Abstract
We show that the subleading soft photon theorem in a (d + 2)-dimensional massless abelian gauge theory gives rise to a Ward identity corresponding to divergent large gauge transformations acting on the celestial sphere at null infinity. We further generalize our analysis to (d + 2)-dimensional non-abelian gauge theories and show that the leading and subleading soft gluon theorem give rise to Ward identities corresponding to asymptotic symmetries of the theory.
Highlights
In addition to Weinberg’s original leading soft theorems, there has been progress in relating the subleading soft photon theorem to asymptotic symmetries of gauge theories in four dimensions [10, 16, 17, 24].1 The corresponding symmetries are large gauge transformations that diverge linearly near null infinity
We show that the subleading soft photon theorem in a (d + 2)-dimensional massless abelian gauge theory gives rise to a Ward identity corresponding to divergent large gauge transformations acting on the celestial sphere at null infinity
Given the results of [21], it is natural to ask whether this equivalence can be extended to all dimensions greater than or equal to four. We tackle this question in this paper and, more generally, attempt to present a systematic method that allows us to study the relationship between asymptotic symmetries and soft theorems in any massless gauge theory living in any dimension greater than or equal to four
Summary
We review the work of [21] and list the relevant notations, conventions, and formulae that will be utilized in the rest of this paper. We can substitute (2.5) and (2.7) into (2.2), determine the components of the field strength in flat null coordinates, and take a large |r| expansion. We assume that the Coulombic field strength and current admit a Taylor series expansion at large |r| consistent with the asymptotic behavior described in [21]. Substituting these Taylor series into Maxwell’s equations (2.1), we obtain equations order-by-order in large |r| that can be solved. We will require an additional constraint derived from the subleading terms in the large |r| expansion of Maxwell’s equations These are obtained from the leading terms in the r and a components of Maxwell’s equations and take the form 2∂uFu(Cr ±,d+1) − ∂aFu(Ca ±,d−1) = e2Ju(±,d+1) 2Fu(Cr ±,d+1) ∓ ∂aFr(aC±,d) = ±e2Jr(±,d+2).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
