  The Distance Conjecture of Ooguri and Vafa holds that any infinite-distance
limit in the moduli space of a quantum gravity theory must be accompanied by a
tower of exponentially light particles, which places tight constraints on the
low-energy effective field theories in these limits. One attempt to extend
these constraints to the interior of moduli space is the refined Distance
Conjecture, which holds that the towers of light particles predicted by the
Distance Conjecture must appear any time a modulus makes a super-Planckian
excursion in moduli space. In this note, however, we point out that a tower
which satisfies the Distance Conjecture in an infinite-distance limit of moduli
space may be parametrically heavier than the Planck scale for an arbitrarily
long geodesic distance. This means that the refined Distance Conjecture, in its
most naive form, does not place meaningful constraints on low-energy effective
field theory. This motivates alternative refinements of the Distance
Conjecture, which place an absolute upper bound on the tower mass scale in the
interior of moduli space. We explore two possibilities, providing evidence for
them and briefly discussing their implications.

High Energy Physics - Theory