Distance Conjecture: Exponential Light Towers at Large Field-Space Distance

Establish that in any consistent quantum theory of gravity, approaching extreme distances in scalar field space necessarily yields an infinite tower of weakly interacting states whose masses decrease exponentially with the field value, m(φ) ≈ exp(−α φ) with α an order-one constant measured in Planck units.

Background

The paper reviews a central Swampland idea inspired by string theory dualities: when parameters of a quantum gravitational system move to extreme values, a dual description becomes suitable due to the emergence of a tower of light states. In particular, large excursions in scalar field space are expected to produce an infinite tower of states with exponentially decreasing masses.

This expectation is formalized as the Distance Conjecture, which has broad support from string theory examples. The conjecture underpins later arguments in the paper connecting the smallness of dark energy to the existence of light towers that can serve as dark matter candidates.