Amplitudes and 4D Gauss-Bonnet Theory

Abstract

It has recently been argued that there may be a nontrivial four-dimensional limit of the higher-dimensional Gauss--Bonnet and Lovelock interactions and that this might provide a loophole allowing for new four-dimensional gravitational theories, possibly without a standard Lagrangian. We investigate this claim by studying tree-level graviton scattering amplitudes, allowing us to draw conclusions independently of the Lagrangian. By taking four-dimensional limits of higher-dimensional scattering amplitudes of the Gauss--Bonnet theory, we find four-dimensional amplitudes that are different from general relativity; however, these amplitudes are not new since they all come from certain scalar-tensor theories. The nontrivial limit that does not lead to infinite strong coupling around flat space leads to $(\partial \varphi {)}^4$ theory. We argue that there cannot be any six-derivative purely gravitational four-point amplitudes in any dimension other than those coming from Lovelock theory by directly constructing the on-shell amplitudes. In particular, there can be no new such amplitudes in four dimensions beyond those of general relativity. We also present some new results on the spin-averaged cross section for graviton-graviton scattering in general relativity and Gauss--Bonnet theory in arbitrary dimensions.

arXiv comment18 pages

References in corpus (36)

• The galileon as a local modification of gravity
• Causality, Analyticity and an IR Obstruction to UV Completion
• Einstein-Gauss-Bonnet gravity in 4-dimensional space-time
• Charged Black Holes in AdS Spaces in $4D$ Einstein Gauss-Bonnet Gravity
• Horndeski Gravity as $D\to 4$ Limit of Gauss-Bonnet
• Causality Constraints in Conformal Field Theory
• Is there a novel Einstein-Gauss-Bonnet theory in four dimensions?
• On Taking the $D\to 4$ limit of Gauss-Bonnet Gravity: Theory and Solutions
• Derivation of Regularized Field Equations for the Einstein-Gauss-Bonnet Theory in Four Dimensions
• Multi-field galileons and higher co-dimension branes
• Arbitrary p-form Galileons
• A consistent theory of $D\to 4$ Einstein-Gauss-Bonnet gravity
• Amplitudes' Positivity, Weak Gravity Conjecture, and Modified Gravity
• The $D\to 2$ Limit of General Relativity
• Einstein gravity with Gauss-Bonnet entropic corrections
• Galileons as Wess-Zumino Terms
• Black holes in the four-dimensional Einstein-Lovelock gravity
• Comment on "Einstein-Gauss-Bonnet Gravity in 4-Dimensional Space-Time''
• Inconsistencies in four-dimensional Einstein-Gauss-Bonnet gravity
• Generalizing Galileons
• Positivity of Curvature-Squared Corrections in Gravity
• Vacua in novel 4D Einstein-Gauss-Bonnet Gravity: pathology and instability?
• Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography
• Ghost-Free Derivative Interactions for a Massive Graviton
• Comment on "Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime"
• Regularized Lovelock gravity
• Testing the nature of Gauss-Bonnet gravity by four-dimensional rotating black hole shadow
• Unitarization from Geometry
• Kaluza-Klein Towers on General Manifolds
• Quantum corrections to gravity
• Tensor Galileons and Gravity
• Pseudo-Linear Spin-2 Interactions
• From Lovelock to Horndeski's generalised scalar-tensor theory
• Generalized gravitational phase transition in novel 4D Einstein-Gauss-Bonnet gravity
• On the uniqueness of ghost-free special gravity
• Conformal/Poincaré Coset, Cosmology, and Descendants of Lovelock Terms

Cited by in corpus (69)

• Derivation of Regularized Field Equations for the Einstein-Gauss-Bonnet Theory in Four Dimensions
• The 4D Einstein-Gauss-Bonnet Theory of Gravity: A Review
• A consistent theory of $D\to 4$ Einstein-Gauss-Bonnet gravity
• A note on the novel 4D Einstein-Gauss-Bonnet gravity
• Charged 4D Einstein-Gauss-Bonnet-AdS Black Holes: Shadow, Energy Emission, Deflection Angle and Heat Engine
• Thermodynamic geometry of the novel 4-D Gauss Bonnet AdS Black Hole
• Inconsistencies in four-dimensional Einstein-Gauss-Bonnet gravity
• (In)stability of black holes in the 4D Einstein-Gauss-Bonnet and Einstein-Lovelock gravities
• Charged black hole in $4D$ Einstein-Gauss-Bonnet gravity: Particle motion, plasma effect on weak gravitational lensing and centre-of-mass energy
• Spinning test particle in four-dimensional Einstein-Gauss-Bonnet Black Hole
• Observational Constraints on the Regularized 4D Einstein-Gauss-Bonnet Theory of Gravity
• Comment on "Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime"
• Gravity with a generalized conformal scalar field: Theory and solutions
• Regularized Lovelock gravity
• Lower-dimensional Gauss-Bonnet Gravity and BTZ Black Holes
• Vacua and Exact Solutions in Lower-$D$ Limits of EGB
• Bending of light in novel 4$D$ Gauss-Bonnet-de Sitter black holes by Rindler-Ishak method
• Anisotropic Stars in 4D Einstein-Gauss-Bonnet Gravity
• Nonlinear magnetically charged black holes in 4D Einstein-Gauss-Bonnet gravity
• Rotating Gauss-Bonnet BTZ Black Holes
• Thin accretion disks around rotating black holes in $4D$ Einstein-Gauss-Bonnet gravity
• Black Holes in the Scalar-Tensor Formulation of 4D Einstein-Gauss-Bonnet Gravity: Uniqueness of Solutions, and a New Candidate for Dark Matter
• Theoretical and observational constraints on regularized 4$D$ Einstein-Gauss-Bonnet gravity
• Equivalence of solutions between the four-dimensional novel and regularized EGB theories in a cylindrically symmetric spacetime
• Canonical variational completion and 4D Gauss-Bonnet gravity
• Null geodesics and shadow of 4$D$ Einstein-Gauss-Bonnet black holes surrounded by quintessence
• Tidal effects in 4D Einstein-Gauss-Bonnet Black Hole Spacetime
• Cosmology and gravitational waves in consistent $D\to 4$ Einstein-Gauss-Bonnet gravity
• Null Geodesics and Thermodynamic Phase Transition of Four-Dimensional Gauss-Bonnet AdS Black Hole
• Charged 4D Einstein-Gauss-Bonnet Black Hole: Vacuum solutions, Cauchy Horizon, Thermodynamics
• Distinguishing modified gravity with just two tensorial degrees of freedom from general relativity: Black holes, cosmology, and matter coupling
• Thermodynamics, Phase Transition and Joule Thomson Expansion of 4-D Gauss-Bonnet AdS Black Hole
• Traversable Thin-shell Wormhole in the 4D Einstein-Gauss-Bonnet Theory
• Page Curve and Island in EGB gravity
• Black Holes in $4D$ AdS Einstein Gauss Bonnet Gravity With Power- Yang Mills Field
• Three Dimensional Modified Gravities as Holographic Limits of Lancsoz-Lovelock Theories
• On the gravitational collapse in 4-dimensional Einstein-Gauss-Bonnet gravity
• Dynamical analysis in regularized $4D$ Einstein-Gauss-Bonnet gravity with non-minimal coupling
• A New Gravitational Action For The Trace Anomaly
• Naked singularity in 4D Einstein-Gauss-Bonnet novel gravity: Echoes and (in)-stability
• Asymptotic structure of Einstein-Gauss-Bonnet theory in lower dimensions
• 3D Lovelock Gravity and the Holographic c-Theorem
• New model of 4D Einstein--Gauss--Bonnet gravity coupled with nonlinear electrodynamics
• Lower-dimensional Limits of Cubic Lovelock Gravity
• Black holes in a new gravitational theory with trace anomalies
• Topological Corrections and Conformal Backreaction in the Einstein Gauss-Bonnet/Weyl Theories of Gravity at D=4
• Accretion onto a Charged Black Hole in Consistent 4D Einstein-Gauss-Bonnet Gravity
• Power Spectra of Slow-Roll inflation in the consistent $D\to 4$ Einstein-Gauss-Bonnet gravity
• Multi-horizons black hole solutions, photon sphere and perihelion shift in weak ghost-free Gauss-Bonnet theory of gravity
• Generalized gravitational phase transition in novel 4D Einstein-Gauss-Bonnet gravity
• Black holes in 4D Einstein-Maxwell-Gauss-Bonnet gravity coupled with scalar fields
• Conformal/Poincaré Coset, Cosmology, and Descendants of Lovelock Terms
• 4D Einstein-Gauss-Bonnet Gravity From Non-Einsteinian Phase
• Anisotropy in constraint 4D Gauss-Bonnet gravity
• Regular black holes from pure gravity in four dimensions
• Einstein Gauss-Bonnet Theories as Ordinary, Wess-Zumino Conformal Anomaly Actions
• A new constant behind the rotational velocity of galaxies
• All $2D$ generalised dilaton theories from $d\ge 4$ gravities
• Scaling symmetry, Smarr relation, and the extended first law in lower-dimensional Lovelock gravity
• Dimensional aspects of Lovelock-Lanczos gravity
• D-dimensional black holes in extended Gauss-Bonnet gravity
• A Post-Newtonian Analysis of Regularized 4D-EGB Theory: Complete Set of PPN Parameters and Observational Constraints
• Deflection of charged massive particles by a four-dimensional charged Einstein-Gauss-Bonnet black hole
• Absence of isolated critical points with nonstandard critical exponents in the four-dimensional regularization of Lovelock gravity
• Strong coupling and instabilities in singularity-free inflation from an infinite sum of curvature corrections
• Inflation with the Trace Anomaly Action and Primordial Black Holes
• Dynamical 4-D Gauss-Bonnet action from matter-graviton interaction at one-loop
• New brane-like solutions in modified four-dimensional Einstein-Gauss-Bonnet gravity
• Lower-dimensional Gauss-Bonnet gravity black holes with quintessence