Revisiting the chiral effective action in holographic models

TL;DR

This paper calculates low-energy constants in the chiral Lagrangian from the holographic Witten-Sakai-Sugimoto model, revealing finite 't Hooft coupling corrections and emphasizing the need for careful derivations of effective actions.

Contribution

It provides a direct holographic computation of pion decay constants and scattering amplitudes, identifying corrections overlooked in previous derivations.

Findings

Finite 't Hooft coupling corrections are present in the effective chiral action.

Direct holographic calculation of two-pion scattering amplitude.

Reevaluation of past holographic derivations of effective actions is necessary.

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 two-pion scattering amplitude, which we compute directly in the holographic dual through tree-level Witten diagrams. Identification of the low energy coefficients in the chiral action is subtle as their values will be shifted when the tower of massive vector bosons are integrated out. Indeed, by a direct comparison with the existing standard procedure of constructing the chiral action with radial modes in the gravity dual, we explicitly show that there are finite 't Hooft coupling corrections that have been missed. This suggests that past derivations of effective actions from holographic models may have to be revisited and future derivations more carefully considered.