Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On NMHV form factors in N=4 SYM theory from generalized unitarity

L. V. Bork

TL;DR

The paper develops a supersymmetric generalized unitarity framework to compute NMHV one-loop form factors in N=4 SYM, focusing on operators from the stress-tensor multiplet in on-shell momentum superspace. It derives explicit 3- and 4-point NMHV results and outlines a recursive strategy for general n-point NMHV form factors, decomposing loop corrections into boxes and triangles with coefficients fixed by quadruple and triple cuts. Key findings include IR structures that factorize with a universal R-graded form and finite parts expressed through dilogarithms and Davydychev functions, along with a discussion of zero-momentum limits relating form factors to amplitude derivatives. The work also hints at potential dualities with Wilson loops and lays groundwork for extending these techniques to broader sectors and higher-point cases, deepening the understanding of symmetry constraints in gauge theory observables.

Abstract

In this paper a supersymmetric version of a generalized unitarity cut method in application to MHV and NMHV for form factors of operators from the N=4 SYM stress-tensor current supermultiplet $T^{AB}$ at one loop is discussed. The explicit answers for 3 and 4 point NMHV form factors at tree and one loop level are obtained. The general structure of n-point NMHV form factor at one loop is discussed as well as the relation between form factor with super momentum equal to zero and the logarithmic derivative of the superamplitude with respect to the coupling constant.

On NMHV form factors in N=4 SYM theory from generalized unitarity

TL;DR

The paper develops a supersymmetric generalized unitarity framework to compute NMHV one-loop form factors in N=4 SYM, focusing on operators from the stress-tensor multiplet in on-shell momentum superspace. It derives explicit 3- and 4-point NMHV results and outlines a recursive strategy for general n-point NMHV form factors, decomposing loop corrections into boxes and triangles with coefficients fixed by quadruple and triple cuts. Key findings include IR structures that factorize with a universal R-graded form and finite parts expressed through dilogarithms and Davydychev functions, along with a discussion of zero-momentum limits relating form factors to amplitude derivatives. The work also hints at potential dualities with Wilson loops and lays groundwork for extending these techniques to broader sectors and higher-point cases, deepening the understanding of symmetry constraints in gauge theory observables.

Abstract

In this paper a supersymmetric version of a generalized unitarity cut method in application to MHV and NMHV for form factors of operators from the N=4 SYM stress-tensor current supermultiplet at one loop is discussed. The explicit answers for 3 and 4 point NMHV form factors at tree and one loop level are obtained. The general structure of n-point NMHV form factor at one loop is discussed as well as the relation between form factor with super momentum equal to zero and the logarithmic derivative of the superamplitude with respect to the coupling constant.

Paper Structure

This paper contains 14 sections, 160 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Amplitudes and form factors in on-shell momentum superspace
  3. Super form factors of the chiral truncation of $\mathcal{N}=4$ stress tensor supermultiplet
  4. Generalized unitarity for form factors at one loop
  5. Grassmann delta functions
  6. Tree level $\hbox{MHV}$ and $\overline{\hbox{MHV}}$ amplitudes and form factors
  7. MHV warm-up
  8. NMHV form factor
  9. 3 point NMHV form factor at tree and one loop level
  10. 4 point NMHV form factor at one loop
  11. Conclusions
  12. $\mathcal{N}=4$ harmonic superspace
  13. Kinematical solutions
  14. Scalar integrals

Figures (11)

  • Figure 1: Vanishing configurations of $\hbox{MHV}_3$ (grey) and $\overline{\hbox{MHV}}_3$ (white) vertexes. Dark grey blob corresponds to other parts of "diagram".
  • Figure 2: All possible cuts for the box scalar integrals to MHV form factor. Dark grey vertex is MHV form factor, grey vertex is MHV amplitude, white vertex is $\overline{\hbox{MHV}}_3$ amplitude.
  • Figure 3: All possible cuts for the triangle scalar integrals to MHV form factor.
  • Figure 4: Example of the dual contur for the MHV n=3 form factor.
  • Figure 5: Diagrammatical representation of the $R^{(1)}_{rst}$.
  • ...and 6 more figures