  There has been considerable recent interest in holographic complexity. The
two leading conjectures on this subject hold that the quantum complexity of the
boundary thermofield double state should be dual to either the volume of the
Einstein-Rosen bridge connecting the two sides (CV conjecture) or to the action
of the Wheeler-de-Witt patch of the bulk spacetime (CA conjecture). Although
these conjectures are frequently studied in the context of pure Einstein
gravity, from the perspective of string theory it is also natural to consider
models of gravity in which general relativity is perturbed by higher powers of
the Riemann tensor, suppressed by powers of the string length; in a holographic
context, these corrections are dual to corrections in inverse powers of the 't
Hooft coupling. In this paper, we investigate the CV and CA conjectures in two
stringy models of higher-curvature gravity. We find that the CV
complexification rate remains well-behaved, but conversely that these
corrections induce new divergences in the CA complexification rate that are
absent in pure Einstein gravity. These divergences are intrinsically linked to
the singularity, and appear to be generic in higher curvature theories. To the
best of our knowledge, infinities originating at the singularity have not yet
been observed elsewhere in the literature. We argue that these divergences
imply that, in the CA picture, the complexification rate of the boundary theory
is a nonanalytic function of the 't Hooft coupling.
