Are Soft Theorems Renormalized?

Abstract

We show that the distributional nature of soft theorems requires the soft limit expansion to take priority over the regulator expansion of Feynman loop integrals. We start the study of soft graviton theorems at loop level from this perspective by considering a five-particle one-loop amplitude in $\mathcal{N}=8$ supergravity. Surprisingly, we find that a soft theorem recently introduced by one of the authors and Strominger is not renormalized in this case. Computations are done in $4-2\epsilon$ dimensions and for terms of order ${\epsilon }^{-2}$, ${\epsilon }^{-1}$ and ${\epsilon }^0$.

New section on soft theorems vs soft expansions included, citations added and typos fixed in v2

References in corpus (10)

• Evidence for a New Soft Graviton Theorem
• Factorization in One-Loop Gauge Theory
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons
• Loop Corrections to Soft Theorems in Gauge Theories and Gravity
• Soft sub-leading divergences in Yang-Mills amplitudes
• Sharpening The Leading Singularity
• Conformal Invariance of the Subleading Soft Theorem in Gauge Theory
• Virtual Color-Kinematics Duality: 6-pt 1-Loop MHV Amplitudes
• Analytic result for the one-loop scalar pentagon integral with massless propagators

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• New Symmetries of Massless QED
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• New Gravitational Memories
• Classical and Quantum Results on Logarithmic Terms in the Soft Theorem in Four Dimensions
• The method of regions and next-to-soft corrections in Drell-Yan production
• Constraining subleading soft gluon and graviton theorems
• More on Soft Theorems: Trees, Loops and Strings
• Sub-sub-leading soft-graviton theorem in arbitrary dimension
• Diagrammatic insights into next-to-soft corrections
• Logarithmic Terms in the Soft Expansion in Four Dimensions
• Loop-Corrected Virasoro Symmetry of 4D Quantum Gravity
• Subleading Soft Factor for String Disk Amplitudes
• Infinite-Dimensional Fermionic Symmetry in Supersymmetric Gauge Theories
• Perturbative gauge theory at null infinity
• Soft Theorems in Superstring Theory
• On the soft limit of closed string amplitudes with massive states
• On the soft limit of open string disk amplitudes with massive states
• Subsubleading soft theorems of gravitons and dilatons in the bosonic string
• On single and double soft behaviors in NLSM
• On Soft Theorems And Form Factors In N=4 SYM Theory
• Factorized soft graviton theorems at loop level
• Soft Theorems from Effective Field Theory
• Soft Graviton Emission at High and Low Energies in Yukawa and Scalar Theories
• Multi-soft theorems in Gauge Theory from MHV Diagrams
• Double-Soft Limits of Gluons and Gravitons
• A factorization approach to next-to-leading-power threshold logarithms
• Double Soft Theorems in Gauge and String Theories
• Note on Identities Inspired by New Soft Theorems
• Zwanziger's pairwise little group on the celestial sphere