Routing (electronic design automation)

Quantum mechanics

Context (archaeology)

Theoretical physics

Supersymmetry

Gravitation

Pure mathematics

Mathematical physics

Biology

Particle physics

Effective field theory

Computer science

Computer network

Paleontology

Routing protocol

Physics

Mathematics

Link-state routing protocol

Conjecture

Planck mass

Black hole (networking)

Unitarity

Causality (physics)

Journal of High Energy Physics

A bstract We consider the shift of charge-to-mass ratio for extremal black holes in the context of effective field theory, motivated by the Weak Gravity Conjecture. We constrain extremality corrections in different regimes subject to unitarity and causality constraints. In the asymptotic IR, we demonstrate that for any supersymmetric theory in flat space, and for all minimally coupled theories, logarithmic running at one loop pushes the Wilson coefficient of certain four-derivative operators to be larger at lower energies, guaranteeing the existence of sufficiently large black holes with Q &gt; M . We identify two exceptional cases of nonsupersymmetric theories involving large numbers of light states and Planck-scale nonminimal couplings, in which the sign of the running is reversed, leading to black holes with negative corrections to Q/M in the deep IR, but argue that these do not rule out extremal black holes as the requisite charged states for the WGC. We separately show that causality and unitarity imply that the leading threshold corrections to the effective action from integrating out massive states, in any weakly coupled theory, can be written as a sum of squares and is manifestly positive for black hole backgrounds. Quite beautifully, the shift in the extremal Q/M ratio is directly proportional to the shift in the on-shell action, guaranteeing that these threshold corrections push Q &gt; M in compliance with the WGC. Our results apply for black holes with or without dilatonic coupling and charged under any number of U(1)s.

Causality, unitarity, and the weak gravity conjecture