Nambu-Goldstone modes in magnetized \(T^{2n}\) extra dimensions

(This seminar is postponed.) The higher dimensional theory with a background magnetic field in the extra-dimensions has bee actively studied from both theoretical and phenomenological aspects. In this talk, we will treat the \({\rm U}(1)\) gauge theory compactified on a torus \(T^{4}\) with a background magnetic field, and focus on the extra-dimensional components of the gauge field. The number of zero modes arising from the extra-dimensional components of the gauge field is determined by the rank of the matrix representing the background magnetic field. We also show that the zero modes arising from the extra-dimensional components of the gauge field have zero mass at 1-loop level. We will mention that these arguments can be extended to \(T^{2n}\). This talk is based on [hep-th/2403.16801].