From Amplitudes to Gravitational Waves

24 Jul 2023, 09:00 → 28 Jul 2023, 18:00 Europe/Stockholm

Albano Building 3

Alessandra Buonanno (Max Planck Institute for Gravitational Physics), Andrea Puhm (Ecole Polytechnique), Daniel Baumann (University of Amsterdam), Henrik Johansson (Nordita/Uppsala U.), John Joseph Carrasco (Northwestern University), Oliver Schlotterer (Uppsala University), Paolo Di Vecchia (Nordita), Zvi Bern (UCLA)

General

The detection of gravitational waves from binary systems composed of black holes and/or neutron stars by the LIGO/Virgo/KAGRA collaborations has initiated a new era for precision studies of the cosmos. At the same time, quantum-field-theory approaches are being used to develop new mathematical tools for studying the non-linear problem of gravity, incorporating the remarkable structures of scattering amplitudes.

This Nordita conference "From Amplitudes to Gravitational Waves" (24–28 Jul 2023) serves as the focus event and grand finale of the adjacent Nordita program "Amplifying Gravity at All Scales" (26 Jun - 21 Jul).  The conference is devoted to QFT-inspired methods applied to general relativity, ranging from scattering amplitudes to gravitational waves. 

 

---

Zoom details:

The conference talks are streamed live on Zoom:
https://uu-se.zoom.us/j/69240630032
Meeting ID: 692 4063 0032

 

---

Speakers

• Massimo Bianchi
• Alessandra Buonanno
• Lucile Cangemi
• Mariana Carrillo-Gonzalez
• Tim Cohen
• Andrea Cristofoli
• Tobias Hansen
• Carlo Heissenberg
• Martijn Hidding
• Gregor Kälin
• Hayden Lee
• Sebastian Mizera
• Gustav Mogull
• Silvia Nagy
• Adam Pound
• Ana-Maria Raclariu
• Michael Ruf
• Evgeny Skvortsov
• Charlotte Sleight
• David Stefanyszyn
• Tom Taylor
• Gabriele Travaglini
• Maarten van de Meent
• Justin Vines
• Congkao Wen
• Akshay Yelleshpur

 

---

Organizers

• Daniel Baumann
• Zvi Bern
• Alessandra Buonanno
• John Joseph Carrasco
• Paolo Di Vecchia
• Henrik Johansson
• Andrea Puhm
• Oliver Schlotterer

 

---

Schedule

Time	Monday	Tuesday	Wednesday	Thursday	Friday
09:30-10:30	Raclariu	Buonanno	Stefanyszyn	Mizera	Pound (9:50am)
10:30-11:00	Coffee	Coffee	Coffee	Coffee	Coffee
11:00-11:40	Roiban	Vines	Cohen	Taylor	Skvortsov
11:40-12:20	Ruf	Cangemi	Lee	Yelleshpur	Sleight
12:20-13:20	Lunch	Lunch	Lunch	Lunch	Lunch
13:20-14:20	Lunch	Lunch	Lunch	Lunch	Lunch
14:20-15:00	Kälin	Travaglini	-	Hansen	-
15:00-15:40	Mogull	Cristofoli	-	Hidding	-
15:40-16:10	Coffee	Coffee	-	Coffee	-
16:10-16:50	Heissenberg	Carrillo-Gonzalez	-	Bianchi	-
16:50-17:30	van de Meent	Nagy	-	Wen	-
18:30	Reception	-	-	Dinner (19:00)	-

 

---

Conference Photo

---

Venue

Talks take place in Auditorium 4, Albano 2 building. 

 

Nordita, Stockholm, Sweden

 

---

Registration

Registration for on-site participation closed on June 15. 

---

Hotels and local transport

Nordita is located within walking distance of several hotels in the northern part of central Stockholm, which all provide high-quality accommodation. The nearest metro stop to Nordita is the red-line "Tekniska högskolan", which allows for convenient commuting to hotels further away. 

---

Sponsored by:

The program is supported through funding from Nordita, Uppsala University and the Knut and Alice Wallenberg Foundation:

                

Monday 24 July

1 Progress in Flat Space Holography

Celestial holography proposes a duality between the gravitational S-matrix and correlators in a conformal field theory living on the celestial sphere. I will review some of the key features of this proposal, highlighting the importance of symmetries and discuss a few recent applications, including new insights into the gravitational phase space, scattering in non-perturbative backgrounds, connections to twistor theory and the flat space limit of AdS/CFT.

Speaker: Ana-Maria Raclariu (University of Amsterdam)

Nordita-review-website.pdf

10:30 Coffee

2 A Field Theory View on Spin-Magnitude Change in Orbital Evolution

An amplitudes-based approach to gravitationally-interacting spinning particles suggested that their description involves more Wilson coefficients than standard worldline approaches. In this talk we discuss the origin and physical interpretation of the additional Wilson coefficients in the simpler context of electrodynamics coupled to various higher-spin fields.

Speaker: Radu Roiban (Penn State University)

Roiban_Nordita_2023_red.pdf

3 Towards gravitational scattering at fifth order in G

Scattering of heavy compact objects is an important process in gravitational physics which has recently attracted interest from different communities including numerical relativity and the approach based on the graviational self-force.
In the weak field limit methods from perturbation theory are admissible. In this context, the amplitudes-based framework has been instrumental in pushing the state of the art to the fourth order in perturbation theory.
In this talk I will discuss recent efforts and challenges in extending these results to the next order in perturbation theory. In particular, I will present a computation in electrodynamics which marks an important step towards the ultimate goal of computing observables for gravitational scattering at the fifth order in Newton's constant.

Speaker: Michael Ruf (UCLA)

Talk_Nordita.pdf

12:20 Lunch

4 Challenges in the Post-Minkowskian Description of the Gravitational Two-Body Problem

In the last few years different approaches have lead to spectacular progress in the Post-Minkowskian description of the motion and gravitational wave emission of a two-body system. Analytical results in such approaches are obtained by studying a hyperbolic encounter using tools from high energy particle physics. On our way towards higher precision and wanting to use the analytical data for bound systems we face several computational and conceptual challenges. I will first talk about challenges that we have overcome while performing these computations in our worldline description before discussing some of these challenges that we will have to overcome in the future.

Speaker: Gregor Kälin

Link to slides

5 Scattering of spinning black holes at 4PM order

In this talk I will review our recent calculation of the observables (impulse, spin kick, scattering angle) involved in the scattering of two spinning black holes at fourth post-Minkowskian order (G^4) using the supersymmetric Worldline Quantum Field Theory (WQFT) formalism. This will include an examination of how to perform the involved three-loop integrals with retarded propagators, and how the observables can be efficiently generated using tree-level Berends-Giele recursion.

Speaker: Gustav Mogull (AEI Potsdam)

stockholm23.pdf

15:40 Coffee

6 Radiative Observables, Angular Momentum Losses and the Eikonal Operator

The classical limit of scattering amplitudes provides a convenient strategy to calculate gravitational observables associated to binary encounters.
Taking this limit requires a resummation in the effective coupling, known as the eikonal exponentiation.
In this talk I will discuss an operator version of this exponentiation, which combines the elastic 2-to-2 channel with inelastic 2-to-3 channels that include graviton emissions,
and illustrate its structure up to O(G^3), corresponding to two loops in the 2-to-2 amplitude and one loop in the 2-to-3 amplitude.
I will then apply it to calculate dissipative observables for binary encounters: the total angular momentum loss, going also beyond the point-particle limit,
the individual losses of angular momentum for each colliding body, and the scattering waveforms.

Speaker: Carlo Heissenberg (Uppsala University)

Slides_Heissenberg_v1.pdf

7 Demystifying the bound to boundary correspondence with Kerr geodesics

The bound-to-boundary (B2B) correspondence allows for the translation of results obtained for scattering encounters to bound orbits and vice versa. To the uninitiated this relationship sometimes appears almost magical. In this talk we seek to understand the B2B correspondence by examining the case of a test particle interacting with a Kerr black hole. This has the distinct advantage of having access to analytic solutions that are valid to all orders in $G$, $c$, and $a$, at cost the cost of having access to only the leading order terms in the mass-ratio.
Taking a more geometric view of the correspondence we find it illustrative to distinguish two separate dualities that together make up the B2B correspondence. The first relates bound geodesics around a Kerr black hole through analytic continuation to a series of scattering orbits that alternate the between the original Kerr spacetime and its negative mass counterpart. The second duality relates the scattering in the positive mass spacetime to that in the negative mass counterpart.
Together the two dualities allow one to start with knowledge of just one type of scattering and recover knowledge of bound orbit dynamics.
We discuss several equivalent formulations of the second duality, including as a positive/negative angular momentum duality (as in the original B2B proposal), a positive/negative eccentricity duality, and as a positive/negative gravitational coupling duality.
The new found formulation of the B2B correspondence applies to fully generic (i.e. with precessing spins) binaries, and applies to both orbit averaged and local quantities.

Speaker: Maarten van de Meent (NBI)

mvdm_nordita.pdf

18:30 Reception

Tuesday 25 July

8 Developing High-Precision Gravitational-Wave Models

Inferring astrophysical and cosmological information from gravitational-wave observations from merging black holes and neutron stars relies on accurate predictions for the two-body dynamics and gravitational radiation. To avoid wrong scientific statements due to systematics in waveform models, upcoming observational runs with existing facilities, and with future detectors on the ground and in space, will require ever more accurate and precise waveform models, which include all physical effects. I will describe what it takes to build faithful waveform models for the entire coalescence combining different analytical methods with numerical relativity, and how perturbative results from scattering-amplitude and effective-field theory techniques could be employed to improve them, helping to achieve the stringent accuracy requirements.

Speaker: Alessandra Buonanno (AEI Potsdam)

Nordita-AB.pdf

10:30 Coffee

9 What's so special about black holes

Much recent work, from an impressively diverse array of approaches, has led to a consensus on results for the conservative dynamics of binary black holes through next-to-leading order in the post-Minkowskian (or post-Newtonian) expansion and through fourth order in each black hole's spin. Much of this work highlights how, at least through fourth order in spin, the case of a black hole is singled out among generic spinning bodies by certain special properties of its effective description, suggesting that new results for fifth and higher orders in spin may be bootstrapped by extrapolating those properties to these orders. We will first briefly review the status of confronting such conjectures with an analysis of the response of a spinning black hole to gravitational perturbations, via solutions of the Teukolsky equation [both for a small-mass-ratio two-body system (with usual self-force calculations) and for a single black hole subjected to a gravitational plane wave (computing a classical Compton amplitude)], pointing out directions for further self-force/Teukolsky calculations, and emphasizing the likely necessity to incorporate absorptive (along with conservative) dynamics into the effective descriptions in order to establish conclusive results.

We will then turn to other (seemingly orthogonal) properties which appear to make spinning black hole dynamics uniquely special, concerning "hidden" conservation laws for the motion of test bodies in a background (exact) Kerr spacetime, arising from the spacetime's "hidden symmetry" (effectively, the existence of the nontrivial Killing-Yano tensor). In the simplest case, for geodesic motion (for a monopolar test/probe body) in Kerr, the hidden symmetry leads to the conservation of the well-known Carter constant, making the dynamics fully integrable. It was later shown by Rüdiger (and independently by Gibbons et al.) that, for a spinning probe (a pole-dipole test body) in Kerr, there exist a generalized Carter constant and a further constant (a certain component of the probe's spin) which are conserved to linear order in the probe's spin. We will review recent work going on to the quadrupolar order in the probe's multipole expansion, specifically considering spin-induced quadrupoles and consistently working to quadratic order in the probe's spin, finding that there are indeed still two hidden constants of motion, but only for the special case when the probe's spin-squared--quadrupole coefficient takes the value appropriate for a black hole.

Speaker: Justin Vines (UCLA)

Nordita_2023_Vines.pdf

10 Higher-spin Compton amplitudes and Kerr

Higher-spin theory and massive gauge invariance can be used as input for constraining root-Kerr and Kerr amplitudes, relevant for calculating gravitational observables with spin. Elegant three-point spin-s amplitudes exist for Kerr black holes, however constructing the corresponding four-point Compton amplitudes is an open problem. In this talk, I will discuss the origin of the Kerr three-point amplitudes from a higher-spin theory perspective. Guided by higher-spin constraints and classical-limit analysis, I will propose quantum and classical tree-level Compton amplitudes relevant for root-Kerr and Kerr to all orders in spin.

Speaker: Lucile Cangemi (Uppsala University)

HSCompton_Cangemi.pdf

12:20 Lunch

11 One-loop scattering waveforms from a Heavy-mass Effective Field Theory

I will describe how using a Heavy-mass Effective Field Theory (HEFT) enables an efficient determination of the classical limit of observables in general relativity. Specifically, quantum-suppressed terms and hyper-classical corrections can be dropped from the get go, i.e. before any integrations. I will then discuss a significant application of the HEFT: the computation of the one-loop gravitational Bremsstrahlung and the associated scattering waveforms in the frequency and time domains. We will also see how HEFT amplitudes appear naturally in the KMOC approach to classical observables. Finally, I will conclude with some prospects for future work.

Speaker: Gabriele Travaglini (QMUL)

GT-Nordita-2023.pdf

12 An on-shell approach to self-force

I will present an on-shell framework for studying the self-force expansion in terms of scattering amplitudes on a curved background and their classical limit. I will first introduce the self-force expansion within the context of a plane wave background, presenting the relevant on-shell building blocks required for evaluating observables, such as scattering waveforms. Following that, I will discuss the self-force expansion on Schwarzschild, focusing on the on-shell data involved and their interpretation as resummation of ordinary perturbative amplitudes in vacuum.

Speaker: Andrea Cristofoli (University of Edinburgh)

Cristofoli (talk).pdf

15:40 Coffee

13 Testing EFTs: amplitudes, gravitational waves, and causality

In this talk, I will review different approaches to testing Effective Field Theories (EFTs). First, I will briefly review how amplitude techniques can allow us to extract classical observables during the merge of a black hole binary for generic EFTs of gravity including minimal and non-minimal couplings. In the second half of my talk, I will focus on how to obtain bounds on Wilson coefficients of EFTs from the requirement of physical principles. I will compare the strength of positivity and causality bounds and show how applying both can be a powerful tool. Both of these techniques allow us to test EFTs effectively when comparing theoretical predictions to observations.

Speaker: Mariana Carrillo Gonzalez (Imperial College)

Testing efts .pdf

14 Gauge choices, kinematic algebras, and (A)dS

Starting with the self-dual sector, I will show how the notion of a kinematic algebra can be generalised in two directions: in the absence of gauge fixing, and in the presence of a cosmological constant, and discuss possible implications for the construction of solutions in (A)dS.

Speaker: Silvia Nagy (Durham University)

slides - Nagy.pdf

Wednesday 26 July

15 Bootstrapping Cosmological Correlators

I will introduce some new techniques for computing cosmological correlators that allows them to be fixed by fundamental physical principles such as symmetry, locality and unitarity. I will illustrate these new ideas by constructing the graviton four-point function in de Sitter space.

Speaker: David Stefanyszyn

10:30 Coffee

16 Large Deviations in the Early Universe

Fluctuations play a critical role in cosmology. They are relevant across a range of phenomena from the dynamics of inflation to the formation of structure. In many cases, these it is a good approximation to coarse grain these fluctuations (in the sense of a Renormalization Group flow), and they follow a Gaussian distribution as a consequence of the Central Limit Theorem. Yet, some classes of observables are dominated by rare fluctuations and are sensitive to the details of the underlying microphysics. In this talk, I will introduce the Large Deviation Principle, and will explain how it can be used to diagnose when effective approaches fail and one must instead to appeal to the microscopic description. I will illustrate this phenomenon in the context of determining the phase transition to eternal inflation, and will briefly mention applications for the distribution of scalar field fluctuations in de Sitter, and the production of primordial black holes.

Speaker: Timothy Cohen

Large Deviations In The Early Universe_Slides_NORDITA.pdf

17 Differential Equations for Cosmological Correlators

In this talk, I will present a new mathematical perspective of cosmological correlators in FRW spacetimes. These correlators have an integral representation in boundary kinematic space, which can be obtained from a finite set of master integrals that satisfy interesting differential equations. I will describe a graphical representation of these differential equations and show how they can be derived from simple graphical rules. This allows us to reformulate bulk time evolution as an energy flow on boundary kinematics, and provides a new way to understand the analytic structure of cosmological correlators.

Speaker: Hayden Lee

Lee.pdf

12:20 Lunch

Thursday 27 July

18 Formal aspects of scattering amplitudes: Lessons and challenges in 2023

I will highlight a few lessons we’ve learned from the recent progress in the field of scattering amplitudes and the challenges they present.

Speaker: Sebastian Mizera

Nordita - Sebastian Mizera.pdf

10:30 Coffee

19 Liouville for Yang-Mills

Speaker: Tomasz Taylor

Stockholm.pdf

20 SUSY and OPE associativity in Celestial CFT

In this talk, I will describe the effects of loop corrections involving both massive and massless particles on OPEs in Celestial CFT. I will go on to show that OPE associativity imposes constraints on the theory which can be cleanly phrased in terms of scattering amplitudes. I will comment on the status of these constraints in supersymmetric theories and string theory.

Speaker: Akshay Yelleshpur Srikant

Yelleshpur_Celestial_OPE_associativity_and_SUSY.pdf

12:20 Lunch

21 Bootstrapping the AdS Virasoro-Shapiro amplitude

I will present a constructive method to compute the Virasoro-Shapiro amplitude on AdS5xS5, order by order in AdS curvature corrections. A simple toy model for strings on AdS indicates that at order k the answer takes the form of a genus zero world-sheet integral involving single-valued multiple polylogarithms of weight 3k. The coefficients in an ansatz in terms of these functions are then fixed by Regge boundedness of the amplitude, which is imposed via a dispersion relation in the holographically dual CFT. We explicitly constructed the first two curvature corrections. Our final answer reproduces all CFT data available from integrability and all localisation results, to this order, and produces a wealth of new CFT data for planar N=4 SYM theory at strong coupling.

Speaker: Tobias Hansen

Hansen_bootstrapping_ads_virasoro-shapiro.pdf

22 Generalizing Polylogarithms to Riemann Surfaces of Arbitrary Genus

In this talk, we explore the important role played by polylogarithms in quantum field theory and string theory scattering amplitudes, along with the challenges in generalizing these functions beyond the realm of elliptic polylogarithms. As our main result, we will present a new construction of homotopy-invariant iterated integrals on a Riemann surface, applicable to any genus. Our method employs convolutions of the Arakelov Green function and holomorphic Abelian differentials to establish higher-genus equivalents of the genus-one integration kernels from the Kronecker-Eisenstein series. These kernels are combined into a flat connection, from which we build a homotopy-invariant, path-ordered exponential generating function. The coefficients of this generating function define higher-genus polylogarithms, which generalize the Brown-Levin construction beyond genus one. The resulting polylogarithms are expected to not only play a fundamental role in higher-genus computations of string amplitudes but to also find broad applications in various other areas of theoretical physics.

Speaker: Martijn Hidding

Talk Nordita.pdf

15:40 Coffee

23 A measure for chaos in string scattering

Scattering processes with highly excited string (HES) states are expected to be chaotic. We show that the spacing ratios of successive peaks in the angular dependence are distributed according to the $\beta$-ensemble of random matrix theory (RMT). For the scattering amplitude of an open bosonic HES state and three tachyons, we discuss the dependence of $\beta$ on the level and helicity of the HES state. Quite remarkably, the Gaussian Unitary Ensemble (GUE) with $\beta=2$, related to the distribution of the nontrivial zeros of Riemann $\zeta$ function, applies to wave scattering on a leaky torus. Finally we explore implications of the chaotic behaviour of HES in view of the string / black-hole correspondence.

Speaker: Massimo Bianchi

MBTalk27July23.pdf

24 Exact integrated correlators in N=4 super Yang-Mills

Over the past few years, it has been shown that, when integrating out the spacetime dependence with a certain integration measure, some four-point correlation functions in N=4 super Yang-Mills (SYM) can be computed exactly. These quantities are called integrated correlators; they depend on the Yang-Mills coupling \tau, and transform under the S-duality symmetry of N=4 SYM theory. I will discuss some of the recent progress on these integrated correlators in this talk.

Speaker: Congkao Wen

NorditaWen.pdf

19:00 Banquet

Friday 28 July

25 Progress in gravitational self-force theory: recent advances in modelling asymmetric binaries

As gravitational-wave detectors become more sensitive to lower frequencies, they will increasingly detect binaries with smaller mass ratios, larger spins, and higher eccentricities. In this talk I describe how gravitational self-force theory, when combined with a method of multiscale expansions, provides an ideal framework for modelling these systems. The framework proceeds from first principles while simultaneously enabling rapid generation of waveforms on a timescale of milliseconds. I discuss the state of the art in this method: nonspinning, quasicircular waveforms at second perturbative order in the mass ratio. I present progress toward extending this second-order model to include spins and to include the final merger and ringdown. I also discuss the domain of validity of these models, focusing on their accuracy for mass ratios in the intermediate regime ~1:10 to 1:100.

Speaker: Adam Pound

Nordita 2023.pdf

10:30 Coffee

26 Higher spins: from quantum gravity to black hole scattering

I will review the recent developments in theories with massless and massive higher spin fields, emphasizing the role of higher spin states for the quantum gravity problem and AdS/CFT correspondence in the case of massless ones (aka higher spin gravities) and for the study of black hole scattering in the case of massive ones.

Speaker: Evgeny Skvortsov

amp_Skvortsov.pdf

27 Holographic Correlators for all Λs

In this talk we will discuss the central role of Euclidean anti-de Sitter space in defining holographic correlation functions on Lorentzian AdS, dS and flat spaces.

Speaker: Charlotte Sleight

Nordita CS.pdf

12:20 Lunch