  Dark matter may self-interact through a continuum of low-mass states. This
happens if dark matter couples to a strongly-coupled nearly-conformal hidden
sector. This type of theory is holographically described by brane-localized
dark matter interacting with bulk fields in a slice of 5D anti-de Sitter space.
The long-range potential in this scenario depends on a non-integer power of the
spatial separation, in contrast to the Yukawa potential generated by the
exchange of a single 4D mediator. The resulting self-interaction cross section
scales like a non-integer power of velocity. We identify the Born, classical
and resonant regimes and investigate them using state-of-the-art numerical
methods. We demonstrate the viability of our continuum-mediated framework to
address the astrophysical small-scale structure anomalies. Investigating the
continuum-mediated Sommerfeld enhancement, we demonstrate that a pattern of
resonances can occur depending on the non-integer power. We conclude that
continuum mediators introduce novel power-law scalings which open new
possibilities for dark matter self-interaction phenomenology.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics