Quantum chromodynamics (QCD), the theory of quarks and gluons, is known to be
the correct description of strong nuclear interactions. At high energy and momenta,
one can use QCD directly to compute quantities of physical interest related to the
strong force. At low energies and momenta, one should use a different description in
terms of the degrees of freedom relevant at that scale. Two approaches to achieve
this end are effective field theories and gauge/gravity dualities. The former involves
a field theory more or less like QCD itself, but with states which are composites
of quarks and gluons. Then a perturbative expansion is made not in terms of the
gauge coupling but instead in terms of the momentum of the fields. This approach
dates back to the 1970s and is on firm theoretical footing. Gauge/gravity dualities
are a newer and less understood technique, which relates the physics of the strong
interactions to a different but likely equivalent theory in a higher dimensional space-
time, where the quantity of interest can be computed more readily. We employ
both effective field theories and gauge/gravity dualities to study the physics of ex-
otic quarkonium states, that is bound states containing a heavy quark-antiquark pair
which nevertheless cannot be be understood working only with the standard quark
model of hadrons. Candidates for such states, long speculated to exist, have recently
been observed at particle colliders, so that the theory of exotic quarkonium is now
of great experimental importance.
