  We show that a dynamical transition from a non-heating to a heating phase of
a periodic $SL(2,\mathbb{R})$ driven two-dimensional conformal field theory
(CFT) with a large central charge is perceived as a first order transition by a
bulk brane embedded in the dual AdS. We construct the dual bulk metric
corresponding to a driven CFT for both the heating and the non-heating phases.
These metrics are different AdS$_{2}$ slices of the pure AdS$_{3}$ metric. We
embed a brane in the obtained dual AdS space and provide an explicit
computation of its free energy both in the probe limit and for an end-of-world
(EOW) brane taking into account its backreaction. Our analysis indicates a
finite discontinuity in the first derivative of the brane free energy as one
moves from the non-heating to the heating phase (by tuning the drive amplitude
and/or frequency of the driven CFT) thus demonstrating the presence of the bulk
first order transition. Interestingly, no such transition is perceived by the
bulk in the absence of the brane. We also provide explicit computations of
two-point, four-point out-of-time correlators (OTOC) using the bulk picture.
Our analysis shows that the structure of these correlators in different phases
match their counterparts computed in the driven CFT. We analyze the effect of
multiple EOW branes in the bulk and discuss possible extensions of our work for
richer geometries and branes.
