  Angle-resolved photoemission spectroscopy (ARPES) has revealed peculiar
properties of mobile dopants in correlated anti-ferromagnets (AFMs). But
describing them theoretically, even in simplified toy models, remains a
challenge. Here we study ARPES spectra of a single mobile hole in the $t-J$
model. Recent progress in the microscopic description of mobile dopants allows
us to use a geometric decoupling of spin and charge fluctuations at strong
couplings, from which we conjecture a one-to-one relation of the one-dopant
spectral function and the spectrum of a constituting spinon in the
\emph{undoped} parent AFM. We thoroughly test this hypothesis for a single hole
doped into a 2D Heisenberg AFM by comparing our semi-analytical predictions to
previous quantum Monte Carlo results and our large-scale time-dependent matrix
product state (td-MPS) calculations of the spectral function. Our conclusion is
supported by a microscopic trial wavefuntion describing spinon-chargon bound
states, which captures the momentum and $t/J$ dependence of the quasiparticle
residue. Our conjecture suggests that ARPES measurements in the pseudogap phase
of cuprates can directly reveal the Dirac-fermion nature of the constituting
spinons. Specifically, we demonstrate that our trial wavefunction provides a
microscopic explanation for the sudden drop of spectral weight around the nodal
point associated with the formation of Fermi arcs, assuming that additional
frustration suppresses long-range AFM ordering. We benchmark our results by
studying the cross-over from two to one dimension, where spinons and chargons
are confined and deconfined respectively.
