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One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity

John Joseph M. Carrasco, Marco Chiodaroli, Murat Gunaydin, Radu Roiban

TL;DR

The paper classifies all factorized orbifold projections of N=8 supergravity that yield N≤4 theories with various matter content and uses the double-copy and unitarity formalisms to compute their one-loop four-point amplitudes. A central result is that the four-graviton amplitudes are largely independent of the detailed matter couplings, and that two distinct realizations of N=4 supergravity with two vector multiplets produce identical one-loop four-point amplitudes, with the likely extension to higher loops and dimensions. The authors also construct one-loop four-point amplitudes for pure YM with less-than-maximal supersymmetry via color-kinematics duality and verify their double-copy counterparts in supergravity, uncovering mild nonlocality in the loop integrands in reduced-supersymmetry theories. The results illustrate the power of color-kinematics duality and double-copy in organizing reduced-supersymmetry theories and highlight new nonlocal structures at loop level.

Abstract

We construct all supergravity theories that can be obtained through factorized orbifold projections of N=8 supergravity, exposing their double-copy structure, and calculate their one-loop four-point scattering amplitudes. We observe a unified structure in both matter and gravity amplitudes, and demonstrate that the four-graviton amplitudes are insensitive to the precise nature of the matter couplings. We show that these amplitudes are identical for the two different realizations of N=4 supergravity with two vector multiplets, and argue that this feature extends to all multiplicities and loop orders as well as to higher dimensions. We also construct a selected set of supergravities obtained through a non-factorized orbifold action. Furthermore we calculate one-loop four-point amplitudes for all pure super-Yang-Mills theories with less-than-maximal supersymmetry using the duality between color and kinematics, finding here a unified expression that holds for all four gluon amplitudes in the theories. We recover the related amplitudes of factorized N<=4 supergravities employing the double-copy construction. We observe a requirement that the four-point loop-level amplitudes have non-local integrand representations, exhibiting a mild non-locality in the form of inverse powers of the three external Mandelstam invariants. These are the first loop-level color-kinematic-satisfying representations in reduced supersymmetry theories.

One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity

TL;DR

The paper classifies all factorized orbifold projections of N=8 supergravity that yield N≤4 theories with various matter content and uses the double-copy and unitarity formalisms to compute their one-loop four-point amplitudes. A central result is that the four-graviton amplitudes are largely independent of the detailed matter couplings, and that two distinct realizations of N=4 supergravity with two vector multiplets produce identical one-loop four-point amplitudes, with the likely extension to higher loops and dimensions. The authors also construct one-loop four-point amplitudes for pure YM with less-than-maximal supersymmetry via color-kinematics duality and verify their double-copy counterparts in supergravity, uncovering mild nonlocality in the loop integrands in reduced-supersymmetry theories. The results illustrate the power of color-kinematics duality and double-copy in organizing reduced-supersymmetry theories and highlight new nonlocal structures at loop level.

Abstract

We construct all supergravity theories that can be obtained through factorized orbifold projections of N=8 supergravity, exposing their double-copy structure, and calculate their one-loop four-point scattering amplitudes. We observe a unified structure in both matter and gravity amplitudes, and demonstrate that the four-graviton amplitudes are insensitive to the precise nature of the matter couplings. We show that these amplitudes are identical for the two different realizations of N=4 supergravity with two vector multiplets, and argue that this feature extends to all multiplicities and loop orders as well as to higher dimensions. We also construct a selected set of supergravities obtained through a non-factorized orbifold action. Furthermore we calculate one-loop four-point amplitudes for all pure super-Yang-Mills theories with less-than-maximal supersymmetry using the duality between color and kinematics, finding here a unified expression that holds for all four gluon amplitudes in the theories. We recover the related amplitudes of factorized N<=4 supergravities employing the double-copy construction. We observe a requirement that the four-point loop-level amplitudes have non-local integrand representations, exhibiting a mild non-locality in the form of inverse powers of the three external Mandelstam invariants. These are the first loop-level color-kinematic-satisfying representations in reduced supersymmetry theories.

Paper Structure

This paper contains 15 sections, 41 equations, 3 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Supergravity orbifolds and truncations of ${\cal N} =8$ supergravity
  3. One-loop amplitudes at four points
  4. On tree-level amplitudes and unitarity cuts
  5. Four-graviton amplitudes
  6. Matter amplitudes
  7. Two presentations of ${{\cal N}=4}$ supergravity with two vector multiplets
  8. ${{\cal N}=1}$ and ${{\cal N}=2}$ sYM one-loop amplitudes from color/kinematics duality
  9. On the color/kinematics duality and the double-copy structure of supergravity amplitudes
  10. Color/kinematics duality in the ${\cal N}=1$ and ${\cal N}=2$ sYM theories
  11. Four-gluon amplitudes in ${{\cal N}=1}$ and ${{\cal N}=2}$ sYM theories
  12. Orbifold supergravities as double-copies
  13. Discussion
  14. Integral Reduction
  15. Jacobi relations

Figures (3)

  • Figure 1: Box graphs contributing to the four-point one-loop amplitudes in ${\cal N}\leq4$ sYM theories.
  • Figure 2: Graphs with triangle subgraphs contributing to the four-point one-loop amplitudes in ${\cal N}<4$ sYM theories.
  • Figure 3: Cubic graphs containing bubble and tadpole subgraphs; they need not contribute to the four-gluon amplitudes in the ${{\cal N}=1}$ and ${{\cal N}=2}$ sYM theory.