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We study the holographic duality between the reflected entropy and theentanglement wedge cross section with the first order correction. In the fieldtheory side, we consider the reflected entropy for $\rho_{AB}^m$, where$\rho_{AB}$ is the reduced density matrix for two intervals in the groundstate. The reflected entropy in the 2d holographic conformal field theories iscomputed perturbatively up to the first order in $m-1$ by using thesemiclassical conformal block. In the gravity side, we compute the entanglementwedge cross section in the backreacted geometry by cosmic branes with tension$T_m$ which are anchored at the AdS boundary. Comparing both results we find aperfect agreement, showing the duality works with the first order correction in$m-1$.

Reflected Entropy and Entanglement Wedge Cross Section with the First Order Correction