Integrability and unitarity

Abstract

We show how generalised unitarity can be used to determine the one-loop dilatation operator in N=4 super Yang-Mills. Our analysis focuses on two sectors, namely the bosonic SO(6) sector and the SU(2|3) sector. The calculation is performed on shell, with no off-shell information introduced at any stage. In this way, we establish a direct connection between scattering amplitudes and the dilatation operator of the N=4 theory.

13 pages. v2: references and comparison of different on-shell approaches added. v3: typos corrected, comments added

References in corpus (19)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• MHV Vertices And Tree Amplitudes In Gauge Theory
• One-Loop Amplitudes for e^+ e^- to Four Partons
• The su(2|3) Dynamic Spin Chain
• One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
• All-Order Collinear Behavior in Gauge Theories
• Search for the ${\Lambda }_b\to \Lambda {\eta }^{\prime }$ and ${\Lambda }_b\to \Lambda \eta$ decays with the LHCb detector
• New Integrable Structures in Large-N QCD
• Cutting through form factors and cross sections of non-protected operators in N=4 SYM
• Amplitudes, Form Factors and the Dilatation Operator in $\mathcal{N}=4$ SYM Theory
• Correlation functions of local composite operators from generalized unitarity
• A Twistorial Approach to Integrability in N=4 SYM
• Integrability and MHV diagrams in N=4 supersymmetric Yang-Mills theory
• Imaginary parts and discontinuities of Wilson line correlators
• Lagrangian Insertion in the Light-Like Limit and the Super-Correlators/Super-Amplitudes Duality

Cited by in corpus (8)

• Renormalization group coefficients and the S-matrix
• On-shell Diagrams, Graßmannians and Integrability for Form Factors
• On-Shell Methods for the Two-Loop Dilatation Operator and Finite Remainders
• The SU(2|3) dynamic two-loop form factors
• Renormalization of effective field theories via on-shell methods: the case of axion-like particles
• Dispersionless (3+1)-dimensional integrable hierarchies
• On Yangian symmetry of scattering amplitudes and the dilatation operator in N=4 super Yang-Mills
• On the Amplitude/Wilson Loop duality in $\mathcal{N}=2$ SCQCD