Simplicity in the Structure of QED and Gravity Amplitudes
arXiv:0811.3405 · doi:10.1088/1126-6708/2009/02/038
Abstract
We investigate generic properties of one-loop amplitudes in unordered gauge theories in four dimensions. For such theories the organisation of amplitudes in manifestly crossing symmetric expressions poses restrictions on their structure and results in remarkable cancellations. We show that one-loop multi-photon amplitudes in QED with at least eight external photons are given only by scalar box integral functions. This QED `no-triangle' property is true for all helicity configurations and has similarities to the `no-triangle' property found in the case of maximal N = 8 supergravity. Results are derived both via a world-line formalism as well as using on-shell unitarity methods. We show that the simple structure of the loop amplitude originates from the extremely good BCFW scaling behaviour of the QED tree-amplitude.
v2: v2: appendix B rephrased and updated, results unchanged. 43 pages. Latex, 7 figures
References in corpus (38)
- Gluon scattering amplitudes at strong coupling
- Reducing full one-loop amplitudes to scalar integrals at the integrand level
- Conformal properties of four-gluon planar amplitudes and Wilson loops
- Scalar one-loop integrals for QCD
- An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
- The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
- Direct extraction of one-loop integral coefficients
- Full one-loop amplitudes from tree amplitudes
- On Tree Amplitudes in Gauge Theory and Gravity
- Three-Loop Superfiniteness of N=8 Supergravity
- On-Shell Methods in Perturbative QCD
- On the Rational Terms of the one-loop amplitudes
- D-dimensional unitarity cut method
- Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
- Is N = 8 Supergravity Ultraviolet Finite?
- Bootstrapping One-Loop QCD Amplitudes with General Helicities
- Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes
- Direct Extraction Of One Loop Rational Terms
- Ultraviolet properties of Maximal Supergravity
- Taming Tree Amplitudes In General Relativity
- Unexpected Cancellations in Gravity Theories
- Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity
- New Higher-Derivative Theorems
- The No-Triangle Hypothesis for N=8 Supergravity
- Absence of Triangles in Maximal Supergravity Amplitudes
- Closed-Form Decomposition of One-Loop Massive Amplitudes
- Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
- Modular properties of two-loop maximal supergravity and connections with string theory
- On-shell recursion relations for all Born QCD amplitudes
- Worldgraph Approach to Yang-Mills Amplitudes from N=2 Spinning Particle
- Three-Loop Leading Singularities and BDS Ansatz for Five Particles
- Six-Photon Amplitudes
- Explicit Cancellation of Triangles in One-loop Gravity Amplitudes
- Worldline Green Functions for Arbitrary Feynman Diagrams
- Polynomial Structures in One-Loop Amplitudes
- Six-Photon Amplitudes in Scalar QED
- On Cancellations of Ultraviolet Divergences in Supergravity Amplitudes
- Unitarity Method with Spurious Pole
Cited by in corpus (35)
- The Ultraviolet Behavior of N=8 Supergravity at Four Loops
- One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts
- Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level
- N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
- Loop amplitudes in gauge theories: modern analytic approaches
- Proof of Gravity and Yang-Mills Amplitude Relations
- The Tree Formula for MHV Graviton Amplitudes
- R^4 counterterm and E7(7) symmetry in maximal supergravity
- Tropical Amplitudes
- No triangles on the moduli space of maximally supersymmetric gauge theory
- An Introduction to On-shell Recursion Relations
- Tree-Level Amplitudes in N=8 Supergravity
- New relations for scattering amplitudes in Yang-Mills theory at loop level
- Chiral approach to massive higher spins
- On powercounting in perturbative quantum gravity theories through color-kinematic duality
- Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts
- The Next-to-Simplest Quantum Field Theories
- UV cancelations in gravity loop integrands
- Higher-loop amplitudes in the non-minimal pure spinor formalism
- String-inspired representations of photon/gluon amplitudes
- Worldline master formulas for the dressed electron propagator, part 2: On-shell amplitudes
- Euler-Heisenberg lagrangians and asymptotic analysis in 1+1 QED, part 1: Two-loop
- Gravitino Interactions from Yang-Mills Theory
- Compact QED Tree-Level Amplitudes From Dressed BCFW Recursion Relations
- Gravitons, Bose-symmetry, and Bonus-scaling
- Factorization of cubic vertices involving three different higher spin fields
- One-loop N=8 supergravity coefficients from N=4 super Yang-Mills
- Integral representations combining ladders and crossed-ladders
- Note on Permutation Sum of Color-ordered Gluon Amplitudes
- A Gauge-Gravity Relation in the One-loop Effective Action
- Rational Terms in Theories with Matter
- Photon-Graviton Amplitudes from the Effective Action
- Low-energy multi-photon scattering at tree-level and one-loop order in a homogeneous electromagnetic field
- Note on Cyclic Sum and Combination Sum of Color-ordered Gluon Amplitudes
- Shifts in BCFW method for QED