New Relations for Gauge-Theory Amplitudes

By Z. Bern, J. J. Carrasco, H. Johansson. 2008

1,250 citations recorded by the source corpus.

We present an identity satisfied by the kinematic factors of diagrams describing the tree amplitudes of massless gauge theories. This identity is a kinematic analog of the Jacobi identity for color factors. Using this we find new relations between color-ordered partial amplitudes. We discuss applications to multiloop calculations via the unitarity method. In particular, we illustrate the relations between different contributions to a two-loop four-point QCD amplitude. We also use this identity to reorganize gravity tree amplitudes diagram by diagram, offering new insight into the structure of the Kawai-Lewellen-Tye (KLT) relations between gauge and gravity tree amplitudes. This insight leads to similar but novel relations. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1dd6f88e9182e55c4f664f3316693045acccf953

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In Nuclear and High Energy Physics

1. R. Roiban
2. Alexander Ochirov
3. S. Frolov
4. L. Alday
5. N. Beisert
6. A. Tseytlin
7. H. Johansson
8. F. Cachazo

Citations in the corpus

• The kinematic algebra from the self-dual sector (2011, background): “Let us set the scene with a description of the BCJ relations [ 2 ].”
• Observables and amplitudes for spinning particles and black holes (2019, methodology): “plitudes Rather than recompute corresponding gravity amplitudes in perturbative GR4, we can easily just apply the double copy. The generalisation of the traditional BCJ gauge theory replacement rules [58, 59] to massive matter states was developed by Johansson and Ochirov [61]. In our context the co”
• Loops in AdS from conformal field theory (2016, background): “For inspiration and contrast, consider the decades of fantastic progress in understanding flat space S-matrices, which contain extremely powerful physical and mathematical structures: they relate loops to trees [18, 19], gravitational theories to gauge theories [20], and have suggested a re-imaginat”
• Double copy for massive quantum particles with spin (2019, methodology): “This duality is present in many physically relevant gauge theories, such as pure Yang-Mills theory [15, 17–19], quantum chromodynamics (QCD) [20–22], Yang-Mills-Higgs models [23], and supersymmetric generalizations thereof [16, 20, 23–28].”
• Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM (2014, methodology): “This formula is telling us the well-known fact that the space of partial amplitudes in YM is only (n − 3)! dimensional [43, 47, 53].”
• From boundary data to bound states (2019, methodology): “The scattering angle to 3PM order was derived more recently, using novel tools from the theory of scattering amplitudes [27–29, 32, 33] via the 3PM Hamiltonian [36, 37].”
• Λ scattering equations (2016, background): “Some of them are gauge invariance, soft limits, BCJ relations and the existence of KLT formulas [17, 45–55].”
• Polylogarithms, multiple zeta values and superstring amplitudes (2013, methodology): “Although this symmetry is obscured on the right hand side of the KLT formula, it can be verified to hold through the KK relations (discovered in [1] and proven in [25]) and BCJ relations [2] obeyed by the amplitudes AYM(σ) and ÃYM(ρ).”
• Complete N-Point Superstring Disk Amplitude II. Amplitude and Hypergeometric Function Structure (2011, background): “As an example we mention the duality between color and kinematics, which exhibits a new structure in gauge theory [4].”
• Scattering equations and Kawai-Lewellen-Tye orthogonality (2013, background): “Secondly, the BCJ fundamental relations for Yang-Mills amplitudes are known to hold in any dimension [15, 17].”
• Explicit BCJ numerators from pure spinors (2011, neutral): “As will now be discussed, the field-theory limit of the superstring amplitude can be used to find supersymmetric and local n-point BCJ-satisfying kinematic numerators [23] in a straightforward manner.”