The SU(2|3) dynamic two-loop form factors

Abstract

We compute two-loop form factors of operators in the $SU(2|3)$ closed subsector of $N=4$ supersymmetric Yang-Mills. In particular, we focus on the non-protected, dimension-three operators $\mathrm{Tr}(X[Y,Z])$ and $\mathrm{Tr}(\psi \psi )$ for which we compute the four possible two-loop form factors, and corresponding remainder functions, with external states $⟨\bar{X}\bar{Y}\bar{Z}|$ and $⟨\bar{\psi }\bar{\psi }|$. Interestingly, the maximally transcendental part of the two-loop remainder of $⟨\bar{X}\bar{Y}\bar{Z}|\mathrm{Tr}(X[Y,Z])|0⟩$ turns out to be identical to that of the corresponding known quantity for the half-BPS operator $\mathrm{Tr}(X^3)$. We also find a surprising connection between the terms subleading in transcendentality and certain a priori unrelated remainder densities introduced in the study of the spin chain Hamiltonian in the SU(2) sector. Next, we use our calculation to resolve the mixing, recovering anomalous dimensions and eigenstates of the dilatation operator in the SU(2|3) sector at two loops. We also speculate on potential connections between our calculations in $N=4$ super Yang-Mills and Higgs + multi-gluon amplitudes in QCD in an effective Lagrangian approach.

40+1 pages, v3: typos corrected, version published in JHEP

References in corpus (15)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Presenting LiteRed: a tool for the Loop InTEgrals REDuction
• Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
• One-loop phi-MHV amplitudes using the unitarity bootstrap
• The last of the simple remainders
• Effective Field Theory for Higgs Plus Jet Production
• Amplitudes, Form Factors and the Dilatation Operator in $\mathcal{N}=4$ SYM Theory
• One-loop helicity amplitudes for H -> gluons: the all-minus configuration
• Composite Operators in the Twistor Formulation of $\mathcal{N}=4$ SYM Theory
• All Tree-Level MHV Form Factors in $\mathcal{N}=4$ SYM from Twistor Space
• A Twistorial Approach to Integrability in N=4 SYM
• Composite operators and form factors in N=4 SYM
• Integrability and MHV diagrams in N=4 supersymmetric Yang-Mills theory
• Integrability and unitarity

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