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Register a new userNew Magnetic Symmetries in $(d+2)$-Dimensional QED
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Previous analyses of asymptotic symmetries in QED have shown that the subleading soft photon theorem implies a Ward identity corresponding to a charge generating divergent large gauge transformations on the asymptotic states at null infinity. In this work, we demonstrate that the subleading soft photon theorem is equivalent to a more general Ward identity. The charge corresponding to this Ward identity can be decomposed into an electric piece and a magnetic piece. The electric piece generates the Ward identity that was previously studied, but the magnetic piece is novel, and implies the existence of an additional asymptotic magnetic symmetry in QED.
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The soft photon theorem in U(1) gauge theories with only massless charged particles has recently been shown to be the Ward identity of an infinite-dimensional asymptotic symmetry group. This symmetry group is comprised of gauge transformations which approach angle-dependent constants at null infinity. In this paper, we extend the analysis to all U(1) theories, including those with massive charged particles such as QED.
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.
We consider three-dimensional sQED with 2 flavors and minimal supersymmetry. We discuss various models which are dual to Gross-Neveu-Yukawa theories. The $U(2)$ ultraviolet global symmetry is often enhanced in the infrared, for instance to $O(4)$ or $SU(3)$. This is analogous to the conjectured behaviour of non-supersymmetric QED with 2 flavors. A perturbative analysis of the Gross-Neveu-Yukawa models in the $D = 4 - varepsilon$ expansion shows that the $U(2)$ preserving superpotential deformations of the sQED (modulo tuning mass terms to zero) are irrelevant, so the fixed points with enhanced symmetry are stable. We also construct an example of $mathcal{N} = 2$ sQED with 4 flavors that exhibits enhanced $SO(6)$ symmetry.
We show that Weinbergs leading soft photon theorem in massless abelian gauge theories implies the existence of an infinite-dimensional large gauge symmetry which acts non-trivially on the null boundaries ${mathscr I}^pm$ of $(d+2)$-dimensional Minkowski spacetime. These symmetries are parameterized by an arbitrary function $varepsilon(x)$ of the $d$-dimensional celestial sphere living at ${mathscr I}^pm$. This extends the previously established equivalence between Weinbergs leading soft theorem and asymptotic symmetries from four and higher even dimensions to emph{all} higher dimensions.
We consider the scattering of massless particles coupled to an abelian gauge field in 2n-dimensional Minkowski spacetime. Weinbergs soft photon theorem is recast as Ward identities for infinitely many new nontrivial symmetries of the massless QED S-matrix, with one such identity arising for each propagation direction of the soft photon. These symmetries are identified as large gauge transformations with angle-dependent gauge parameters that are constant along the null generators of null infinity. Almost all of the symmetries are spontaneously broken in the standard vacuum and the soft photons are the corresponding Goldstone bosons. Our result establishes a relationship between soft theorems and asymptotic symmetry groups in any even dimension.
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