  In strongly correlated quantum materials, the behavior of charge carriers is
dominated by strong electron-electron interactions. These can lead to
insulating states with spin order, and upon doping to competing ordered states
including unconventional superconductivity. The underlying pairing mechanism
remains poorly understood however, even in strongly simplified theoretical
models. Recent advances in quantum simulation allow to study pairing in
paradigmatic settings, e.g. in the $t-J$ and $t-J_z$ Hamiltonians. Even there,
the most basic properties of paired states of only two dopants, such as their
dispersion relation and excitation spectra, remain poorly studied in many
cases. Here we provide new analytical insights into a possible string-based
pairing mechanism of mobile holes in an antiferromagnet. We analyze an
effective model of partons connected by a confining string and calculate the
spectral properties of bound states. Our model is equally relevant for
understanding Hubbard-Mott excitons consisting of a bound doublon-hole pair or
confined states of dynamical matter in lattice gauge theories, which motivates
our study of different parton statistics. Although an accurate semi-analytic
estimation of binding energies is challenging, our theory provides a detailed
understanding of the internal structure of pairs. For example, in a range of
settings we predict heavy states of immobile pairs with flat-band dispersions
-- including for the lowest-energy $d$-wave pair of fermions. Our findings shed
new light on the long-standing question about the origin of pairing and
competing orders in high-temperature superconductors.
