Local integrand representations of all two-loop amplitudes in planar SYM

DOI10.1007/JHEP08(2015)119zbMath1388.81710arXiv1505.05886MaRDI QIDQ2635744

Jaroslav Trnka, Jacob L. Bourjaily

Publication date: 31 May 2018

Published in: Journal of High Energy Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.05886

zbMATH Keywords

scattering amplitudessupersymmetric gauge theory\(1/N\) expansion

Mathematics Subject Classification ID

Topological field theories in quantum mechanics (81T45)

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Uses Software

• Mathematica
• positroids

Cites Work

• Unnamed Item
• The four-loop remainder function and multi-Regge behavior at NNLLA in planar \( \mathcal{N} = 4\) super-Yang-Mills theory
• Eliminating spurious poles from gauge-theoretic amplitudes
• The Grassmannian origin of dual superconformal invariance
• A duality for the S matrix
• The all-loop integrand for scattering amplitudes in planar \({\mathcal N} = 4\) SYM
• Dual superconformal symmetry of scattering amplitudes in \({\mathcal N}=4\) super-Yang-Mills theory
• The differential of all two-loop MHV amplitudes in \( \mathcal{N}=4 \) Yang-Mills theory
• Multivariate residues and maximal unitarity
• Hexagon functions and the three-loop remainder function
• New recursion relations for tree amplitudes of gluons
• Generalized unitarity and one-loop amplitudes in \(\mathcal N=1\) super-Yang-Mills
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• Local integrals for planar scattering amplitudes
• Integrand-level reduction of loop amplitudes by computational algebraic geometry methods
• One-loop \(n\)-point gauge theory amplitudes, unitarity and collinear limits.
• The amplituhedron
• What is the simplest quantum field theory?
• Bootstrapping the three-loop hexagon
• Analytic result for the two-loop six-point NMHV amplitude in \(\mathcal{N} = {4}\) super Yang-Mills theory
• OPE for all helicity amplitudes
• Grassmannian Geometry of Scattering Amplitudes
• Cluster polylogarithms for scattering amplitudes
• Lectures on differential equations for Feynman integrals