[Paper Review] New Magnetic Symmetries in $(d+2)$-Dimensional QED

Temple He, Prahar Mitra|arXiv (Cornell University)|Jul 5, 2019

Black Holes and Theoretical Physics26 references4 citations

TL;DR

This paper introduces a novel class of asymptotic symmetries in $(d+2)$-dimensional quantum electrodynamics (QED), arising from the subleading soft photon theorem. By proposing a vector matching condition for the angular components of the magnetic field at null infinity, the authors derive a new Ward identity associated with a magnetic charge, extending the known electric large gauge symmetries and revealing previously unrecognized 'magnetic' asymptotic symmetries in QED.

ABSTRACT

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.

Motivation & Objective

• To resolve the ambiguity in the origin of $d-1$ independent subleading soft theorems in QED beyond the known electric Ward identity.
• To identify a new class of asymptotic symmetries in QED that are not of electric origin but arise from magnetic field behavior at null infinity.
• To establish a matching condition for the $d$ angular components of the magnetic field that leads to a consistent Ward identity.
• To demonstrate that the subleading soft photon theorems are equivalent to a generalized Ward identity with both electric and magnetic charge components.
• To show that the magnetic part of the charge generates finite large gauge transformations, implying new physical symmetries in QED.

Proposed method

• Propose a vector matching condition for the $d$ angular components of the magnetic field at future and past null infinity ($\mathscr{I}^{\pm}$).
• Derive a Ward identity from this matching condition, showing it corresponds to a charge with both electric and magnetic parts.
• Show that the electric part reproduces the known subleading electric Ward identity, while the magnetic part generates a new symmetry.
• Prove equivalence between the $d$ independent subleading soft photon theorems and the new Ward identity via asymptotic analysis of the gauge field.
• Use the asymptotic expansion of the gauge field in flat null coordinates to derive the behavior of the field strength and its components at $\mathscr{I}^{\pm}$.
• Apply commutator algebra and large-$r$ limits to extract the leading-order charges and their transformation properties under the Lorentz algebra.

Experimental results

Research questions

• RQ1 What is the origin of the $d-1$ independent subleading soft theorems in QED, beyond the known electric Ward identity?
• RQ2 Can a matching condition for the angular components of the magnetic field at null infinity reproduce the subleading soft theorems?
• RQ3 Do the resulting Ward identities correspond to new asymptotic symmetries in QED, and if so, what is their structure?
• RQ4 Is the magnetic part of the charge associated with a finite large gauge transformation, and does it generate a new symmetry algebra?
• RQ5 How do the new magnetic charges relate to the standard electric charges and the full asymptotic symmetry algebra?

Key findings

• The subleading soft photon theorem is equivalent to a generalized Ward identity that decomposes into an electric and a novel magnetic component.
• The magnetic component of the charge generates finite large gauge transformations, implying the existence of new 'magnetic' asymptotic symmetries in QED.
• The $d$ independent subleading soft theorems arise from a vector matching condition on the angular components of the magnetic field at $\mathscr{I}^{\pm}$, not from the radial electric field.
• The new magnetic Ward identities correspond to charges that are finite and generate symmetries distinct from the standard electric large gauge symmetries.
• The magnetic charges commute with the Lorentz generators and transform under the $SO(d+1)$ little group, indicating a non-trivial representation of the asymptotic symmetry algebra.
• The full charge generating the Ward identity is a sum of an electric and a magnetic piece, with the magnetic piece being the key new contribution.