  Twist fields were introduced a few decades ago as a quantum counterpart to
classical kink configurations and disorder variables in low dimensional field
theories. In recent years they received a new incarnation within the framework
of geometric entropy and strong coupling limit of four-dimensional scattering
amplitudes. In this paper, we study their two-point correlation functions in a
free massless scalar theory, namely, twist--twist and twist--anti-twist
correlators. In spite of the simplicity of the model in question, the
properties of the latter are far from being trivial. The problem is reduced,
within the formalism of the path integral, to the study of spectral
determinants on surfaces with conical points, which are then computed exactly
making use of the zeta function regularization. We also provide an insight into
twist correlators for a massive complex scalar by means of the Lifshitz-Krein
trace formula.
