A replica trick for computing fluctuations in time-symmetric quantum systems*

Motivated by ideas from free probability theory, we propose a replica trick for computing the covariance of real Wishart matrices. Given the holographic duality between low-dimensional quantum gravity and random matrix integrals, we argue that this replica trick enables a diagrammatic calculation of general 2-point functions involving random matrices, suggesting a connection to novel replica wormholes in the gravitational path integral. We present an overview of quantities that can be studied within this formalism, highlighting a new perspective on a recent puzzle arising from the inclusion of "observers" in holographic models.