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One-loop four-graviton amplitudes in N=4 supergravity models

Piotr Tourkine, Pierre Vanhove

TL;DR

The paper addresses the one-loop four-graviton amplitude in four-dimensional $N=4$ supergravity by deriving field-theory limits from various string constructions, including CHL heterotic, asymmetric Type II, and symmetric Type II orbifolds. It decomposes the result into $N=4$ multiplets with spins $s=1,3/2,2$ and shows that, for fixed vector multiplet content $n_v$, the pure gravity amplitude is universal across models after integrating over vertex positions. The authors provide explicit field-theory amplitudes for the vector, gravitino, and graviton multiplets, analyze IR/UV behavior, and demonstrate that vector-multiplet differences are model-dependent while gravity-sector amplitudes agree, in line with duality expectations. This work confirms the UV finiteness and universality of one-loop $N=4$ supergravity amplitudes and clarifies how model-dependent vector content affects intermediate steps, with implications for perturbative gravity and cross-model consistency.

Abstract

We evaluate in great detail one-loop four-graviton field theory amplitudes in pure N=4 D=4 supergravity. The expressions are obtained by taking the field theory limits of (4,0) and (2,2) space-time supersymmetric string theory models. For each model we extract the contributions of the spin-1 and spin-2 N=4 supermultiplets running in the loop. We show that all of those constructions lead to the same four-dimensional result for the four-graviton amplitudes in pure supergravity even though they come from different string theory models.

One-loop four-graviton amplitudes in N=4 supergravity models

TL;DR

The paper addresses the one-loop four-graviton amplitude in four-dimensional supergravity by deriving field-theory limits from various string constructions, including CHL heterotic, asymmetric Type II, and symmetric Type II orbifolds. It decomposes the result into multiplets with spins and shows that, for fixed vector multiplet content , the pure gravity amplitude is universal across models after integrating over vertex positions. The authors provide explicit field-theory amplitudes for the vector, gravitino, and graviton multiplets, analyze IR/UV behavior, and demonstrate that vector-multiplet differences are model-dependent while gravity-sector amplitudes agree, in line with duality expectations. This work confirms the UV finiteness and universality of one-loop supergravity amplitudes and clarifies how model-dependent vector content affects intermediate steps, with implications for perturbative gravity and cross-model consistency.

Abstract

We evaluate in great detail one-loop four-graviton field theory amplitudes in pure N=4 D=4 supergravity. The expressions are obtained by taking the field theory limits of (4,0) and (2,2) space-time supersymmetric string theory models. For each model we extract the contributions of the spin-1 and spin-2 N=4 supermultiplets running in the loop. We show that all of those constructions lead to the same four-dimensional result for the four-graviton amplitudes in pure supergravity even though they come from different string theory models.

Paper Structure

This paper contains 30 sections, 164 equations, 1 figure.

Table of Contents

  1. Introduction
  2. One-loop String theory amplitudes in $(4,0)$ and $(2,2)$ models
  3. Heterotic CHL models
  4. Type II asymmetric orbifold
  5. Example: A model with six vector multiplets
  6. Example: Models with zero vector multiplet
  7. Type II symmetric orbifold
  8. Comparison of the string models
  9. Massless spectrum
  10. Amplitudes and supersymmetry
  11. Comparing of the string models
  12. Comparing the $(4,0)$ models
  13. Comparing the $(4,0)$ and $(2,2)$ models
  14. Field theory one-loop amplitudes in $\mathcal{N}=4$ supergravity
  15. Supersymmetry in the loop
  16. ...and 15 more sections

Figures (1)

  • Figure 1: Contribution to the IR divergences when two external gravitons (double wavy lines) become soft. If a graviton is exchanged as in (a) the amplitude presents an IR divergence. No IR divergences are found when another massless state of spin different from two is exchanged as in (b).