An open bosonic string with one end fixed

TL;DR

This paper introduces a novel bosonic string model with one fixed end, featuring only odd oscillator modes, no tachyons, and a modified Regge slope, potentially useful for describing mesons with asymmetric quark masses.

Contribution

It presents a new string model with unique boundary conditions, odd modes, and a simplified Virasoro algebra, expanding the theoretical framework of string theory.

Findings

No negative or null norm states in the spectrum

Absence of tachyons in the model

Asymptotic density of states estimated for large D

Abstract

We study a bosonic string with one end free and the other confined to a D-brane. Only the odd oscillator modes are allowed, which leads 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 tachyon. The Regge slope is twice that of the open string; this can serve as a test of the usefulness of the 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 can be estimated by adapting the Hardy-Ramanujan analysis to a partition of odd integers; the estimate becomes exact as D goes to infinity.