39 research outputs found
Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics
We develop an Effective Field Theory (EFT) formalism to solve for the
conservative dynamics of binary systems in gravity via Post-Minkowskian (PM)
scattering data. Our framework combines a systematic EFT approach to compute
the deflection angle in the PM expansion, together with the 'Boundary-to-Bound'
(B2B) dictionary introduced in [1910.03008, 1911.09130]. Due to the nature of
scattering processes, a remarkable reduction of complexity occurs both in the
number of Feynman diagrams and type of integrals, compared to a direct EFT
computation of the potential in a PM scheme. We provide two illustrative
examples. Firstly, we compute all the conservative gravitational observables
for bound orbits to 2PM, which follow from only one topology beyond leading
order. The results agree with those in [1910.03008, 1911.09130], obtained
through the 'impetus formula' applied to the classical limit of the one loop
amplitude in Cheung et al. [1808.02489]. For the sake of comparison we
reconstruct the conservative Hamiltonian to 2PM order, which is equivalent to
the one derived in [1808.02489] from a matching calculation. Secondly, we
compute the scattering angle due to tidal effects from the electric- and
magnetic-type Love numbers at leading PM order. Using the B2B dictionary we
then obtain the tidal contribution to the periastron advance. We also construct
a Hamiltonian including tidal effects at leading PM order. Although relying on
(relativistic) Feynman diagrams, the EFT formalism developed here does not
involve taking the classical limit of a quantum amplitude, neither integrals
with internal massive fields, nor additional matching calculations, nor
spurious ('super-classical') infrared singularities. By construction, the EFT
approach can be automatized to all PM orders.Comment: 40 pages. 3 figure
The Full-Color Two-Loop Four-Gluon Amplitude in Super-QCD
We present the fully integrated form of the two-loop four-gluon amplitude in
supersymmetric quantum chromodynamics with gauge group
SU and with massless supersymmetric quarks (hypermultiplets) in
the fundamental representation. Our result maintains full dependence on
and , and relies on the existence of a compact integrand representation
that exhibits the duality between color and kinematics. Specializing to the
superconformal theory, where , we obtain
remarkably simple amplitudes that have an analytic structure close to that of
super-Yang-Mills theory, except that now certain lower-weight
terms appear. We comment on the corresponding results for other gauge groups.Comment: 5 pages + refs, 1 figure, 2 ancillary file
Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
We derive the conservative dynamics of non-spinning binaries to third
Post-Minkowskian order, using the Effective Field Theory (EFT) approach
introduced in [2006.01184] together with the Boundary-to-Bound dictionary
developed in [1910.03008, 1911.09130]. The main ingredient is the scattering
angle, which we compute to via Feynman diagrams. Adapting to
the EFT framework powerful tools from the amplitudes program, we show how the
associated (master) integrals are bootstrapped to all orders in velocities via
differential equations. Remarkably, the boundary conditions can be reduced to
the same integrals that appear in the EFT with Post-Newtonian sources. For the
sake of comparison, we reconstruct the Hamiltonian and the classical limit of
the scattering amplitude. Our results are in perfect agreement with those in
Bern et al. [1901.04424, 1908.01493].Comment: 7 pages. 1 figure. v2: Typos and misprints fixed (notably in Eq. 19).
To appear in Phys. Rev. Let
Conservative Tidal Effects in Compact Binary Systems to Next-to-Leading Post-Minkowskian Order
Using the Effective Field Theory approach together with the Boundary-to-Bound
map, we compute the next-to-leading order (NLO) Post-Minkowskian (PM) tidal
effects in the conservative dynamics of compact binary systems. We derive the
mass and current quadrupole and, for the first time, octupole corrections to
the binding energy for circular orbits at . Our results are
consistent with the test-body limit as well as the existent Post-Newtonian
literature. We also reconstruct a Hamiltonian incorporating tidal effects to
NLO in the PM expansion and find complete agreement with the recent derivation
of its quadrupolar part using the classical limit of scattering amplitudes.Comment: 5+4 pages. 1 figur
Machine Learning Post-Minkowskian Integrals
We study a neural network framework for the numerical evaluation of Feynman
loop integrals that are fundamental building blocks for perturbative
computations of physical observables in gauge and gravity theories. We show
that such a machine learning approach improves the convergence of the Monte
Carlo algorithm for high-precision evaluation of multi-dimensional integrals
compared to traditional algorithms. In particular, we use a neural network to
improve the importance sampling. For a set of representative integrals
appearing in the computation of the conservative dynamics for a compact binary
system in General Relativity, we perform a quantitative comparison between the
Monte Carlo integrators VEGAS and i-flow, an integrator based on neural network
sampling.Comment: 26 pages + references, 3 figures, 3 table
Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach
We present the contribution from potential interactions to the dynamics of
non-spinning binaries to fourth Post-Minkowskian (4PM) order. This is achieved
by computing the scattering angle to using the effective field
theory approach and deriving the bound radial action through analytic
continuation. We reconstruct the Hamiltonian and center-of-mass momentum in an
isotropic gauge. The (three-loop) integrals involved in our calculation are
computed via differential equations, including a sector yielding elliptic
integrals. As a prelude of radiation-reaction effects, using the universal link
between potential and tail terms, we also report: 1) The instantaneous energy
flux at ; 2) The contribution to the 4PM unbound/bound radial
action(s) depending on logarithms of the binding energy; 3) The
(scheme-independent) logarithmic contribution to the 4PM non-local tail
Hamiltonian for circular orbits. Our results in the potential region are in
agreement with the recent derivation from scattering amplitudes. We also find
perfect agreement in the overlap with the state-of-the-art in Post-Newtonian
theory.Comment: 9 pages, 1 figure. 1 ancillary file (txt format
Radiation Reaction and Gravitational Waves at Fourth Post-Minkowskian Order
We obtain the total impulse in the scattering of non-spinning binaries in
general relativity at fourth Post-Minkowskian order, i.e. ,
including linear, nonlinear, and hereditary radiation-reaction effects. We
derive the total radiated spacetime momentum as well as the associated energy
flux. The latter can be used to compute gravitational-wave observables for
generic (un)bound orbits. We employ the ("in-in") Schwinger-Keldysh worldline
effective field theory framework in combination with modern "multi-loop"
integration techniques from collider physics. The complete results are in
agreement with various partial calculations in the Post-Newtonian/Minkowskian
expansion.Comment: 6 pages + Refs + Supplemental. 1 figure and 1 table. 1
computer-readable ancillary fil
Scattering Amplitudes in Supersymmetric Quantum Chromodynamics and Gravity
Quantum field theory is a theoretical framework for the description of nature in terms of fundamental particles, fields and their interactions. In the quantum regime, elementary scattering processes are observables in many experiments and studied in theoretical physics. The theoretical understanding of scattering amplitudes is often based on a perturbative analysis in powers of the coupling strength of the fundamental forces. Whereas the computation of scattering amplitudes has been dominated by Feynman diagram constructions for a long time, new methods have lead to a multitude of novel results in the last 20-30 years. Thereafter discoveries of new representations, dualities and construction methods have enormously increased our understanding of the mathematical structure of scattering amplitudes. In this thesis we focus on a particular structure of gauge theory amplitudes known as the color-kinematics duality. Closely tied to this duality is the double copy construction of gravitational amplitudes, and a set of identities among basic building blocks of the gauge theory, the BCJ identities. Using methods developed for the study of this duality, we obtain new results for scattering amplitudes in non-maximal supersymmetric Yang-Mills coupled to massless fundamental matter at one and two loops. We immediately construct amplitudes in supergravity theories via the double copy. Furthermore, we include methods and results for the integration of gauge theory amplitudes and the ultraviolet structure of supergravity amplitudes. In a second part we present ideas related to the identification of basic building blocks that underlie the construction of scattering amplitudes. A decomposition of gauge theory amplitudes into color- and kinematic-dependent contributions exposes a set of primitive objects. Relations among these objects allow us to identify a minimal set of independent kinematic building blocks
Scattering Amplitudes in Supersymmetric Quantum Chromodynamics and Gravity
Quantum field theory is a theoretical framework for the description of nature in terms of fundamental particles, fields and their interactions. In the quantum regime, elementary scattering processes are observables in many experiments and studied in theoretical physics. The theoretical understanding of scattering amplitudes is often based on a perturbative analysis in powers of the coupling strength of the fundamental forces. Whereas the computation of scattering amplitudes has been dominated by Feynman diagram constructions for a long time, new methods have lead to a multitude of novel results in the last 20-30 years. Thereafter discoveries of new representations, dualities and construction methods have enormously increased our understanding of the mathematical structure of scattering amplitudes. In this thesis we focus on a particular structure of gauge theory amplitudes known as the color-kinematics duality. Closely tied to this duality is the double copy construction of gravitational amplitudes, and a set of identities among basic building blocks of the gauge theory, the BCJ identities. Using methods developed for the study of this duality, we obtain new results for scattering amplitudes in non-maximal supersymmetric Yang-Mills coupled to massless fundamental matter at one and two loops. We immediately construct amplitudes in supergravity theories via the double copy. Furthermore, we include methods and results for the integration of gauge theory amplitudes and the ultraviolet structure of supergravity amplitudes. In a second part we present ideas related to the identification of basic building blocks that underlie the construction of scattering amplitudes. A decomposition of gauge theory amplitudes into color- and kinematic-dependent contributions exposes a set of primitive objects. Relations among these objects allow us to identify a minimal set of independent kinematic building blocks