  In four-dimensional axion electrodynamics, a Chern-Simons coupling of the
form $\theta F \wedge F$ leads to a higher-group global symmetry between
background gauge fields. At the same time, such a Chern-Simons coupling leads
to a mixing between the Weak Gravity Conjectures for the axion and the gauge
field, so that the charged excitations of a Weak Gravity Conjecture-satisfying
axion string will also satisfy the Weak Gravity Conjecture for the gauge field.
In this paper, we argue that these higher-group symmetries and this phenomenon
of Weak Gravity Conjecture mixing are related to one another. We show that this
relationship extends to supergravities in 5, 6, 7, 8, 9, and 10 dimensions, so
higher-dimensional supergravity is endowed with precisely the structure needed
to ensure consistency with emergent higher-group symmetries and with the Weak
Gravity Conjecture. We further argue that a similar mixing of Weak Gravity
Conjectures can occur in two-term Chern-Simons theories or in theories with
kinetic mixing, though the connection with higher-group symmetries here is more
tenuous, and accordingly the constraints on effective field theory are not as
sharp.
