Ben Heidenreich (Perimeter Institute) “The Weak Gravity Conjecture and UV Cutoffs”

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I motivate lattice variants of the Weak Gravity Conjecture (WGC), and show that they have consequences for ultraviolet cutoffs: a parametrically weak gauge coupling requires a quantum gravity scale parametrically below the Planck scale. This result is distinct from older “magnetic WGC” arguments about UV cutoffs, which constrain a “new physics” scale not directly related to the quantum gravity scale. Under certain assumptions, lattice weak gravity naturally leads to a unification of couplings at the quantum gravity scale and I argue that conversely unification of couplings implies the WGC. This is reminiscent of Harlow’s proposal that the WGC is related to emergent gauge fields.