A Holographic Perspective on the Axion Quality Problem

Abstract: The axion provides a compelling solution to the strong CP problem as well as a candidate for the dark matter of the universe. However, the axion solution relies on the spontaneous breaking of a global $U(1){PQ}$ symmetry, which is also explicitly violated by quantum gravity. To preserve the axion solution, gravitational violations of the $U(1){PQ}$ symmetry must be suppressed to sufficiently high order. We present a simple, geometric solution of the axion quality problem by modelling the axion with a bulk complex scalar field in a slice of AdS$5$, where the $U(1){PQ}$ symmetry is spontaneously broken in the bulk but explicitly broken on the UV brane. By localising the axion field towards the IR brane, gravitational violations of the PQ symmetry on the UV brane are sufficiently sequestered. This geometric solution is holographically dual to 4D strong dynamics where the global $U(1)_{PQ}$ is an accidental symmetry to sufficiently high order.