Pseudo-Nambu–Goldstone Dark Matter in Flux Compactification

Abstract We study a 6D U(1)$_\chi$ gauge theory compactified on a magnetized torus, where the zero mode of the extra-dimensional gauge field (a Wilson-line scalar field) plays the role of a pseudo-Nambu–Goldstone (pNG) dark matter (DM) candidate. The pNG DM is naturally included by construction without introducing an additional scalar field. We show that the leading spin-independent DM-nucleus amplitude is suppressed by momentum transfer in our model, as expected from the pNG DM model. This suppression allows the model to evade the current severe direct detection bounds while achieving the observed thermal relic abundance in well-defined regions of parameter space.