Brane Detectors of a Dynamical Phase Transition in a Driven CFT

TL;DR

This paper demonstrates a first order bulk phase transition in a driven 2D CFT via brane free energy analysis, linking boundary dynamical phases to bulk geometric and correlator changes.

Contribution

It constructs dual AdS metrics for driven CFT phases, embeds branes to detect phase transitions, and computes correlators showing phase-dependent behavior.

Findings

Finite discontinuity in brane free energy derivative at transition

Bulk correlators match driven CFT correlators in different phases

No transition observed in bulk without branes

Abstract

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.