Holographic Penta and Hepta Quark State in Confining Gauge Theories

We study a new embedding solutions of D5 brane in an asymptotic AdS${}_5\times S^5$ space-time, which is dual to a confining $SU(N_c)$ gauge theory. The D5 brane is wrapped on $S^5$ as in the case of the vertex of holographic baryon. However, the solution given here is different from the usual baryon vertex in the point that it couples to $k$-anti-quarks and $N_c+k$ quarks on the opposite two points of $S^5$, the north and south poles, respectively. The total quark number of this state is preserved as $N_c$ when minus one is assigned to anti-quark, then it forms a color singlet like the baryon. However, this includes anti-quarks and quarks, whose number is larger than that of the baryon. When we set as $N_c=3$, we find the so called penta and hepta-quark states. We study the dynamical properties of these states by solving the vertex and string configurations for such states. The mass spectra of these states and the tension of the stretched vertex are estimated, and they are compared with that of the baryon.