Revisiting the chiral effective action in holographic models

Abstract

We obtain the pion decay constant and coefficients of fourth derivative terms in the chiral Lagrangian for massless quarks in the Witten-Sakai-Sugimoto model. We extract these quantities from the twopion scattering amplitude, which we compute directly in the holographic dual through tree-level Witten diagrams. We compare our results with the existing standard procedure of constructing the chiral action with radial modes in the gravity dual. While the pion decay constant agrees, we point out that the values of the other coefficients have not been correctly identified. This suggests that past derivations of effective actions from holographic models may have to be revisited and future derivations more carefully considered.