  A common feature of tree-level holography is that a correlator in one theory
can serve as a generating function for correlators in another theory with less
continuous symmetry. This is the case for a family of 4d CFTs with eight
supercharges which have protected operators dual to gluons in the bulk. The
most recent additions to this family were defined using S-folds which combine a
spatial identification with an action of the S-duality group in type IIB string
theory. Differences between these CFTs which have a dynamical origin first
become manifest at one loop. To explore this phenomenon at the level of
anomalous dimensions, we use the AdS unitarity method to bootstrap a one-loop
double discontinuity. Compared to previous studies, the subsequent analysis is
performed without any assumption about which special functions are allowed.
Instead, the Casimir singular and Casimir regular terms are extracted
iteratively in order to move from one Regge trajectory to the next. Our results
show that anomalous dimensions in the presence of an S-fold are no longer
rational functions of the spin.
