Entanglement negativity, reflected entropy, and anomalous gravitation

We investigate mixed state entanglement measures of negativity and reflected entropy for bipartite states in two dimensional conformal field theories with an anomaly through appropriate replica techniques. Furthermore we propose holographic constructions these from the corresponding bulk dual geometries involving topologically massive gravity ${\mathrm{AdS}}_{3}$ find exact agreement theory results. In this connection extend earlier proposal to action a gravitational Chern-Simons term compute its contribution wedge cross section entropy.