Loop Corrections to Soft Theorems in Gauge Theories and Gravity

Abstract

In this paper, we study loop corrections to the recently proposed new soft theorem of Cachazo-Strominger, for both gravity and gauge theory amplitudes. We first review the proof of its tree-level validity based on BCFW recursion relations, which also establishes an infinite series of universals soft functions for MHV amplitudes, and a generalization to supersymmetric cases. For loop corrections, we focus on infrared finite, rational amplitudes at one loop, and apply recursion relations with boundary or double-pole contributions. For all-plus amplitudes, we prove that the subleading soft-theorems are exact to all multiplicities for both gauge and gravity amplitudes. For single-minus amplitudes, while the subleading soft-theorems are again exact for the minus-helicity soft leg, for plus-helicity loop corrections are required. Using recursion relations, we identify the source of such mismatch as stemming from the special contribution containing double poles, and obtain the all-multiplicity one-loop corrections to the subleading soft behavior in Yang-Mills theory. We also comment on the derivation of soft theorems using BCFW recursion in arbitrary dimensions.

arXiv comment19 pages 1 figure. v2: references added, typos corrected

References in corpus (36)

• New Relations for Gauge-Theory Amplitudes
• On BMS Invariance of Gravitational Scattering
• Scattering of Massless Particles in Arbitrary Dimension
• What is the Simplest Quantum Field Theory?
• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Scattering Equations and KLT Orthogonality
• Asymptotic Symmetries of Yang-Mills Theory
• On Tree Amplitudes in Gauge Theory and Gravity
• The Infrared Behavior of One-Loop Gluon Amplitudes at Next-to-Next-to-Leading Order
• Evidence for a New Soft Graviton Theorem
• One-Loop Splitting Amplitudes in Gauge Theory
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• One-Loop N Gluon Amplitudes with Maximal Helicity Violation via Collinear Limits
• On-Shell Recurrence Relations for One-Loop QCD Amplitudes
• On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons
• Factorization Properties of Soft Graviton Amplitudes
• Soft sub-leading divergences in Yang-Mills amplitudes
• String-Based Methods in Perturbative Gravity
• Calculation of Graviton Scattering Amplitudes using String-Based Methods
• Subleading soft theorem in arbitrary dimension from scattering equations
• Taming Tree Amplitudes In General Relativity
• Multigluon Helicity Amplitudes Involving a Quark Loop
• The Last of the Finite Loop Amplitudes in QCD
• BCJ duality and the double copy in the soft limit
• On the U(1) duality anomaly and the S-matrix of N=4 supergravity
• All-Orders Singular Emission in Gauge Theories
• Constructing Amplitudes from Their Soft Limits
• Generating All Tree Amplitudes in N=4 SYM by Inverse Soft Limit
• Recursion Relations for One-Loop Gravity Amplitudes
• Augmented Recursion For One-loop Gravity Amplitudes
• Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation
• The n-point MHV one-loop Amplitude in N=4 Supergravity
• A Note on Single Soft Scalar Emission of $\mathcal{N}=8$ SUGRA and $E_{7(7)}$ Symmetry
• Higher Codimension Singularities Constructing Yang-Mills Tree Amplitudes

Cited by in corpus (130)

• Soft Hair on Black Holes
• New Symmetries of Massless QED
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• Superrotation Charge and Supertranslation Hair on Black Holes
• A Conformal Basis for Flat Space Amplitudes
• Scattering of Spinning Black Holes from Exponentiated Soft Factors
• Gluon Amplitudes as 2d Conformal Correlators
• A 2D Stress Tensor for 4D Gravity
• Low's Subleading Soft Theorem as a Symmetry of QED
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• 2D Kac-Moody Symmetry of 4D Yang-Mills Theory
• 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
• Subleading soft photons and large gauge transformations
• Sub-subleading soft gravitons and large diffeomorphisms
• 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
• BMS Supertranslations and Not So Soft Gravitons
• Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities
• Next-to-soft corrections to high energy scattering in QCD and gravity
• Loop-Corrected Virasoro Symmetry of 4D Quantum Gravity
• Ambitwistor strings at null infinity and subleading soft limits
• New Double Soft Emission Theorems
• Extended Super BMS Algebra of Celestial CFT
• Next to subleading soft-graviton theorem in arbitrary dimensions
• Sub-subleading Soft Graviton Theorem in Generic Theories of Quantum Gravity
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Subleading Soft Factor for String Disk Amplitudes
• Building Blocks for Subleading Helicity Operators
• A double copy for asymptotic symmetries in the self-dual sector
• Gravity Waves from Soft Theorem in General Dimensions
• EPFL Lectures on General Relativity as a Quantum Field Theory
• Loop-corrected subleading soft theorem and the celestial stress-tensor
• Infinite-Dimensional Fermionic Symmetry in Supersymmetric Gauge Theories
• Perturbative gauge theory at null infinity
• BMS, String Theory, and Soft Theorems
• Lectures on Celestial Holography
• Soft Theorems in Superstring Theory
• Subleading Power Factorization with Radiative Functions
• Celestial operator products from the worldsheet
• Subleading Soft Theorem for Multiple Soft Gravitons
• Notes on Conformal Soft Theorems and Recursion Relations in Gravity
• Classical Sub-subleading Soft Photon and Soft Graviton Theorems in Four Spacetime Dimensions
• Conformal Structure of Massless Scalar Amplitudes Beyond Tree level
• On Effective Field Theories with Celestial Duals
• Are Soft Theorems Renormalized?
• On the soft limit of closed string amplitudes with massive states
• Goldilocks Modes and the Three Scattering Bases
• Conformal Invariance of the Subleading Soft Theorem in Gauge Theory
• Subleading Soft Graviton Theorem for Loop Amplitudes
• Infinite Soft Theorems from Gauge Symmetry
• UV considerations on scattering amplitudes in a web of theories
• On the soft limit of open string disk amplitudes with massive states
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Subsubleading soft theorems of gravitons and dilatons in the bosonic string
• Double Soft Theorems and Shift Symmetry in Nonlinear Sigma Models
• On the Subleading-Soft Behaviour of QCD Amplitudes
• Soft behavior of a closed massless state in superstring and universality in the soft behavior of the dilaton
• Asymptotic dynamics on the worldline for spinning particles
• Asymptotic charges in massless QED revisited: A view from Spatial Infinity
• Soft Photon Theorem for High Energy Amplitudes in Yukawa and Scalar Theories
• Classical double copy from Color Kinematics duality: A proof in the soft limit
• $n$-point amplitudes with a single negative-helicity graviton
• Black Holes in Klein Space
• Soft Matters, or the Recursions with Massive Spinors
• On single and double soft behaviors in NLSM
• Subleading soft dressings of asymptotic states in QED and perturbative quantum gravity
• Asymptotically flat spacetimes with BMS${}_3$ symmetry
• On the exactness of soft theorems
• Double-soft behavior for scalars and gluons from string theory
• Celestial superamplitude in $\mathcal{N}=4$ SYM theory
• Soft pion theorem, asymptotic symmetry and new memory effect
• Note on asymptotic symmetries and soft gluon theorems
• Double Soft Theorem for Perturbative Gravity
• Propagators, BCFW Recursion and New Scattering Equations at One Loop
• Implications of Superrotations
• Factorized soft graviton theorems at loop level
• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• Conformal Invariance of the One-Loop All-Plus Helicity Scattering Amplitudes
• Testing Subleading Multiple Soft Graviton Theorem for CHY Prescription
• Double Soft Limit of Graviton Amplitude from the Cachazo-He-Yuan Formalism
• IR dynamics and entanglement entropy
• Symmetries in Celestial CFT${}_d$
• Soft Theorems from Effective Field Theory
• Soft theorem for the graviton, dilaton and the Kalb-Ramond field in the bosonic string
• Magnetic Soft Charges, Dual Supertranslations and 't Hooft Line Dressings
• Asymptotic Charges and Coherent States in QCD
• Soft Graviton Emission at High and Low Energies in Yukawa and Scalar Theories
• Tree level amplitudes from soft theorems
• Multi-soft theorems in Gauge Theory from MHV Diagrams
• Asymptotic Symmetries, Holography and Topological Hair
• Double-Soft Limits of Gluons and Gravitons
• New Asymptotic Conservation laws for Electromagnetism
• One-Loop Soft Theorems via Dual Superconformal Symmetry
• String Memories ... Lost and Regained
• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• Soft Theorem of N=4 SYM in Grassmannian Formulation
• A Note on Soft Factors for Closed String Scattering
• Multiloop Soft Theorem for Gravitons and Dilatons in the Bosonic String
• Soft Theorems from Compactification
• Spinning-off stringy electro-magnetic memories
• A factorization approach to next-to-leading-power threshold logarithms
• Deformed $w_{1+\infty }$ Algebras in the Celestial CFT
• Remarks on infinite towers of gravitational memories
• Soft factors from classical scattering on the Reissner-Nordström spacetime
• Note on Identities Inspired by New Soft Theorems
• Double Soft Theorems in Gauge and String Theories
• Universality of soft theorem from locality of soft vertex operators
• Leading soft theorem for multiple gravitini
• Soft and Collinear Limits in $\mathcal{N}=8$ Supergravity using Double Copy Formalism
• CHY formulae in 4d
• Asymptotic conservation law with Feynman boundary condition
• Diagrammar in an Extended Theory of Gravity
• Leading multi-soft limits from scattering equations
• Topics in Asymptotic Symmetries and Infrared Effects
• Soft Theorems from Boundary Terms in the Classical Point Particle Currents
• From U(1) to E8: soft theorems in supergravity amplitudes
• Asymptotic Higher Spin Symmetries III: Noether Realization in Yang-Mills Theory
• Charge algebra for non-abelian large gauge symmetries at $O(r)$
• Loop corrections versus marginal deformation in celestial holography
• Soft Theorems and the KLT-Relation
• Soft-Theorems for Scalar Particles: The Dilatons Story
• Sudakov Representation of the Cachazo-He-Yuan Scattering Equations Formalism
• Soft Theorems in Chern-Simons Matter Theories
• Subleading soft radiation during scattering of dressed states in QED
• Perturbatively Exact $w_{1+\infty }$ Asymptotic Symmetry of Quantum Self-Dual Gravity
• QCD Beyond Leading Power