Holographic Heavy-Light Chiral Effective Action

Abstract

We propose a variant of the $D4$-$D8$ construction to describe the low energy effective theory of heavy-light mesons, interacting with the lowest lying pseudoscalar and vector mesons. The heavy degrees of freedom are identified with the $D8_L$-$D8_H$ string low energy modes, and are approximated near the world volume of $N_f-1$ light $D8_L$ branes, by fundamental vector field valued in $U(N_f-1)$. The effective action follows from the reduction of the bulk D-brane Born-Infeld (DBI) and Chern-Simons (CS) actions, and is shown to exhibit both chiral and heavy-quark symmetry. The action interpolates continuously between the $U(N_f)$ case with massless mesons, and the $U(N_f-1)$ case with heavy-light mesons. The heavy-light meson radial spectrum is Regge-like. The one-pion and two-pion couplings to the heavy-light multiplets are evaluated. The partial widths for the charged decays $G\rightarrow H+\pi$ are shown to be comparable to the recently reported full widths for both the charm and bottom mesons.