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${\rm w}_{1+\infty}$ in 4D Gravitational Scattering
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abstract
In four-dimensional asymptotically flat spacetimes, an infinite tower of soft graviton modes is known to generate the symmetry algebra of ${\rm w}_{1+\infty}$ at tree-level. Here we demonstrate that the symmetry action follows from soft graviton theorems and acts non-trivially on massive scalar particles. By generalizing previous analyses that were specifically tailored to the scattering of massless particles, our results clarify that ${\rm w}_{1+\infty}$ symmetry is a universal feature of tree-level gravitational scattering in four-dimensional asymptotically flat spacetimes and originates from minimally-coupled gravitational interactions. In addition, we show that the ${\rm w}_{1+\infty}$ symmetry acts non-diagonally on massive states by mixing an infinite number of conformal families. We also present a concrete example of non-local behavior on the celestial sphere in the presence of massive scattering states.
Forward citations
Cited by 7 Pith papers
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Infinite Symmetry Algebras in Four-Dimensional Conformal Field Theories
Universal light-ray operators from the stress tensor generate the wedge subalgebra of w_{1+∞} in generic interacting 4D CFTs, with finite one-point functions matching the full tower of soft graviton and gluon factors.
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Kerr Soft Dressing and the $w_{1+\infty}$ Frame Algebra at Null Infinity
The Kerr soft exponent generates a parity-alternating hierarchy of null-infinity frame generators—displacement memory at s=0, spin memory at s=1, and higher moments alternating by Kerr multipole parity—realized as the...
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Soft Algebras via Bulk Double Soft Limits
Bulk double soft limits of gravitational amplitudes fail to reproduce the recursive generation of higher-order soft theorems that celestial soft algebras suggest from the first three terms alone.
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Generating Hodges' Graviton MHV Formula with an $Lw_{1+\infty}$ Ward Identity
Hodges' all-multiplicity graviton MHV determinant is exactly generated by a one-particle recursion that takes the form of an Lw_{1+∞} Ward identity.
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$w_{1+\infty}$ as the Frame Algebra of Kerr Soft Dressing
Kerr soft dressing exponentiates into a parity-alternating tower of frame shifts whose chiral-projected composition law is the w1+∞ bracket, solved in closed form for aligned spin.
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Multi-Particle Contributions to the Celestial Algebra in the ${\cal N}=8$ Supergravity
Multi-particle OPEs of single-particle celestial operators with two-particle operators in N=8 supergravity yield ninety-five (anti)commutators of the soft current algebra plus amplitude relations.
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Celestial Chiral Algebras and Self-Dual Gravity
This thesis derives deformations of celestial chiral algebras in self-dual gravity on curved backgrounds, obtaining W(infinity) on Eguchi-Hanson space, Ldiff_q(C) under Moyal deformation, and a two-parameter deformati...
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