Perturbative expansion of N<8 Supergravity

Abstract

We characterise the one-loop amplitudes for N=6 and N=4 supergravity in four dimensions. For N=6 we find that the one-loop n-point amplitudes can be expanded in terms of scalar box and triangle functions only. This simplification is consistent with a loop momentum power count of n-3, which we would interpret as being n+4 for gravity with a further -7 from the N=6 superalgebra. For N=4 we find that the amplitude is consistent with a loop momentum power count of n, which we would interpret as being n+4 for gravity with a further -4 from the N=4 superalgebra. Specifically the N=4 amplitudes contain non-cut-constructible rational terms.

13 pages. v2 adds analytic expression for rational parts of 5-pt 1-loop N=4 SUGRA amplitude; v3 normalisations clarified

References in corpus (16)

• New Relations for Gauge-Theory Amplitudes
• Direct extraction of one-loop integral coefficients
• Three-Loop Superfiniteness of N=8 Supergravity
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• E7(7) constraints on counterterms in N=8 supergravity
• Taming Tree Amplitudes In General Relativity
• The No-Triangle Hypothesis for N=8 Supergravity
• Proof of Gravity and Yang-Mills Amplitude Relations
• Stringy KLT relations, global symmetries, and E_7(7) violation
• On duality symmetries of supergravity invariants
• New Identities among Gauge Theory Amplitudes
• Constraints and Generalized Gauge Transformations on Tree-Level Gluon and Graviton Amplitudes
• Explicit Cancellation of Triangles in One-loop Gravity Amplitudes
• Analytic Structure of Three-Mass Triangle Coefficients
• Note on New KLT relations
• One-Loop Six Gluon Amplitude

Cited by in corpus (18)

• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• Loop amplitudes in gauge theories: modern analytic approaches
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
• Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
• An R^4 non-renormalisation theorem in N=4 supergravity
• Cancelling the U(1) Anomaly in the S-matrix of N=4 Supergravity
• One-loop four-graviton amplitudes in N=4 supergravity models
• Manifesting enhanced cancellations in supergravity: integrands versus integrals
• Complex Factorisation and Recursion for One-Loop Amplitudes
• Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation
• The n-point MHV one-loop Amplitude in N=4 Supergravity
• Obtaining One-loop Gravity Amplitudes Using Spurious Singularities
• The $\mathcal{N}=4$ Supergravity NMHV six-point one-loop amplitude