ar X iv : h ep - t h / 03 03 21 7 v 1 2 5 M ar 2 00 3 A Ramond - Neveu - Schwarz string with one end fixed

We study an RNS string with one end fixed on a D0-brane and the other end free as a qualitative guide to the spectrum of hadrons containig one very heavy quark. The mixed boundary conditions break half of the world-sheet supersymmetry. Boson-fermion masses can still be matched if space-time is 9 dimensional; thus SO(8) triality still plays a role in the spectrum, although full space-time supersymmetry does not survive. We quantize the system in a temporal-like gauge where X ∼ τ . Only odd α and even d R modes remain, while the NS oscillators b become odd-integer moded. Although the gauge choice eliminates negative-norm states at the outset, there are still even-moded Virasoro and even(odd) moded super-Virasoro constraints to be imposed in the NS(R) sectors. The Casimir energy is now positive for R states, but vanishes for NS; there are no tachyons. States for αM ≤ 3 are explicitly constructed and found to be organized into SO(8) irreps by (super)constraints, which include a novel “ √ L0” operator in the NS and Γ 0 ± I in the R sectors. GSO projections are not allowed. The distinctive physical signatures of the system are (i) a slope twice that of the open string, (ii) absence of all but leading trajectories, yielding an asympotic level density ∼ N D−1 2 instead of exp √ N . When both ends are fixed, all leading and subleading trajectories are eliminated instead, resulting in a spectrum qualitatively similar to the J/ψ and Υ particles.