  Recent lattice results strongly support the Axionic String Ansatz (ASA) for
quantum numbers of glueballs in 3D Yang-Mills theory. The ASA treats glueballs
as closed bosonic strings. The corresponding worldsheet theory is a deformation
of the minimal Nambu-Goto theory. In order to understand better the ASA strings
and as a first step towards a perturbative calculation of the glueball mass
splittings we compare the ASA spectrum to the closed effective string theory.
Namely, we model glueballs as excitations around the folded rotating rod
solution with a large angular momentum $J$. The resulting spectrum agrees with
the ASA in the regime of validity of the effective theory, i.e., in the
vicinity of the leading Regge trajectory. In particular, closed effective
string theory correctly predicts that only glueballs of even spin $J$ show up
at the leading Regge trajectory. Interestingly though, the closed effective
string theory overestimates the number of glueball states far above the leading
Regge trajectory.
