Glueball-baryon interactions in holographic QCD

Abstract

Studying the Witten-Sakai-Sugimoto model with type IIA string theory, we find the glueball-baryon interaction is predicted in this model. The glueball is identified as the 11D gravitational waves or graviton described by the M5-brane supergravity solution. Employing the relation of M-theory and type IIA string theory, glueball is also 10D gravitational perturbations which are the excited modes by close strings in the bulk of this model. On the other hand, baryon is identified as a D4-brane wrapped on $S^{4}$ which is named as baryon vertex, so the glueball-baryon interaction is nothing but the close string/baryon vertex interaction in this model. Since the baryon vertex could be equivalently treated as the instanton configurations on the flavor brane, we identify the glueball-baryon interaction as "graviton-instanton" interaction in order to describe it quantitatively by the quantum mechanical system for the collective modes of baryons. So the effective Hamiltonian can be obtained by considering the gravitational perturbations in the flavor brane action. With this Hamiltonian, the amplitudes and the selection rules of the glueball-baryon interaction can be analytically calculated in the strong coupling limit. We show our calculations explicitly in two characteristic situations which are "scalar and tensor glueball interacting with baryons". Although there is a long way to go, our work provides a holographic way to understand the interactions of baryons in hadronic physics and nuclear physics by the underlying string theory.