The Weak Gravity Conjecture and emergence from an ultraviolet cutoff

Abstract

We study ultraviolet cutoffs associated with the Weak Gravity Conjecture (WGC) and Sublattice Weak Gravity Conjecture (sLWGC). There is a magnetic WGC cutoff at the energy scale with an associated sLWGC tower of charged particles. A more fundamental cutoff is the scale at which gravity becomes strong and field theory breaks down entirely. By clarifying the nature of the sLWGC for nonabelian gauge groups we derive a parametric upper bound on this strong gravity scale for arbitrary gauge theories. Intriguingly, we show that in theories approximately saturating the sLWGC, the scales at which loop corrections from the tower of charged particles to the gauge boson and graviton propagators become important are parametrically identical. This suggests a picture in which gauge fields emerge from the quantum gravity scale by integrating out a tower of charged matter fields. We derive a converse statement: if a gauge theory becomes strongly coupled at or below the quantum gravity scale, the WGC follows. We sketch some phenomenological consequences of the UV cutoffs we derive.

The Swampland: Introduction and Review

“…In this section we will adopt the idea of emergence, in particular that the kinetic terms for emergent fields are induced at one‐loop in the infrared from integrating out states, but apply it in a different way to the previous section which is more in line with how it is realized in string theory. This analysis then follows the results of []. While the ‐model is a toy model for an emergent gauge field, in this section we will consider all fields, including even gravity, to have emergent dynamics from some scale .…”

“…We will discuss this in detail in string theory settings in section 4. From a more general perspective, it was suggested in [] that it would be strange to have a spectrum where a single field, the Higgs field, has parametrically larger charge, of order N , than all the other charged fields in the theory. The Higgs would also have to be parametrically super‐extremal, since if its mass was of order its charge, then it would have a mass above the cutoff of the original ultraviolet theory.…”

“…The proposal is based on ideas and results in [] . In order to present a coherent proposal, in this section we will make general statements that are closely related to, but not exactly, those made in []. We will try to emphasize the differences from the specific results in the published papers when possible.…”

“…With these caveats in mind, the emergence proposal can then be stated as follows.

The Emergence Proposal (based on ideas in []) The dynamics (kinetic terms) for all fields are emergent in the infrared by integrating out towers of states down from an ultraviolet scale , which is below the Planck scale .

…”

“…Assuming a weakly‐coupled description in the infrared, this practically leads to the same results as taking the classical contribution to the kinetic terms in the ultraviolet to be sub‐dominant to the 1‐loop renormalisation group running down from the ultraviolet. Conceptually, however, the statements are quite different, with the former being the picture advocated in [], and the latter in [].…”