Son-Yamamoto relation and Holographic RG flows

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Motivated by the Son-Yamamoto (SY) relation which connects the three point and two-point correlators we consider the holographic RG flows in the bottom-up approach to holographic QCD via the Hamilton-Jacobi (HJ) equation with respect to the radial coordinate. It is shown that the SY relation is diagonal with respect to the RG flow in the 5d YM-CS model while the RG equation acquires the inhomogeneous term in the model with the additional scalar field which encodes the chiral condensate.