Holographic heavy-light mesons from non-Abelian DBI

Abstract

In the context of gauge/gravity duals with flavor, we examine heavy-light mesons which involve a heavy and a light quark. For this purpose we embed two D7 brane probes at different positions into the gravity background. We establish the non-Abelian Dirac-Born-Infeld (DBI) action for these probes, in which the U(2) matrix describing the embedding is diagonal. The fluctuations of the brane probes correspond to the mesons. In particular, the off-diagonal elements of the U(2) fluctuation matrix correspond to the heavy-light mesons, while the diagonal elements correspond to the light-light and heavy-heavy mesons, respectively. The heavy-light mesons scale differently with the 't Hooft coupling than the mesons involving quarks of equal mass. The model describes both scalar and vector mesons. For different dilaton-deformed gravity backgrounds, we also calculate the Wilson loop energy, and compare with the meson masses.