Co-Scaling and Alignment of Electric and Magnetic Towers

Abstract

Towers of electrically and magnetically charged states in quantum gravity often exhibit two important properties. First, the ratio of the mass (or tension) of electrically charged states to magnetically charged states is of order $e^2/(4\pi)$, which we refer to as "co-scaling." Second, in theories of multiple gauge fields, the towers of states that exhibit co-scaling have charges that point in approximately the same direction in charge space as measured by the gauge kinetic matrix, which we refer to as "alignment." After motivating these ideas with some heuristic arguments, we examine the spectrum of BPS states in the 5d supergravity landscape arising from M-theory on a Calabi-Yau threefold. In this setting, every tower of magnetically charged strings is paired with a corresponding tower of electrically charged particles that exhibits co-scaling and rapid alignment. In particular, this motivates a sharp mathematical characterization of the magnetic infinity cone in Calabi-Yau geometry. We propose a universal conjecture about quantum gravity: towers of charged states which, in some limit in moduli space, have maximally divergent charge-to-mass ratios always have corresponding magnetic partner states exhibiting co-scaling and alignment. Co-scaling is not a general feature of extremal black hole solutions in theories of gauge fields and scalars, suggesting that it is a principle of UV complete quantum gravity. We briefly remark on possible phenomenological applications, including to axion physics.