<p>In this work, we study the classical phase space for the gravitational degrees of freedom along a null ray. We construct gauge-invariant observables localized on a null ray segment that commute with those localized on the complement; thus, the phase space describes a genuine gravitational subsystem compatible with both locality and diffeomorphism invariance. Our construction employs “dressing time” (a null time coordinate built from spin 0 gravitational degrees of freedom) as a dynamical reference frame. The existence of such a frame depends on the use of edge mode variables, which we argue are generally required to upgrade a local gauge-fixing condition to a global “frame fixing.” To analyze the effects of quantum diffeomorphism anomalies on these structures, we then establish an “effective” classical description in which the Raychaudhuri equation, symplectic form, and edge mode variables all acquire Virasoro-type deformations. Within this framework, we identify three distinct diffeomorphism actions: reparametrizations (gauge transformations), reorientations (physical symmetries of the reference frame), and dressed reparametrizations. Each acquires its own central extension and plays a different crucial role in the effective theory. The resulting structures provide a foundation for quantizing gravitational null ray segments, including promoting dressing time to a genuine quantum reference frame.</p>

Canada

Laurent Freidel

Josh Kirklin

Localization and anomalous reference frames in gravity

We quantize the degrees of freedom on a gravitational null ray segment in a fully gauge-invariant manner by using the dressing time as a quantum reference frame (QRF). Our work goes beyond previous models in that the QRF we employ is made out of the gravitational field itself, and accounts for the full group of diffeomorphisms along the ray, not just a locally compact subgroup. The key tool we introduce is covariant normal ordering, a QRF-dependent but background-independent renormalization prescription that restores diffeomorphism covariance at the quantum level. This enables the definition of a quantum dressing map whose image is the algebra of gauge-invariant observables. We find that this algebra carries the structure of a Virasoro crossed product, and that the dressing map induces a deformed product on gauge-fixed operators which can be understood as a quantization of the Dirac bracket, with consequences for the fluctuations of observables. We explain how to cancel anomalies in the physical Hilbert space representation of the gauge-invariant algebra by including a deformation at the classical level, thereby eliminating all spurious degrees of freedom at the quantum level. The physical Hilbert space admits a Page-Wootters reduction map to the perspective of the dressing time, and we show that the dressing time is non-ideal in the sense that its distinct coherent states have non-vanishing overlaps governed by the Teo-Takhtajan energy, i.e. the Kähler potential for Virasoro coadjoint orbits.

Gravitational null rays: covariant quantization and the dressing time

<p>We propose a renormalization group flow equation for a functional that generates <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-matrix elements and which captures similarities to the well-known Wetterich and Polchinski equations. While the latter ones, respectively, involve the effective action and Schwinger functional, which are genuine off-shell objects, the presented flow equation has the advantage of working more directly with observables, i.e., scattering amplitudes. Compared to the Wetterich equation, our flow equation also greatly simplifies the notion of going on shell, in the sense of satisfying the quantum equations of motion. In addition, unlike the Wetterich equation, it is polynomial and does not require a Hessian inversion. The approach is a promising direction for nonperturbative quantum field theories, allowing one to work more directly with scattering amplitudes.</p>

José Padua-Argüelles

Susanne Schander

Netherlands

Marc Schiffer

Nonperturbative <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math>-Matrix Renormalization

In this paper we construct a non-perturbative action of the higher spin symmetry algebra on the gravitational phase space. We introduce a symmetry algebroid $$ \mathcal{T} $$ which allows us to include radiation in an algebraic framework. We show that $$ \mathcal{T} $$ admits a non-linear realization on the asymptotic phase space generated by a Noether charge defined non-perturbatively for all spins. Besides, this Noether charge is conserved in the absence of radiation. Moreover, at non radiative cuts, the algebroid can be restricted to the wedge symmetry algebra studied in [1]. The key ingredient for our construction is to consider field and time dependent symmetry parameters constrained to evolve according to equations of motion dual to (a truncation of) the asymptotic Einstein’s equations. This result then guarantees that the underlying symmetry algebra is also represented canonically.

Nicolas Cresto

Asymptotic higher spin symmetries II: Noether realization in gravity

We generalize the analysis of the asymptotic higher spin symmetries developed in the first three parts of this series by considering the minimal coupling of Einstein Gravity and Yang-Mills theory. We show that there exist symmetry parameters that satisfy a collection of dual equations of motion, which allow the construction of an infinite collection of charges that are conserved in the absence of radiation. These Noether charges act on the Einstein Yang-Mills phase space canonically and non-linearly. Their action defines a symmetry algebroid which reduces to a symmetry algebra at non-radiative cuts and generalizes the celestial $\textit{sw}$ algebra. The corresponding symmetry bracket is shown to satisfy the Jacobi identity and an interesting cross-product structure, which is analyzed in details.

Asymptotic higher spin symmetries. Part IV. Einstein-Yang-Mills theory

In this work, we demonstrate that quantizing gravity on a null hypersurface leads to the emergence of a CFT associated with each null ray. This result stems from the ultralocal nature of null physics and is derived through a canonical analysis of the Raychaudhuri equation, interpreted as a constraint generating null time reparametrizations. The CFT exhibits a non-zero central charge, providing a mechanism for the quantum emergence of time in gravitational systems and an associated choice of vacuum state. Our analysis reveals that the central charge quantifies the degrees of freedom along each null ray. Throughout our investigation, the area element of a cut plays a crucial role, necessitating its treatment as a quantum operator due to its dynamic nature in phase space or because of quantum backreaction. Furthermore, we show that the total central charge diverges in a perturbative analysis due to the infinite number of null generators. This divergence is resolved if there is a discrete spectrum for the area form operator. We introduce the concept of ‘embadons’ to denote these localized geometric units of area, the fundamental building blocks of geometry at a mesoscopic quantum gravity scale.

Luca Ciambelli

United States

Robert Leigh

Quantum null geometry and gravity

The membrane paradigm displays underlying connections between a timelike stretched horizon and a null boundary (such as a black hole horizon) and bridges the gravitational dynamics of the horizon with fluid dynamics. In this work, we revisit the membrane viewpoint of a finite-distance null boundary and present a unified geometrical treatment of the stretched horizon and the null boundary based on the rigging technique of hypersurfaces. This allows us to provide a unified geometrical description of null and timelike hypersurfaces, which resolves the singularity of the null limit appearing in the conventional stretched horizon description. We also extend the Carrollian fluid picture and the geometrical Carrollian description of the null horizon, which have been recently argued to be the correct fluid picture of the null boundary, to the stretched horizon. To this end, we draw a dictionary between gravitational degrees of freedom on the stretched horizon and the Carrollian fluid quantities and show that Einstein’s equations projected onto the horizon are the Carrollian hydrodynamic conservation laws. Lastly, we report that the gravitational pre-symplectic potential of the stretched horizon can be expressed in terms of conjugate variables of Carrollian fluids and also derive the Carrollian conservation laws and the corresponding Noether charges from symmetries.

Japan

Puttarak Jai-akson

Carrollian hydrodynamics and symplectic structure on stretched horizons

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 been previously identified in terms of conformal primary wavefunctions labeled by a boost weight ∆ = 1+iλ with λ ∈ ℝ. Here we show that a discrete orthogonal and complete basis exists for ∆ ∈ 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+∞  loop algebra (in the same helicity sector) in terms of the new discrete basis.

Italy

Daniele Pranzetti

Ana-Maria Raclariu

A discrete basis for celestial holography

We initiate a study of gravity focusing on generic null hypersurfaces, non-perturbatively in the Newton coupling. We present an off-shell account of the extended phase space of the theory, which includes the expected spin-2 data as well as spin-0, spin-1 and arbitrary matter degrees of freedom. We construct the charges and the corresponding kinematic Poisson brackets, employing a Beltrami parameterization of the spin-2 modes. We explicitly show that the constraint algebra closes, the details of which depend on the non-perturbative mixing between spin-0 and spin-2 modes. Finally we show that the spin zero sector encodes a notion of a clock, called dressing time, which is dynamical and conjugate to the constraint.

Null Raychaudhuri: canonical structure and the dressing time

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+∞.