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Six-Point One-Loop N=8 Supergravity NMHV Amplitudes and their IR behaviour

N. E. J. Bjerrum-Bohr, David C. Dunbar, Harald Ita

TL;DR

This work analyzes the six-point NMHV one-loop amplitude in ${\cal N}=8$ supergravity and provides compact expressions for the box-coefficients, demonstrating that the amplitude can be written as a sum of scalar box integrals with rational coefficients. Using unitarity, KLT relations, and generating functions, the authors show the box contributions reproduce the full IR singularity structure and that triangle functions do not contribute, supporting a box-only conjecture analogous to ${\cal N}=4$ SYM. They connect the box-coefficient structure to recursion relations, deriving compact IR-driven forms for the tree amplitude that align with recursive constructions. The results suggest deeper symmetries and a CSW-like perspective for gravity amplitudes, with potential implications for the UV behavior of higher-loop ${\cal N}=8$ supergravity.

Abstract

We present compact formulas for the box coefficients of the six-point NMHV one-loop amplitudes in N=8 supergravity. We explicitly demonstrate that the corresponding box integral functions, with these coefficients, have the complete IR singularities expected of the one-loop amplitude. This is strong evidence for the conjecture that N=8 one-loop amplitudes may be expressed in terms of scalar box integral functions. This structure, although unexpected from a power counting viewpoint, is analogous to the structure of N=4 super-Yang-Mills amplitudes. The box-coefficients match the tree amplitude terms arising from recursion relations.

Six-Point One-Loop N=8 Supergravity NMHV Amplitudes and their IR behaviour

TL;DR

This work analyzes the six-point NMHV one-loop amplitude in supergravity and provides compact expressions for the box-coefficients, demonstrating that the amplitude can be written as a sum of scalar box integrals with rational coefficients. Using unitarity, KLT relations, and generating functions, the authors show the box contributions reproduce the full IR singularity structure and that triangle functions do not contribute, supporting a box-only conjecture analogous to SYM. They connect the box-coefficient structure to recursion relations, deriving compact IR-driven forms for the tree amplitude that align with recursive constructions. The results suggest deeper symmetries and a CSW-like perspective for gravity amplitudes, with potential implications for the UV behavior of higher-loop supergravity.

Abstract

We present compact formulas for the box coefficients of the six-point NMHV one-loop amplitudes in N=8 supergravity. We explicitly demonstrate that the corresponding box integral functions, with these coefficients, have the complete IR singularities expected of the one-loop amplitude. This is strong evidence for the conjecture that N=8 one-loop amplitudes may be expressed in terms of scalar box integral functions. This structure, although unexpected from a power counting viewpoint, is analogous to the structure of N=4 super-Yang-Mills amplitudes. The box-coefficients match the tree amplitude terms arising from recursion relations.

Paper Structure

This paper contains 5 sections, 34 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Box Coefficients of $M^{\rm 1-loop}(1^-,2^-,3^-,4^+,5^+,6^+)$
  3. IR Singularities
  4. Connection to Recursion Relations
  5. Conclusions

Figures (1)

  • Figure 1: Examples of non-singlet and singlet contributions to a two-mass hard and a one-mass box integral. The dashed line indicates the cut to which the singlet and non-singlet description refer.