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.

Sweden

Lucile Cangemi

Marco Chiodaroli

Henrik Johansson

United Kingdom

China

Alexander Ochirov

Paolo Pichini

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

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

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

Five-dimensional gauge and gravity theories are known to exhibit striking properties. D = 5 is the lowest dimension where massive tensor states appear naturally, providing a testing ground for perturbative insights into six-dimensional tensor theories. Five-dimensional supergravities are highly constrained and admit elegant geometric and algebraic formulations, with global symmetries manifest at the Lagrangian level.

Spinor-helicity formalism for massive and massless amplitudes in five dimensions

Quantum scattering amplitudes for massive matter have received new attention in connection to classical calculations relevant to gravitational-wave physics. Amplitude methods and insights are now employed for precision computations of observables needed for describing the gravitational dynamics of bound massive objects such as black holes. An important direction is the inclusion of spin effects needed to accurately describe rotating (Kerr) black holes. Higher-spin amplitudes introduced by Arkani-Hamed, Huang and Huang at three points have by now a firm connection to the effective description of Kerr black-hole physics. The corresponding Compton higher-spin amplitudes remain however an elusive open problem. Here we draw from results of the higher-spin literature and show that physical insights can be used to uniquely fix the Compton amplitudes up to spin 5/2, by imposing a constraint on a three-point higher-spin current that is a necessary condition for the existence of an underlying unitary theory. We give the unique effective Lagrangians up to spin 5/2, and show that they reproduce the previously-known amplitudes. For the multi-graviton amplitudes analogous to the Compton amplitude, no further corrections to our Lagrangians are expected, and hence such amplitudes are uniquely predicted. As an essential tool, we introduce a modified version of the massive spinor-helicity formalism which allows us to conveniently obtain higher-spin states, propagators and compact expressions for the amplitudes.

Compton black-hole scattering for s ≤ 5/2

Scattering amplitudes have the potential to provide new insights to the study of supergravity theories with gauged R-symmetry and Minkowski vacua. Such gaugings break supersymmetry spontaneously, either partly or completely. In this paper, we develop a framework for double-copy constructions of Abelian and non-Abelian gaugings of   <math> <mi>N</mi> <mo>=</mo> <mn>8</mn> </math>  $$ \mathcal{N}=8 $$  supergravity with these properties. They are generally obtained as the double copy of a spontaneously-broken (possibly supersymmeric) gauge theory and a theory with explicitly-broken supersymmetry. We first identify purely-adjoint deformations of   <math> <mi>N</mi> <mo>=</mo> <mn>4</mn> </math>  $$ \mathcal{N}=4 $$  super-Yang-Millstheorythatpreservethedualitybetweencolorandkinematics. A combination of Higgsing and orbifolding yields the needed duality-satisfying gauge-theory factors with multiple matter representations. We present three explicit examples. Two are Cremmer-Scherk-Schwarz gaugings with unbroken   <math> <mi>N</mi> <mo>=</mo> <mn>6</mn> <mo>,</mo> <mspace width="0.12em"></mspace> <mn>4</mn> </math>  $$ \mathcal{N}=6,\;4 $$  supersymmetry and U(1) gauge group. The third has unbroken   <math> <mi>N</mi> <mo>=</mo> <mn>4</mn> </math>  $$ \mathcal{N}=4 $$  supersymmetry and SU(2) × U(1) gauge group. We also discuss examples in which the double-copy method gives theories with explicitly-broken supersymmetry.

Non-Abelian gauged supergravities as double copies

We compute one-loop matter amplitudes in homogeneous Maxwell-Einstein supergravities with   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 supersymmetry using the double-copy construction. We start from amplitudes of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 super-Yang-Mills theory with matter that obey manifestly the duality between color and kinematics. Taking advantage of the fact that amplitudes with external hypermultiplets have kinematical numerators which do not present any explicit dependence on the loop momentum, we find a relation between the one-loop divergence of the supergravity amplitudes and the beta function of the non-supersymmetric gauge theory entering the construction. Two distinct linearized counterterms are generated at one loop. The divergence corresponding to the first is nonzero for all homogeneous supergravities, while the divergence associated to the second vanishes only in the case of the four Magical supergravities.

Maor Ben-Shahar

One-loop amplitudes for   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 homogeneous supergravities

Previous work has shown that massless tree amplitudes of the type I and IIA/B superstrings can be dramatically simplified by expressing them as double copies between field-theory amplitudes and scalar disk/sphere integrals, the latter containing all the α′-corrections. In this work, we pinpoint similar double-copy constructions for the heterotic and bosonic string theories using an α  ′ -dependent field theory and the same disk/sphere integrals. Surprisingly, this field theory, built out of dimension-six operators such as (D  μ  F  μν )2, has previously appeared in the double-copy construction of conformal supergravity. We elaborate on the α  ′  → ∞ limit in this picture and derive new amplitude relations for various gauge-gravity theories from those of the heterotic string.

Thales Azevedo

Canada

Germany

Oliver Schlotterer

Heterotic and bosonic string amplitudes via field theory

Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + ϕ 3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism. Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. We also present explicit expressions for all-loop single-graviton Einstein-Yang-Mills amplitudes in terms of Yang-Mills amplitudes and, through gauge invariance, derive new all-loop amplitude relations for Yang-Mills theory.