Abstract:
We study an open string with one end free and the other fixed on a D0-brane as a qualitative guide to the spectrum of hadrons containing one very heavy quark. We first consider the bosonic degrees of freedom, then introduce the fermionic degrees offreedom through the world sheet supersymmetry. The mixed boundary conditions break half of the world sheet supersymmetry and allow only odd-moded a and even-moded d oscillators in the Ramond sector, while the Neveu-Schwarz oscillators b's become odd-integer moded. 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^0 ~ t. 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 in both sectors; there are no tachyons. States for a' M^2 b 13/4 are explicitly constructed and found to be organized into SO(8) irreps by (super)constraints, which include a novel ``" operator in the NS and I in the R-sectors. GSO projections are not allowed. The pre-constraint states above the ground state have matching multiplicities, indicating spacetime supersymmetry is broken by the (super)constraints. A distinctive physical feature of the system is a slope twice that of the open RNS string. When both ends are fixed, all leading and subleading trajectories are eliminated, resulting in a spectrum qualitatively similar to the J/ and particles.
