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 Kac-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.

中文翻译：

---

电磁麦克斯韦理论的全息投影

考虑了具有单边平面边界的 4D Maxwell 理论。由于边界的存在，恢复了两个破碎的沃德身份，这在壳上产生了两个生活在边缘的守恒电流。获得了由体场子集形成的 Kac-Moody 代数，其中心电荷与麦克斯韦耦合常数的倒数成正比，边界理论的自由度被确定为两个矢量场，也表明 3D 理论应该是规范理论。最后，体积理论和边界理论之间的全息接触以两种不等价的方式实现，这两种方式都导致了独特的 3D 动作，描述了两个耦合矢量场的新规范理论，其中包含具有质量系数的拓扑陈-西蒙斯项。为了检查 4D Maxwell 理论的 3D 投影是否定义良好，我们计算了能量-动量张量和传播子。简要讨论了离散对称性的作用。