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

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. Off-shell holography is a formalism most suitable for derivation of boundary effective actions. In this manuscript, we revisit the original Sakai-Sugimoto model using the off-shell formalism. Thus 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 $\pi$-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.