Relative Rényi entropy under local quenches in 2D CFTs

A bstract We study the relative Rényi entropy (RRE) under local quenches in two-dimensional conformal field theories (CFTs), focusing on rational CFTs (RCFTs) and holographic CFTs. In RCFTs, the RRE evolves as a monotonic function over time, depending on finite-dimensional matrices. It is sometimes symmetric, prompting an investigation into its relationship with the squared trace distance. We also observe that relative entropy can fail to distinguish between operators, as it only captures information entering/exiting the subsystem. In holographic CFTs, an analytic continuation of the RRE reveals insights into the entanglement wedge, offering a new perspective on bulk geometry in AdS/CFT. Our results deepen the understanding of quantum information measures in RCFTs and holographic CFTs, highlighting connections to distinguishability and bulk reconstruction.