A noncritical Ramond-Neveu-Schwarz string with one end fixed

Official URL: http://dx.doi.org/10.1142/S0217751X06022798

We study a Ramond–Neveu–Schwarz string with one end fixed on a D0-brane and the other end free as a qualitative guide to the spectrum of hadrons containing one very heavy quark. The mixed boundary conditions break half of the worldsheet supersymmetry and allow only odd α and even d modes 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 nine-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 X0 ~ τ. 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 α′ M2 ≤ 13/4are explicitly constructed and found to be organized into SO(8) irreps by (super)constraints, which include a novel "" operator in the Neveu–Schwarz and Γ0 ± I in the Ramond sectors. GSO projections are not allowed. The preconstraint states above the ground state have matching multiplicities, indicating space–time supersymmetry is broken by the (super)constraints. A distinctive physical signature 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/ψ and ϒ particles.