  Depending on the value of the coupling, BPS states of type II string theory
compactified on a Calabi-Yau manifold can be described as multicenter
supergravity solutions or as states on the Coulomb or the Higgs branch of a
quiver gauge theory. While the Coulomb-branch states can be mapped one-to-one
to supergravity states, this is not automatically so for Higgs-branch states.
In this paper we explicitly compute the BPS spectrum of the Higgs branch of a
three-center quiver with a closed loop, and identify the subset of states that
are in one-to-one correspondence with Coulomb/supergravity multicenter states.
We also show that there exist additional "pure-Higgs" states, that exist if and
only if the charges of the centers can form a scaling solution. Using
generating function techniques we compute the large charge degeneracy of the
"pure-Higgs" sector and show that it is always exponential. We also construct
the map between Higgs- and Coulomb-branch states, discuss its relation to the
Higgs-Coulomb map of one of the authors and Verlinde, and argue that the pure
Higgs states live in the kernel of this map. Given that these states have no
obvious description on the Coulomb branch or in supergravity, we discuss
whether they can correspond to a single-center black hole or can be related to
more complicated horizonless configurations.
