Quantum higher-spin theory applied to Compton amplitudes has proven to be surprisingly useful for elucidating Kerr black hole dynamics. Here we apply the framework to compute scattering amplitudes and observables for a binary system of two rotating black holes, at second post-Minkowskian order, and to all orders in the spin-multipole expansion for certain quantities. Starting from the established three-point and conjectured Compton quantum amplitudes, the infinite-spin limit gives classical amplitudes that serve as building blocks that we feed into the unitarity method to construct the 2-to-2 one-loop amplitude. We give scalar box, vector box, and scalar triangle coefficients to all orders in spin, where the latter are expressed in terms of Bessel-like functions. Using the Kosower-Maybee-O’Connell formalism, the classical 2PM impulse is computed, and in parallel we work out the scattering angle and eikonal phase. We give novel all-order-in-spin formulae for certain contributions, and the remaining ones are given up to $$ \mathcal{O}\left({S}^{11}\right) $$ . Since Kerr 2PM dynamics beyond $$ \mathcal{O}\left({S}^{\ge 5}\right) $$ is as of yet not completely settled, this work serves as a useful reference for future studies.

Switzerland

Lara Bohnenblust

Sweden

United Kingdom

Lucile Cangemi

Henrik Johansson

Paolo Pichini

Binary Kerr black-hole scattering at 2PM from quantum higher-spin Compton

We develop massive higher-spin theory as a framework for describing dynamics of rotating compact objects, such as Kerr black holes. In this paper, we explore gauge interactions up to quartic order and corresponding Compton amplitudes of higher-spin massive objects coupled to electromagnetism and Yang-Mills theory. Their classical counterparts are known as root-Kerr gauge-theory solutions, whose amplitudes are closely related to those of Kerr black holes. We use three distinct approaches: (i) massive higher-spin gauge symmetry to introduce cubic interactions for all spins and the quartic interactions up to spin 3, which is implemented both off shell and via Ward identities; (ii) a chiral higher-spin approach to construct quartic Lagrangians with correct degrees of freedom to all spins; (iii) on-shell functional patterns before and after taking the classical limit to constrain the Compton amplitudes. As final results, we arrive at simple local formulae for the candidate root-Kerr Compton amplitudes both in the quantum regime and classical limit, to all orders in spin. This is a precursor to the gravitational Kerr case, which is presented in a follow-up paper.

Marco Chiodaroli

China

Alexander Ochirov

Belgium

Russia

Evgeny Skvortsov

From higher-spin gauge interactions to Compton amplitudes for root-Kerr

We construct a candidate tree-level gravitational Compton amplitude for a rotating Kerr black hole, for any quantum spin <math><mrow><mi>s</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>∞</mi></mrow></math>, from which we extract the corresponding classical amplitude to all orders in the spin vector <math><msup><mi>S</mi><mi>μ</mi></msup></math>. We use multiple insights from massive higher-spin quantum field theory, such as massive gauge invariance and improved behavior in the massless limit. A chiral-field approach is particularly helpful in ensuring correct degrees of freedom, and for writing down compact off-shell interactions for general spin. The simplicity of the interactions is echoed in the structure of the spin-<math><mi>s</mi></math> Compton amplitude, for which we use homogeneous symmetric polynomials of the spin variables. Where possible, we compare to the general-relativity results in the literature, available up to eighth order in spin.

Compton Amplitude for Rotating Black Hole from QFT

We significantly extend recent work on the kinematic Hopf algebra, a structure that was shown to underlie the color-kinematics duality in Yang-Mills (YM) theory coupled to two heavy scalars, known as the heavy-mass effective theory (HEFT) limit. First, staying in the HEFT limit, we show the same kinematic Hopf algebra can be used to obtain Bern-Carrasco-Johansson (BCJ) numerators in <math><msup><mi>DF</mi><mn>2</mn></msup><mo>+</mo><mrow><mi>YM</mi></mrow></math> theory, a theory containing an infinite number of higher derivative corrections to YM, used to obtain string amplitudes via the double copy. Second, we exploit the intricate structure induced by the massive poles to obtain an efficient and direct expression for local BCJ numerators in pure YM based on the same kinematic Hopf algebra. This demonstrates that the kinematic Hopf algebra works even beyond the HEFT limit, strongly suggesting this structure universally underlies the color-kinematics duality.

Denmark

Gang Chen

Laurentiu Rodina

Congkao Wen

Kinematic Hopf algebra and Bern-Carrasco-Johansson numerators at finite <math><msup><mi>α</mi><mo>′</mo></msup></math>

Scattering amplitudes in Yang-Mills-Einstein theories have been investigated mostly for compact gauge groups. While non-compact gauge groups are not physically viable in Yang-Mills theory, non-compact gaugings feature prominently in the supergravity literature, where any choice of perturbative vacuum spontaneously breaks the gauge group to a compact subgroup. In this paper, we formulate double-copy constructions for several five-dimensional   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 supergravities with non-compact gauge groups. On one side of the double copy, we employ amplitudes from a super-Yang-Mills theory with a massive hypermultiplet. On the other, we use amplitudes from particular non-supersymmetric Yang-Mills-scalar theories with massive fermions, chosen to obey constraints coming from color/kinematics duality. Supergravities with massive self-dual tensors in five dimensions are also considered, showing that tensors are straightforwardly realized as double copies of gauge-theory fermions with suitable choices of signs in the corresponding solutions of the Dirac equation. We present several examples of these constructions, noting in particular the appearance of Heisenberg groups in the supergravity gauge symmetry and, in some cases, the possibility of exotic tensor-vector matter couplings.

United States

Murat Günaydin

Radu Roiban

Non-compact gauge groups, tensor fields and Yang-Mills-Einstein amplitudes

<p>We introduce a novel approach for deriving one-loop Bern-Carrasco-Johansson (BCJ) numerators and reveal the world-sheet origin of the one-loop double copy. Our work shows that expanding Cachazo-He-Yuan half-integrands into generalized Parke-Taylor factors intrinsically generates BCJ numerators on quadratic propagators satisfying Jacobi identities. We validate our methodology by successfully reproducing one-loop BCJ numerators for the nonlinear sigma model as well as those of pure Yang-Mills theory in four dimensions with all-plus or single-minus helicities.</p>

Jin Dong

Yao-Qi Zhang

Canada

Yong Zhang

One-loop Bern-Carrasco-Johansson numerators on quadratic propagators from the worldsheet

We propose that the dynamics of Kerr black holes is strongly constrained by the principle of gauge symmetry. We initiate the construction of effective field theories for Kerr black holes of any integer quantum spin <math><mi>s</mi></math> using Stückelberg fields, and show that the known three-point Kerr amplitudes are uniquely predicted using massive higher-spin gauge symmetry. This symmetry is argued to be connected to an enhanced range of validity for the Kerr effective field theories. We consider the closely related root-Kerr electromagnetic solution in parallel, for which the dynamical interactions with photons are also constrained by massive higher-spin gauge symmetry. Finally, the spin-<math><mi>s</mi></math> Compton amplitudes are analyzed, and we discuss contact-term constraints at <math><mi>s</mi><mo>=</mo><mn>2</mn></math> from Ward identities.

Kerr Black Holes from Massive Higher-Spin Gauge Symmetry

In this paper, we study tree-level scattering amplitudes of scalar particles in the context of effective field theories. We use tools similar to the soft bootstrap to build an ansatz for cyclically ordered amplitudes and impose the Bern-Carrasco-Johansson (BCJ) relations as a constraint. We obtain a set of BCJ-satisfying amplitudes as solutions to our procedure, which can be thought of as special higher-derivative corrections to SU(N) nonlinear sigma model amplitudes satisfying BCJ relations to arbitrary multiplicity at leading order. The surprising outcome of our analysis is that BCJ conditions on higher-point amplitudes impose constraints on lower-point amplitudes, and they relate coefficients at different orders in the derivative expansion. This shows that BCJ conditions are much more restrictive than soft limit behavior, allowing only for a very small set of solutions.

Taro V. Brown

Czechia

Karol Kampf

Umut Oktem

Shruti Paranjape

Jaroslav Trnka

Scalar Bern-Carrasco-Johansson bootstrap

Scattering amplitudes in Yang-Mills theory are known to exhibit kinematic structures which hint to an underlying kinematic algebra that is dual to the gauge group color algebra. This color-kinematics duality is still poorly understood in terms of conventional Feynman rules, or from a Lagrangian formalism. In this work, we present explicit Lagrangians whose Feynman rules generate duality-satisfying tree-level BCJ numerators, to any multiplicity in the next-to-MHV sector of pure Yang-Mills theory. Our Lagrangians make use of at most three pairs of auxiliary fields (2, 1, 0-forms) — surprisingly few compared to previous attempts of Lagrangians at low multiplicities. To restrict the Lagrangian freedom it is necessary to make several non-trivial assumptions regarding field content, kinetic terms, and interactions, which we discuss in some detail. Future progress likely hinges on relaxing these assumptions.

Maor Ben-Shahar

Lucia Garozzo

Lagrangians manifesting color-kinematics duality in the NMHV sector of Yang-Mills

We revisit the four-point function of super gluons in <math><msub><mi>AdS</mi><mn>5</mn></msub><mo>×</mo><msup><mi>S</mi><mn>3</mn></msup></math> and show how the integrand of a generalized Mellin transform satisfies the <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> decoupling identity, Bern-Carrasco-Johansson relations and color-kinematic duality, in a way that directly mirrors the analogous flat space relations. We unmix the spectrum of double-trace operators at large <math><mi>N</mi></math> and find all anomalous dimensions at leading order which follow a very simple pattern, as in other theories with hidden conformal symmetries.

J. M. Drummond

R. Glew

M. Santagata

Bern-Carrasco-Johansson relations in <math><msub><mrow><mi>AdS</mi></mrow><mn>5</mn></msub><mo>×</mo><msup><mi>S</mi><mn>3</mn></msup></math> and the double-trace spectrum of super gluons