We consider the frequency-domain leading order and next-to-leading order post-Minkowskian waveforms obtained from the tree-level and one-loop amplitudes describing the scattering of two massive scalar objects and the emission of one graviton. We explicitly calculate their post-Newtonian (PN) limit obtaining an expansion up to the third subleading PN order in all ingredients: the tree-level amplitude, the odd and even parts of the real one-loop kernel, and the Compton or “rescattering” cuts, thus reaching 3PN precision for the latter. We provide explicit expressions for the multipole decomposition of these results in the center-of-mass frame and compare them with the results obtained from the classical multipolar post-Minkowskian method. We find perfect agreement between the two, once the Bondi-Metzner-Sachs supertranslation frame is properly adjusted and the infrared divergences due to rescattering are suitably subtracted in dimensional regularization. This shows that the approach proposed in Georgoudis et al. [An eikonal-inspired approach to the gravitational scattering waveform, J. High Energy Phys. 03 (2024) 089] can be applied beyond the soft-regime ensuring the agreement between amplitude-based and multipolar post-Minkowskian results for generic frequencies.

United Kingdom

Alessandro Georgoudis

Carlo Heissenberg

Rodolfo Russo

Post-Newtonian multipoles from the next-to-leading post-Minkowskian gravitational waveform

We revisit the amplitude-based derivation of gravitational waveform for the scattering of two scalar black holes at subleading post-Minkowskian (PM) order. We take an eikonal-inspired approach to the two-massive-particle cut needed in the KMOC framework, as highlighted in [1], and show that its effect is to implement a simple change of frame. This clarifies one of the points raised in [2] when comparing with the post-Newtonian (PN) results. We then provide an explicit PM expression for the waveform in the soft limit, ω → 0, including the first non-universal, ω log ω, contribution. Focusing on this regime, we show that the small-velocity limit of our result agrees with the soft limit of the PN waveform of [2], provided that the two quantities are written in the same asymptotic frame. Performing the BMS supertranslation that, as discussed in [3], is responsible for the  $$\mathcal{O}$$ (G) static contribution to the asymptotic field employed in the PN literature, we find agreement between the amplitude-based and the PN soft waveform up to and including G 3/c 5 order.

An eikonal-inspired approach to the gravitational scattering waveform

Sweden

Ingrid Vazquez-Holm

Addendum to: Inelastic exponentiation and classical gravitational scattering at one loop

We revisit the space of gapped quantum field theories with a global O(N) symmetry in two spacetime dimensions. Previous works using S-matrix bootstrap revealed a rich space in which integrable theories such as the non-linear sigma model appear at special points on the boundary, along with an abundance of unknown models hinting at a non conventional UV behaviour. We extend the S-matrix set-up by including into the bootstrap form factors and spectral functions for the stress-energy tensor and conserved O(N) currents. Sum rules allow us to put bounds on the central charges of the conformal field theory (CFT) in the UV. We find that a big portion of the boundary can only flow from CFTs with infinite central charges. We track this result down to a particular behaviour of the amplitudes in physical kinematics and discuss its physical implications.

CERN

Lucía Córdova

Canada

Switzerland

Miguel Correia

Antoine Vuignier

The O(N) monolith reloaded: sum rules and Form Factor Bootstrap

We calculate the inelastic 2 → 3 one-loop amplitude for the scattering of two point-like, spinless objects with generic masses involving the additional emission of a single graviton. We focus on the near-forward, or classical, limit. Our results include the leading and subleading orders in the soft-region expansion, which captures all non-analytic contributions in the transferred momentum and in the graviton’s frequency. This allows us to check the first constraint arising from the inelastic exponentiation put forward in refs. [1–3], and to calculate the 2 → 3 one-loop matrix element of the N-operator, linked to the S-matrix by S = e  iN , showing that it is real, classical and free of infrared divergences. We discuss how our results feature in the calculation of the   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (G 3) corrections to the asymptotic waveform.

Inelastic exponentiation and classical gravitational scattering at one loop

We present a conjecture for the three-point functions of single-trace operators in planar <math><mi>N</mi><mo>=</mo><mn>4</mn></math> super-Yang-Mills theory at finite coupling, in the case where two operators are protected. Our proposal is based on the hexagon representation for structure constants of long operators, which we complete to incorporate operators of any length using data from the TBA-QSC formalism. We perform various tests of our conjecture, at weak and strong coupling, finding agreement with the gauge theory through 5 loops for the shortest three-point function and with string theory in the classical limit.

France

Benjamin Basso

Arthur Klemenchuk Sueiro

Structure Constants of Short Operators in Planar <math><mi>N</mi><mo>=</mo><mn>4</mn></math> Supersymmetric Yang-Mills Theory

We compute ε-expansions around 4 dimensions of a complete set of master integrals for momentum space five-loop massless propagator integrals in dimensional regularization, up to and including the first order with contributions of transcendental weight nine. Our method is the glue-and-cut technique from Baikov and Chetyrkin, which proves extremely effective in that it determines all expansion coefficients to this order in terms of recursively one-loop integrals and only one further integral. We observe that our results are compatible with conjectures that predict π-dependent contributions.

Brazil

Portugal

Vasco Goncalves

Erik Panzer

Ireland

Raul Pereira

Russia

Alexander Smirnov

Vladimir Smirnov

Glue-and-cut at five loops

We study the four-point function of the superconformal primary of the stress-tensor multiplet in four-dimensional <math><mi>N</mi><mo>=</mo><mn>4</mn></math> super Yang-Mills theory, at strong coupling and in a large-<math><mi>N</mi></math> expansion. This observable is holographically dual to a four-graviton amplitude in type IIB supergravity on <math><msub><mi>AdS</mi><mn>5</mn></msub><mo>×</mo><msup><mi>S</mi><mn>5</mn></msup></math>. We construct the maximal transcendental weight piece of the correlator at order <math><msup><mi>N</mi><mrow><mo>−</mo><mn>6</mn></mrow></msup></math> and compare it with the flat-space limit of the corresponding two-loop amplitude. This allows us to conjecture structures of the correlator/amplitude which should be present at any loop order.

Agnese Bissi

Giulia Fardelli

Towards all loop supergravity amplitudes on <math><msub><mi>AdS</mi><mn>5</mn></msub><mo>×</mo><msup><mi>S</mi><mn>5</mn></msup></math>

We introduce an algebro-geometrically motived integration-by-parts (IBP) re- duction method for multi-loop and multi-scale Feynman integrals, using a framework for massively parallel computations in computer algebra. This framework combines the com- puter algebra system Singular with the workflow management system GPI-Space, which are being developed at the TU Kaiserslautern and the Fraunhofer Institute for Industrial Mathematics (ITWM), respectively. In our approach, the IBP relations are first trimmed by modern tools from computational algebraic geometry and then solved by sparse linear algebra and our new interpolation method. Modelled in terms of Petri nets, these steps are efficiently automatized and automatically parallelized by GPI-Space. We demonstrate the potential of our method at the nontrivial example of reducing two-loop five-point non- planar double-pentagon integrals. We also use GPI-Space to convert the basis of IBP reductions, and discuss the possible simplification of master-integral coefficients in a uni- formly transcendental basis.

Germany

Dominik Bendle

Janko Böhm

Wolfram Decker

Franz-Josef Pfreundt

Mirko Rahn

Pascal Wasser

China

Yang Zhang

Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space

We use the method of asymptotic expansions to study the OPE limit of a fourpoint function of protected operators in   <math> <mi>N</mi> <mo>=</mo> <mn>4</mn> </math>  $$ \mathcal{N}=4 $$  SYM. We use a new method for evaluating the resulting propagator-type integrals and then extract the OPE coefficient with Konishi at the five loop order.

Vasco Gonçalves

Konishi OPE coefficient at the five loop order