Abstract
Infinite sets of asymptotic soft-charges were recently shown to be related to new symmetries of the S-matrix, spurring a large amount of research on this and related questions. Notwithstanding, the raison-d’être of these soft-charges rests on less firm ground, insofar as their known derivations through generalized Noether procedures tend to rely on the fixing of (gauge-breaking) boundary conditions rather than on manifestly gauge- invariant computations. In this article, we show that a geometrical framework anchored in the space of field configurations singles out the known leading-order soft charges in gauge theories. Our framework unifies the treatment of finite and infinite regions, and thus it explains why the infinite enhancement of the symmetry group is a property of asymptotic null infinity and should not be expected to hold within finite regions, where at most a finite number of physical charges — corresponding to the reducibility parameters of the quasi-local field configuration — is singled out. As a bonus, our formalism also suggests a simple proposal for the origin of magnetic-type charges at asymptotic infinity based on spacetime (Lorentz) covariance rather than electromagnetic duality.
Highlights
(For clarity: by symmetry-related configurations, we mean distinct but otherwise degenerate configurations; by gauge-related configurations, we mean fully degenerate configurations that should be identified within a “reduced” physical phase space.)
We show that a geometrical framework anchored in the space of field configurations singles out the known leading-order soft charges in gauge theories
Our framework unifies the treatment of finite and infinite regions, and it explains why the infinite enhancement of the symmetry group is a property of asymptotic null infinity and should not be expected to hold within finite regions, where at most a finite number of physical charges — corresponding to the reducibility parameters of the quasi-local field configuration — is singled out
Summary
Let {Σt}t be a Cauchy foliation of a (3 + 1)-dimensional spacetime M ∼= Σt × R. Let ξ ∈ X1(Φ) be the field-space vector associated to an infinitesimal gauge transformation ξ ∈ Lie(G). Notice that a (local) gauge fixing σ : Φ/G → Φ defines a unique such that ImTσ ⊂ H, the converse is not true: first, because the horizontal distribution H might not be Frobenious-integrable (if F = δ + 2 = 0), and second, because is defined along the entire gauge orbit and cannot select any one section of Φ At this point it is important to notice that is not uniquely defined, since the algebraic split TΦ = V ⊕ H is not canonical. No boundary condition is imposed on the gauge field
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