An open bosonic string with one end fixed (Q2752481)

A bosonic string with one end free and the other confined to a \(D0\)-brane is studied. Only the odd oscillator modes are allowed, which lead to a Virasoro algebra of even Virasoro modes only. The theory is quantized in a gauge where world-sheet time and ordinary time are identified. There are no negative or null norm states, and no tachyons. The Regge slope is twice that of the open string; this can serve as a test of the usefulness of the model as a semi-quantitative description of mesons with one light and one extremely heavy quark when such higher spin mesons are found. The Virasoro conditions select specific \(SO(D-1)\) irreps. The asymptotic density of states is estimated by adapting the Hardy-Ramanujan analysis to a partition of odd integers and is \(d_{n}\approx \exp (4\pi \sqrt{n(D-2)/24})n^{-3/4}n^{-(D-2)/4}\), and the estimate becomes exact as \(D\) goes to infinity.