Sakai-Sugimoto Model in an Off-Shell: Chiral Lagrangian to All Orders

TL;DR

This work reformulates the Sakai-Sugimoto holographic model in an off-shell, boundary-centric formalism to derive an all-orders, non-local effective action for the boundary theory. By partitioning the bulk EOM into dynamical and constraint sectors and solving the dynamical part to arbitrary derivative order, the authors integrate in a KK tower of vector mesons and obtain a boundary action that encompasses the $U(N_f)$ pion multiplet, the $\eta'$ meson, and the vector mesons. The resulting action reduces to the Chiral Lagrangian in a local gradient expansion and yields the bare and effective low-energy constants for arbitrary $N_f$, matching known results for $N_f=2$ and clarifying the distinction between bare and physical LECs. The formalism highlights non-local interactions generated by integrating out bulk degrees of freedom and distinguishes CS-induced (parity-preserving) from DBI-induced (parity-structured) vector meson interactions, with implications for pion scattering and vector-meson phenomenology. Overall, the paper provides a comprehensive, all-orders holographic description of chiral dynamics in the SS model and opens avenues for phenomenology and spectral analyses beyond the leading-order framework.

Abstract

The Sakai-Sugimoto holographic model is famous for implementing the approximate chiral symmetry of QCD and reproducing the Chiral Lagrangian in a top-down approach. In this manuscript, we revisit the model in a formalism that is somewhat different from the original work by Sakai and Sugimoto: We start by identifying boundary degrees of freedom and splitting the bulk equations of motion into dynamical ones and constraints. The former are then solved to all orders in derivatives of the boundary fields. The constraints are left unsolved, leaving the dynamical degrees of freedom off-shell. This approach enables us to systematically derive the effective action of the boundary theory. The derived effective action is very rich in physics: it contains an $U(N_f)$ multiplet of massless pseudoscalars interacting (via trilinear and higher terms) with towers of massive (axial-)vector mesons. In contrast to the previous studies, our effective action is non-local. The original Chiral Lagrangian is recovered as its local expansion in small $π$-meson momenta (derivative expansion). We particularly zoom in on the values of four derivative terms couplings, the low energy constants, and compare those with the ones reported in the literature.

Figures (1)

• Figure 1: Meson mass spectra.