  Correlation function of twist operators is a natural quantity of interest in
two-dimensional conformal field theory (2d CFT) and finds relevance in various
physical contexts. For computing twist operator correlators associated with
generic branched covers of genus zero and one, we present a generalization of
the conventional stress-tensor method to encompass generic 2d CFTs without
relying on any free field realization. This is achieved by employing a
generalization of the argument of Calabrese-Cardy in the cyclic genus zero
case. The generalized stress-tensor method reveals a compelling relation
between the twist operator correlator and the tau function on Hurwitz space,
the moduli space of branched covers, of Kokotov-Korotkin. This stems from the
close relation between stress-tensor one-point function and Bergman projective
connection of branched cover. The tau function on Hurwitz space is in turn
related to the more general isomonodromic tau function, and this chain of
correspondence thus relates the twist operator correlator to a canonical
algebro-geometric object and endows it with an integrable system
interpretation. Conversely, the tau function on Hurwitz space essentially
admits a CFT interpretation as the holomorphic part of the twist operator
correlator of $c=1$ free boson.
