Amplifying Gravity at All Scales

26 Jun 2023, 09:00 → 21 Jul 2023, 18:00 Europe/Stockholm

Albano 3: 4204 - SU Conference Room (56 seats) (Albano Building 3)

Alessandra Buonanno (Albert Einstein Institute), Andrea Puhm (École polytechnique), Daniel Baumann (University of Amsterdam), Henrik Johansson, 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 studying the cosmos. Yet again gravity is at the center of fundamental physics, both for experiment and theory, and we are heading towards the high-precision frontier. Analytical approaches constitute the future of gravitational waves, cosmology and quantum gravity. Remarkably, quantum field theory provides the mathematical tool of scattering amplitudes which display remarkable simplicity when applied to the non-linear problem of gravity.

This Nordita program is devoted to amplitudes- and QFT-inspired analytic methods for gravity at all scales. The topics covered will include: recent progress for gravitational amplitudes, new perturbative/effective formalisms, and relations between gravity and gauge theory. Higher-order calculations for: post-Newtonian/Minkowskian and self-force corrections to the gravitational potential/wave emission, cosmological correlators and ultraviolet physics probing quantum gravity, and applications to string theory. Challenges of incorporating spin and tidal effects in general relativity, and scattering amplitudes for Kerr black holes. Flat space holography in the form of celestial amplitudes, asymptotic symmetries and gravitational memory.

 

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Themes and preliminary program schedule

A tentative outline for the themes of the four-week program June 26-July 21: 

• week 1: intro/tutorials: amplitudes/EFT methods, double copy, gravitational waves, celestial/cosmo correlators  
• week 2: celestial amplitudes, inflation, cosmology
• week 3: string/GR amplitudes, UV/IR divergences, multi-loop integration
• week 4: gravitational waves, EFT methods, PN/PM/GSF results, spin/tidal effects 

 

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Organizers

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

 

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Venue

Nordita, Stockholm, Sweden

Main lecture room: 4th floor Nordita (Albano 3, room 4204)

 

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Application/Registration

Application for on-site participation will close on: 31 March 2023. Application form. Registrants will receive an on-site/remote participation confirmation from the organizers after this date.

 

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Conference

The program will be immediately followed by the focus-event conference “From Amplitudes to Gravitational Waves” 24-28 July, 2023. A separate registration is required for this event (deadline: June 15).

 

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Accommodation

Nordita provides a limited number of rooms in the Stockholm apartment hotel, BizApartments, free of charge for accepted participants and after application evaluation.

 

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Sponsored by

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

Monday 26 June

09:00 Registration

1 Welcome -- 1st week

2 Classical Double Copy: Solutions, Scattering, and Horizons

We will review the classical double copy, beginning with the map between exact solutions. We will cover both the Kerr-Schild and Weyl formulations. Following a survey of known exact solutions, we will review why a position-space classical solution double copy is even feasible. We will briefly discuss some perturbative approaches, and then close by relating several gravitational objects (including horizons) to their gauge theory analogues.

Speaker: Cynthia Keeler (Arizona State University)

18:30 Reception

Tuesday 27 June

3 EFT S-matrix boostrap

I will review the recent revival of S-matrix bootstrap in the context of massless EFTs. We will begin with the EFT of massless scalars, spinning and colored states and identify the data which we can hope to constrain. We will lay out the constraints of unitarity and locality in the UV and how it can be utilized to bound the low energy couplings through dispersion relations. We will focus in particular on gravitation systems, where the presence of massless poles requires a modern update to the bootstrap methods are required.

Speaker: Yu-tin Huang (NTU Taiwan)

4 Color-Dual Constraints on Gravitational EFT

I will discuss the recent developments regarding how color-kinematics duality places surprisingly rigid constraints on gravitational EFTs constructed from the double copy. We will begin with a review of color-kinematics and highlight the graphical simplicity that underlies the double-copy construction. This background will pave the way for our main finding: the realization that color-dual structure with factorization is sufficient to induce an infinite tower of constraints on higher derivative four-point operators. Remarkably, these color-dual towers can be resummed, unveiling concealed particle residues, which are consistent with known UV completions of gravity.

Speaker: Nic Pavao

Pavao_Nordita.pdf

Wednesday 28 June

5 An introduction to flat space holography

I will review some aspects of gravity in asymptotically flat spacetime and mention important challenges to obtain a holographic description in this framework. I will then present two important approaches towards flat space holography, namely Carrollian and celestial holography, and briefly explain how they are related to each other. Similarities and difference between flat and anti-de Sitter spacetimes will be emphasized throughout the talk.

Speaker: Romain Ruzziconi (Vienna University of Technology)

Slides v2.pdf

6 Celestial Soft Algebras

Gauge and gravity amplitudes have near-universal behavior in the limit where gravitons or gluons have low energies. In celestial CFT, these universal soft algebras imply the existence of higher-spin current algebras. After discussing the origins of these celestial soft algebras from collinear limits of successive soft insertions, I will describe how gauge soft algebra of Yang-Mills is extended when coupled to neutral complex scalars. Central extensions of the soft algebra for Yang-Mills are generated by expanding around sourced scalar backgrounds.

Speaker: Walker Melton

nordita_melton.pdf

Thursday 29 June

7 Scattering amplitudes methods for gravitational waves

I will review recent developments in techniques for the computation of scattering amplitudes in quantum field theory, and their application to the modelling of black-hole binaries and their waveforms.

I will show the computation of a two body Hamiltonian, and a scattering angle in the second post-Minkowskian approximation. Through this relatively simple example we will illustrate the use of spinor helicity, amplitudes bootstrap, double copy and unitarity, as well as diverse techniques to translate (the classical limit of) amplitudes into observables.

Speaker: Andres Luna (NBI Copenhagen)

8 On Massive Higher Spins and their Interactions

There are several problems with modelling massive particles with spin higher than 1 coupled to electromagnetism or gravity. In this talk I will briefly outline these problems, and then show how gauge symmetry can solve some of them. I will also demonstrate that not every choice of gauge symmetry used in the formulation of massive higher spins is
sufficient for this purpose.

Speaker: Lukas Lindwasser

On massive higher spins and their interactions.pdf

18:30 Dinner downtown

Friday 30 June

9 Observables in expanding universes

The physics occurring in an expanding universe is encoded in
correlation functions at his boundary. Part of its structure is
inherited from the probability distributions of the field configuration
at such boundary, or equivalently in the so-called wavefunction of the
universe. I'll review the analytic structure of both the wavefunction
and a certain class of correlation functions, their physical content
their relation and how to compute the latter from the former. I'll
finally discuss a geometrical picture which allows to talk about both
quantities at once and to extract physical information that are obscure
in the standard field theory language.

Speaker: Paolo Benincasa (MPI Munich)

Monday 3 July

09:00 Registration

10 Welcome -- 2nd week

11 Double Copy in (A)dS

The double copy is a powerful theoretical tool which allows one to reduce complicated gravitational calculations to simpler ones in gauge theory. In this talk, I will describe recent progress in extending these techniques to (A)dS background. First I will explain how to formulate self-dual gravity in AdS4 in terms of a simple scalar theory which makes the double copy manifest and reveals some surprising new connections to celestial holography. I will then describe recent work which extends these ideas beyond the self-dual sector. In particular, I will present a compact new formula for the tree-level wavefunction coefficient of four gravitons in dS4, which was obtained by combining recently developed cosmological bootstrap methods with double copy intuition.

Speaker: Arthur Lipstein (Durham)

ads_double_v2.pdf

18:30 Reception

Tuesday 4 July

12 W algebras and ALE spaces

I’ll explain how the celestial chiral algebra of an ALE space can be easily read off from its twistor space. The simplest example is flat space, where the CCA is the loop algebra of the Poisson algebra of holomorphic functions on $\mathbb{C}^2$. We’ll also discuss the case of Eguchi-Hanson space in some detail, where the CCA is related to a certain scaling limit of the family of W-algebras defined by Pope et al., where the scaling limit is controlled by the radius of the Eguchi-Hanson core. The loop algebra of a general W-algebra (away from the scaling limit) similarly arises as the celestial chiral algebra of non-commutative self-dual gravity on Eguchi-Hanson space. I’ll comment on the relevance of these results for potential top-down models of celestial holography in ALE spaces.

Speaker: David Skinner (Cambridge)

Walg_ALE.pdf

Wednesday 5 July

13 On structures of celestial OPE and algebras

In this talk I will discuss several recent studies about soft OPE and algebra in celestial CFT. We first compute the deformation of the $w_{1+\infty}$ algebra of soft graviton, gluon and scalar currents in the Celestial CFT due to non-minimal couplings. We find that the Jacobi identity of the algebra, as well as the associativity of the OPE between these soft current operators, are satisfied only when the spectrum and couplings of the theory obey certain constraints. We also study the effect of these constraints on the amplitudes in the 4d bulk theory. We also determine tree level, all-order celestial operator product expansions (OPEs) of gluons and gravitons in the maximally helicity violating (MHV) sector from inverse soft recursion.

Speaker: Lecheng Ren (Brown University)

all_order_OPE (1).pdf

14 Discussion on Celestial OPEs

I will lead a discussion on celestial OPE (non)associativity, effective field theories and their celestial duals, and related topics. The discussion is intended to be interactive, engaging, and provocative, so audience participation is expected.

Speaker: Marcus Spradlin (Brown University)

Thursday 6 July

15 Asymptotic symmetries and scattering amplitudes in flat space

In this talk I will describe some works related to bootstrapping graviton ( and gluon) scattering amplitudes using asymptotic symmetries in four dimensional flat space time.

Speaker: Shamik Banerjee (Bhubaneswar, Inst. Phys.)

16 Celestial holography on backgrounds

The study of celestial holography on non-trivial backgrounds has recently gained interest. In this talk, I will give two specific examples. In the first example, I will show that the celestial MHV gluon amplitudes evaluated in the presence of a spherical dilaton shockwave are given by the correlation functions of primary field operators factorized into the holomorphic current operators times the “light” Liouville operators. They are evaluated in the semiclassical limit of Liouville CFT. A simple supersymmetric generalization in this context reveals celestial supersymmetry of the current sector. Then I will consider MHV amplitudes on self-dual radiative backgrounds as the second example. I will show that celestial soft gluon algebra and $w_{1+\infty}$ algebra are undeformed on these backgrounds.

Speaker: Bin Zhu (University of Edinburgh)

celestial_Nordita.pdf

18:00 Dinner downtown

Friday 7 July

17 The Kallen–Lehmann representation in de Sitter spacetime

We study two-point functions of symmetric traceless local operators in the bulk of de Sitter spacetime. We derive the Kallen-Lehmann spectral decomposition for any spin and show that unitarity implies its spectral densities are nonnegative. In addition, we recover the Kallen-Lehmann decomposition in Minkowski space by taking the flat space limit. Using harmonic analysis and the Wick rotation to Euclidean Anti de Sitter, we derive an inversion formula to compute the spectral densities. Using the inversion formula, we relate the analytic structure of the spectral densities to the late-time boundary operator content. We apply our technical tools to study two-point functions of composite operators in free and weakly coupled theories. In the weakly coupled case, we show how the Kallen-Lehmann decomposition is useful to find the anomalous dimensions of the late- time boundary operators. We also derive the Kallen-Lehmann representation of two-point functions of spinning primary operators of a Conformal Field Theory on de Sitter.

Speaker: Kamran Salehi Vaziri (Amsterdam University)

Talk.pdf

Monday 10 July

09:00 Registration

18 Welcome -- 3rd week

19 String-based vs. string-inspired in quantum gravity

It has been understood since the eighties that string theory amplitudes are in various aspects better organised than amplitudes in ordinary quantum field theory. One can try to exploit this fact either by representing field theory amplitudes as the infinite string-tension limit of string amplitudes (string-based formalism’’), or by representing them by worldline path integrals and evaluating those in a way analogous to string theory (string-inspired formalism’’). Here I review and compare both approaches with an emphasis on gravity amplitudes and aspects of Yang-Mills theory that bear a relevance for gravity such as color-kinematics duality and multi-particle states. A central role is played by the cycle-and-tail decomposed worldline integrands of the one-loop N-gluon amplitudes that have recently tuned out to provide a natural route to the construction of Berends-Giele currents in BCJ gauge for Yang-Mills theory as well as gravity.

Speaker: Christian Schubert

talk_schubert.pdf

20 11D superfields and vertex operators in the pure spinor formalism

To compute observables in the pure spinor description of 11D supergravity we need vertex operators, a good handle on the pure spinor measure, and a prescription for constructing invariants in pure spinor superspace. In this talk I will describe recent work [2305.19898 ] on the construction of superfields and vertex operators. This entails obtaining recursion relations for the superfields by appropriately gauge fixing the linearized superspace equations of motion. At the end of the talk I will also discuss upcoming work on the pure spinor measure.

Speaker: Maor Ben-Shahar (Uppsala University)

18:00 Reception

Tuesday 11 July

21 Modular constraints on N=4 SYM / type IIB holography

Speaker: Michael Green

Nordita 11062023.pdf

22 The Road to Seven Loops in N=8 SUGRA

I'll provide a brief history of the multiloop N=8 integrand program: how three and four loops were relatively straightforward, what goes wrong at five loops, and why that means going further requires new insights. I'll then discuss some recent, in-progress, and near-future calculations at lower loops that are searching for these insights.

Speaker: Alex Edison (Northwestern University)

road-to-seven.pdf

23 Kawai-Lewellen-Tye relations / constructions

Speaker: Johannes Broedel and Stephan Stieberger .

Wednesday 12 July

24 Higher-order calculations: Recent developments from Feynman integrals

In this talk I will review recent developments in the field of analytical Feynman integral calculations. In particular, I will discuss Feynman integrals related to non-trivial geometries like an elliptic curve, or more general a Calabi-Yau manifold, and methods how to compute these Feynman integrals.

Speaker: Stefan Weinzierl

nordita.pdf

Thursday 13 July

25 Revisiting Hyperelliptic Feynman Integrals

While Feynman diagrams that give rise to elliptic curves and higher-dimensional Calabi-Yau manifolds have received a great deal of attention in recent years, much less attention has been paid to examples that involve hyperelliptic curves. In this talk, I will revisit some of the simplest Feynman diagrams that are known to be hyperelliptic, and show that the curves these diagrams give rise to satisfy a hidden involution symmetry that allow them to be mapped to curves of lower genus. This represents a significant simplification in the types of functions that these diagrams are expected to evaluate to. I will then go on to motivate the importance of studying hyperelliptic Feynman diagrams by constructing an all-loop class of vacuum diagrams that give rise to hyperelliptic curves of every genus.

Speaker: Andrew McLeod

26 New probes of the string spectrum

As is well known, the string spectrum comprises infinitely many states that can collectively be visualised along Regge trajectories of increasing mass and spin. Its massless level, low spins as well as certain higher spins including the leading Regge trajectory have been the focus of past studies. In this talk, we will discuss new probes beyond the leading Regge, starting with recent work on the interactions of subleading massive spin-2 superstring states and proceeding to ongoing work on whole families of subleading Regge trajectories as well as their interactions using string scattering amplitudes.

Speaker: Chrysoula Markou (University of Mons)

18:00 Dinner downtown

Friday 14 July

27 Seven-Point Singularities and the One-Loop n-gon Integral

This talk will cover two separate topics on the mathematical structure of Feynman integrals and scattering amplitudes. In the first part, I will discuss an attempt to determine what can be said, on general grounds, about the singularities of seven-point amplitudes in massless planar theories. One motivation is that this provides essential input into the bootstrap program that has allowed the computation of these amplitudes to high loop order in N=4 Yang-Mills. In the second part, I will explain how a recent mathematical result on volumes of orthoschemes can be used to provide an explicit analytic result for the one-loop scalar n-gon Feynman integral in n dimensions, for even n, with massless or massive internal and external edges.

Speaker: Anastasia Volovich (Brown University)

Monday 17 July

09:00 Registration

28 Welcome -- 4th week

29 Gravitational Waveforms from Amplitudes

Scattering amplitudes are useful for computing many quantities in gravitational wave physics. In this talk I I will discuss the determination of gravitational waveforms in scattering encounters at LO and NLO in the post-Minkowskian expansion. I will explain some of the methods which can be used to simplify the calculation, and comment on links to more classical methods.

Speaker: Donal O'Connell (University of Edinburgh)

18:30 Reception

Tuesday 18 July

30 High-precision gravitational wave physics from a worldline quantum field theory

I will review the worldline approach to reach high order PM results for the general relativistic two-body scattering problem thereby importing powerful multi-loop techniques from quantum field theory. We will discuss the simple structure of the classical limit amounting to the need to evaluate one-point functions in worldline quantum field theory at the tree-level, the inclusion of spin degrees of freedom via a worldline supersymmetry, the need to use the Schwinger-Keldysh formalism leading to the use of retarded propagators, as well as a discussion of the integration pipeline used in our approach. I will report on the recent completion of the 4PM spin-orbit computation for the impulse, scattering angle and spin-kick — both in the conservative and disspative cases. The later confirming the 4PM radiation reaction non-spinning results of Porto, Källen, Dlapa, Neff and Liu.

Speaker: Jan Plefka (Humboldt University)

WQFT_Nordita.pdf

Wednesday 19 July

31 Self-force in hyperbolic scattering

The first part will review the foundations of gravitational self-force theory in classical GR: a perturbative approach to the 2-body problem based on a systematic expansion of the field equations in the mass ratio, assumed small. The second part will describe recent work to apply self-force methods to the black-hole scattering problem, including a comparison with post-Minkowskian results from Amplitude calculations in a scalar-charge toy model.

Speaker: Leor Barack (University of Southampton)

Nordita23.pdf

Thursday 20 July

32 Massive gravity in the Swampland

I will discuss new positivity bounds at finite momentum transfer, showing that massive gravity parametrically violates these bounds unless the cutoff is within one order of magnitude of the graviton mass. These results effectively rule out massive gravity as a long distance theory consistent with a causal and unitary UV completion.

Speaker: Giulia Isabella (Geneva University)

33 Higher spins, the Teukolsky equation and Super-Extremal Kerr Binary Systems

In this talk, we will review the extraction of a higher spin gravitational Compton amplitude from low-energy solutions of the Teukolsky equation in the super-extremal (SE) Kerr region (a/Gm ≫ 1), for the scattering of a gravitational wave off the Kerr black hole (BH). We will then use this amplitude to study the non-radiative dynamics for binary systems formed by SE Kerr BHs with their spin oriented in generic directions, up to second order in the post-Minkowskian expansion.

Speaker: Fabian Bautista (IPhT Saclay)

19:00 Dinner downtown

Friday 21 July

34 Kerr black holes from amplitudes and effective field theory

Spin effects for Kerr black holes can be included systematically in field-theoretic calculations of the two-body problem. I will discuss one approach to incorporate spin which uses the synergy between on-shell scattering amplitudes and heavy particle effective theory (HPET). This framework is tailored to extract the classical parts of the computation and it exposes structure in the spin-multipole expansion. Some results from this approach include recent calculations to all orders in the spins of the black holes.

Speaker: Andreas Helset (Caltech)