Holographic Projection of Electromagnetic Maxwell Theory

TL;DR

This paper explores the holographic projection of 4D Maxwell theory with a boundary, revealing conserved edge currents, a Ka-Moody algebra, and a novel 3D gauge theory with topological terms.

Contribution

It introduces a new boundary gauge theory derived from 4D Maxwell theory, including a detailed holographic correspondence and the structure of edge states.

Findings

Identified conserved edge currents and their algebraic structure.

Derived a unique 3D gauge theory with Chern-Simons term.

Validated the boundary theory through energy-momentum tensor and propagator calculations.

Abstract

The 4D Maxwell theory with single-sided planar boundary is considered. As a consequence of the presence of the boundary, two broken Ward identities are recovered, which, on-shell, give rise to two conserved currents living on the edge. A Ka\c{c}-Moody algebra formed by a subset of the bulk fields is obtained with central charge proportional to the inverse of the Maxwell coupling constant, and the degrees of freedom of the boundary theory are identified as two vector fields, also suggesting that the 3D theory should be a gauge theory. Finally the holographic contact between bulk and boundary theory is reached in two inequivalent ways, both leading to a unique 3D action describing a new gauge theory of two coupled vector fields with a topological Chern-Simons term with massive coefficient. In order to check that the 3D projection of 4D Maxwell theory is well defined, we computed the energy-momentum tensor and the propagators. The role of discrete symmetries is briefly discussed.