Glueballs in the string quark model

We show that the eigenstates of the quantized simplest closed (elliptic) Nambu–Goto string interpreted as glueballs have the quantum numbers $I^Gj^{PC}=0^+j^{++}$. The lightest glueballs have the spins $j=0,1,2$ and the same mass $1500\pm20$MeV, which corresponds to the $f_0(1500)$, $f_1(1510)$, and $f_2(1565)$ mesons. Excitation of higher Fourier modes leads to the glueball with $j=0$ and the mass $2200\pm30$MeV corresponding to the $f_0(2200)$ meson. The next glueballs have $j=0,1,2,3,4$ with the masses $2610\pm20$MeV. The slope of the glueball Regge trajectories is half the slope for the quark-antiquark mesons. The leading (Pomeron) glueball trajectory has the value $1.07\pm0.03$ at zero transferred momentum.