Meson modes of probe $D7$-branes in Klebanov-Strassler background

We examine the properties of 4-d bosonic and fermionic (mesons and mesinos) modes on $D7$-branes wrapped over Kuperstein 4-cycle of the Klebanov-Strassler background. The wave equations are derived in a convenient parameterization of the warped deformed conifold metric. The mass spectra, wave functions and couplings of bosonic modes are evaluated by means of semi-classical tools. We explore the possible existence of fermionic zero modes.