Soft Theorems from Compactification

Abstract

We analyze the single subleading soft graviton theorem in $(d+1)$ dimensions under compactification on $S^1$. This produces the single soft theorems for the graviton, vector and scalar fields in $d$ dimension. For the compactification of $11$-dimensional supergravity theory, this gives the soft factorization properties of the single graviton, dilaton and RR 1-form fields in type IIA string theory in ten dimensions. For the case of the soft vector field, we also explicitly check the result obtained from compactification by computing the amplitudes with external massive spin two and massless finite energy states interacting with soft vector field. The former are the Kaluza-Klein excitations of the $d+1$ dimensional metric. Describing the interaction of the KK-modes with the vector field at each level by the minimally coupled Fierz-Pauli Lagrangian, we find agreement with the results obtained from the compactification if the gyromagnetic ratio in the minimally coupled Fierz-Pauli Lagrangian is taken to be $g=1$.

22 pages + appendix

References in corpus (20)

• Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance
• On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons
• Loop Corrections to Soft Theorems in Gauge Theories and Gravity
• Subleading soft theorem in arbitrary dimension from scattering equations
• The method of regions and next-to-soft corrections in Drell-Yan production
• Constraining subleading soft gluon and graviton theorems
• Sub-subleading soft gravitons and large diffeomorphisms
• Diagrammatic insights into next-to-soft corrections
• Next to subleading soft-graviton theorem in arbitrary dimensions
• Sub-subleading Soft Graviton Theorem in Generic Theories of Quantum Gravity
• Subleading Soft Factor for String Disk Amplitudes
• Subleading Soft Theorem for Multiple Soft Gravitons
• Conformal Invariance of the Subleading Soft Theorem in Gauge Theory
• The Double Copy Structure of Soft Gravitons
• Intrinsic Cutoff and Acausality for Massive Spin 2 Fields Coupled to Electromagnetism
• Unitarization from Geometry
• Soft behavior of a closed massless state in superstring and universality in the soft behavior of the dilaton
• Double-soft behavior of the dilaton of spontaneously broken conformal invariance
• Double Soft Theorem for Perturbative Gravity
• Note on Soft Graviton theorem by KLT Relation

Cited by in corpus (4)

• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Lorentz Symmetry and IR Structure of The BFSS Matrix Model
• Revisiting Higher-Spin Gyromagnetic Couplings
• Soft-Theorems for Scalar Particles: The Dilatons Story