Carrollian conformal field theory offers an alternative description of massless scattering amplitudes, that is holographic in nature. In an effort to build a framework that is both predictive and constraining, we construct operator product expansions (OPE) that are compatible with carrollian symmetries. In this way, we unify and extend preliminary works on the subject, and demonstrate that the carrollian OPEs indeed control the short-distance expansion of carrollian correlators and amplitudes. In the process, we extend the representation theory of carrollian conformal fields such as to account for composite operators like the carrollian stress tensor or those creating multiparticle states. In addition we classify 2- and 3-point carrollian correlators and amplitudes with complex kinematics, and give the general form of the 4-point function allowed by symmetry.

Belgium

Kevin Nguyen

Jakob Salzer

Operator product expansion in Carrollian CFT

<p>The soft photon and soft graviton theorems of Weinberg are known to derive from conservation laws associated with asymptotic symmetries. Within the corresponding classical theories, one often speaks of spontaneous symmetry breaking and vacuum degeneracy, but a genuine quantum description of this phenomenon has largely been lacking. Here we establish spontaneous symmetry breaking of asymptotic symmetries and the existence of Goldstone particles using exclusively the language of quantum field theory. This is made possible through the reformulation of massless scattering theory in terms of Carrollian conformal field theory, and the observation that soft theorems correspond to Ward identities of broken symmetries. A suitable version of Goldstone theorem shows that there must exist zero-momentum particles described by conformal fields on the celestial sphere, in agreement with the common lore. More specifically, these belong to unitary representations in the discrete series of the Lorentz group, and are therefore naturally equipped with logarithmic two-point functions. We discuss the relevance of these observations to the problem of infrared divergences that scattering amplitudes suffer from.</p>

Italy

Shreyansh Agrawal

Soft theorems and spontaneous symmetry breaking

<p>We provide a detailed decomposition of Wigner’s particles, defined as unitary irreducible representations of the Poincaré group, in terms of unitary representations of its Lorentz subgroup. As pointed out before us, this decomposition only involves Lorentz representations belonging to the principal continuous series, and further underpins the connection between scattering amplitudes and conformal correlation functions discussed in the context of celestial holography. We provide very explicit formulas for the decomposition of particles of arbitrary mass and (half-)integer spin and for any spacetime dimension. We emphasize that this decomposition is unique and comes equipped with a specific inner product on the corresponding Hilbert space. We also confirm that unitary translations mix Lorentz representations within the principal continuous series only, as required. Implications to the celestial holography program are indicated.</p>

Lorenzo Iacobacci

Celestial decomposition of Wigner’s particles

Motivated by flat space holography, we demonstrate that massive spin-s fields in Minkowski space near timelike infinity are massive carrollian fields on the carrollian counterpart of anti-de Sitter space called Ti. Its isometries form the Poincaré group, and we construct the carrollian spin-s fields using the method of induced representations. We provide a dictionary between massive carrollian fields on Ti and massive fields in Minkowski space, as well as to fields in the conformal primary basis used in celestial holography. We show that the symmetries of the carrollian structure naturally account for the BMS charges underlying the soft graviton theorem. Finally, we initiate a discussion of the correspondence between massive scattering amplitudes and carrollian correlation functions on Ti, and introduce physical definitions of detector operators using a suitable notion of conserved carrollian energy-momentum tensor.

Denmark

Emil Have

Austria

Stefan Prohazka

Massive carrollian fields at timelike infinity

Laura Donnay

United Kingdom

Romain Ruzziconi

Erratum to: Loop-corrected subleading soft theorem and the celestial stress tensor

Soft graviton theorems receive one-loop contributions that are logarithmic in the energy of the soft graviton, and which are closely related to tails of gravitational waveforms. We demonstrate that these logarithmic corrections are encoded in the Ward identity of superrotation symmetries, i.e. they follow from conservation of superrotation charge across spatial infinity i 0. Our proof relies on a careful analysis of the radiative phase space admitting such gravitational tails, and the determination of the fluxes through null infinity   <math> <mi>I</mi> </math>  $$ \mathcal{I} $$  that act as canonical generators of superrotations on both gravitational and matter fields. All logarithmic terms are derived from the fluxes through correlations of the supertranslation Goldstone mode, provided care is taken in manipulating gravitationally interacting (i.e. dressed) rather than free fields. In cases where massive particles take part in the scattering process, logarithmic corrections also partly arise from the superrotation charge generator at timelike infinity i  ± .

Logarithmic soft graviton theorems from superrotation Ward identities

The theory of particle scattering is concerned with transition amplitudes between states that belong to unitary representations of the Poincaré group. The latter acts as the isometry group of Minkowski spacetime 𝕄, making natural the introduction of relativistic tensor fields encoding the particles of interest. Since the Poincaré group also acts as a group of conformal isometries of null infinity ℐ, massless particles can also be very naturally encoded into Carrollian conformal fields living on ℐ. In this work we classify the two- and three-point correlation functions such Carrollian conformal fields can have in any consistent quantum theory of massless particles and arbitrary dimension. We then show that bulk correlators of massless fields in 𝕄 explicitly reduce to these Carrollian conformal correlators when evaluated on ℐ, although in the case of time-ordered bulk correlators this procedure appears singular at first sight. However we show that the Carrollian correlators of the descendant fields are perfectly regular and precisely carry the information about the corresponding S-matrix elements.

Carrollian conformal correlators and massless scattering amplitudes

We present a unified treatment of the conserved asymptotic charges associated with any bosonic massless particle in any spacetime dimension. In particular we provide master formulae for the asymptotic charges and the central extensions in the corresponding charge algebras. These formulae can be explicitly evaluated for any given theory. For illustration we apply them to electromagnetism and gravity, thereby recovering earlier results.

Peter West

Universal derivation of the asymptotic charges of bosonic massless particles

An effective theory designed to compute Virasoro identity blocks at large central charge, expressed in terms of the propagation of a reparametrization/shadow mode between bilocal vertices, was recently put forward. In this paper I provide the formal theoretical framework underlying this effective theory by reformulating it in terms of standard concepts: conformal geometry, generating functionals and Feynman diagrams. A key ingredient to this formalism is the bilocal vertex operator, or reparametrized two-point function, which is shown to generate arbitrary stress tensor insertions into a two-point function of reference. I also suggest an extension of the formalism designed to compute generic Virasoro blocks.

Virasoro blocks and the reparametrization formalism

The constrained Hamiltonian analysis of geometric actions is worked out before applying the construction to the extended Bondi-Metzner-Sachs group in four dimensions. For any Hamiltonian associated with an extended BMS4 generator, this action provides a field theory in two plus one spacetime dimensions whose Poisson bracket algebra of Noether charges realizes the extended BMS4 Lie algebra. The Poisson structure of the model includes the classical version of the operator product expansions that have appeared in the context of celestial holography. Furthermore, the model reproduces the evolution equations of non-radiative asymptotically flat spacetimes at null infinity.