A Ramond-Neveu-Schwarz string with one end fixed

TL;DR

This paper explores a modified Ramond-Neveu-Schwarz string with one end fixed, revealing a spectrum with broken supersymmetry, no tachyons, and a unique slope, providing insights into heavy quark hadron spectra.

Contribution

It introduces a novel RNS string model with mixed boundary conditions, analyzing its spectrum and constraints, and highlights its potential relevance to heavy quark hadron phenomenology.

Findings

Spectrum has no tachyons and positive Casimir energy.

States are organized into SO(8) irreducible representations.

The string slope is twice that of the standard open RNS string.

Abstract

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 containing 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 $X^0 \sim \tau$. Only odd $\alpha$ 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 in both sectors; there are no tachyons. States for $\alpha' M^2 \leq 3$ are explicitly constructed and found to be organized into SO(8) irreps by (super)constraints, which include a novel "$\sqrt{L_0}$" operator in the NS and $\Gamma^0 \pm I$ 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 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 $J/\psi$ and $\Upsilon$ particles.