Soft charges from the geometry of field space
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Springer
Received: May 3, Revised: February 11, Accepted: May 3, Published: May 26,
2019 2020 2020 2020
Aldo Riello Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON N2L2Y5, Canada
E-mail: [email protected] 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’ˆetre 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 gaugeinvariant 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. Keywords: Gauge Symmetry, Global Symmetries ArXiv ePrint: 1904.07410
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2020)125
JHEP05(2020)125
Soft charges from the geometry of field space
Contents 1 Configuration space geometry
4
2 Quasi-local degrees of freedom
6
3 Symmetries and charges
9 10
5 Massive charged matter
13
6 Towards magnetic soft charges
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A Generalization to higher dimensions, D + 1 > 4
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B The radiative symplectic form
15
C Lapse N 6= 1
16
The work of Strominger and collaborators on the “soft-triangle” ([1] and references therein) unveiled fascinating and unexpected relations among (i ) Weinberg’s soft theorems and their generalizations [2–4], (ii ) the so-called (nonlinear) memory effects [5–7], and (iii ) an enlarged group of asymptotic symmetries for the S-matrix, in both gauge theories and gravity. Strong evidence for these enlarged symmetries has been gathered from the study of the soft theorems. However, while descriptions in the asymptotic phase space exist (e.g. [1, 8–11]), a derivation of these charges from first principles is still missing. In particular, the relationship between what is “gauge” and what is “symmetry” is most often obscured by the employment of gauge-fixings that happen to leave only the sought-after symmetry parameters unfixed. In other words, the a-priori justification for the existence of these symmetries seems to often rely at some step on the fixing of appropriate (gauge-breaking) boundary conditions. This often leads to the question of whether even larger
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