derived from a partial gauge fixing of the full Loop Quantum Gravity Hilbert space, this time including the inverse volume and coherent state subleading corrections. Our derived effective Hamiltonian differs crucially from the ones introduced in the minisuperspace models. This distinction is reflected in the class of homogeneous bouncing geometries that replace the classical singularity and are labeled by a set of quantum parameters associated with the structure of coherent states used to derive the effective Hamiltonian. By fixing these quantum parameters through geometrical considerations, the post-bounce interior geometry reveals a high sensitivity to the value of the Barbero-Immirzi parameter $γ$. Surprisingly, we find that $γ\approx 0.274$ results in an asymptotically de Sitter geometry in the interior region, where now a cosmological constant is generated purely from quantum gravitational effects. The striking fact is the exact coincidence of this value for $γ$ with the one derived from the SU(2) black hole entropy calculations in Loop Quantum Gravity. The emergence of this value in two entirely unrelated theoretical frameworks and computational setups is strongly suggestive of deep ties between the area gap in Loop Quantum Gravity, black hole physics, and the observable Universe. In connection to the latter, we point out an intriguing relation between the measured value of the cosmological constant and the observed mass in the Universe from a proposal for a spin quantum number renormalization effect associated to the microscopic dynamics.

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arXiv2020

Edge modes of gravity -- II: Corner metric and Lorentz charges

In this second paper of the series we continue to spell out a new program for quantum gravity, grounded in the notion of corner symmetry algebra and its representations. Here we focus on tetrad gravity and its corner symplectic potential. We start by performing a detailed decomposition of the various geometrical quantities appearing in BF theory and tetrad gravity. This provides a new decomposition of the symplectic potential of BF theory and the simplicity constraints. We then show that the dynamical variables of the tetrad gravity corner phase space are the internal normal to the spacetime foliation, which is conjugated to the boost generator, and the corner coframe field. This allows us to derive several key results. First, we construct the corner Lorentz charges. In addition to sphere diffeomorphisms, common to all formulations of gravity, these charges add a local $\mathfrak{sl}(2,\mathbb{C})$ component to the corner symmetry algebra of tetrad gravity. Second, we also reveal that the corner metric satisfies a local $\mathfrak{sl}(2,\mathbb{R})$ algebra, whose Casimir corresponds to the corner area element. Due to the space-like nature of the corner metric, this Casimir belongs to the unitary discrete series, and its spectrum is therefore quantized. This result, which reconciles discreteness of the area spectrum with Lorentz invariance, is proven in the continuum and without resorting to a bulk connection. Third, we show that the corner phase space explains why the simplicity constraints become non-commutative on the corner. This fact requires a reconciliation between the bulk and corner symplectic structures, already in the classical continuum theory. Understanding this leads inevitably to the introduction of edge modes.

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arXiv2020

Kinematical Gravitational Charge Algebra

When formulated in terms of connection and coframes, and in the time gauge, the phase space of general relativity consists of a pair of conjugate fields: the flux 2-form and the Ashtekar connection. On this phase-space, one has to impose the Gauss constraints, the vector, and scalar Hamiltonian constraints. These are respectively generating local SU(2) gauge transformations, spatial diffeomorphisms, and time diffeomorphisms. We write the Gauss and space diffeomorphism constraints as conservation laws for a set of boundary charges, representing spin and momenta, respectively. We prove that these kinematical charges generate a local Poincaré ISU(2) symmetry algebra. This gives strong support to the recent proposal of Poincaré charge networks as a new realm for discretized general relativity [Classical Quantum Gravity 36, 195014 (2019)].

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