The number of open-string states at level in spacetime dimensions is

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Beyond the Standard Model · Beyond the Standard Model

Symmetry and Flavour, Ch The relativistic string: action, light-cone quantisation, spectrum and D-branes

Problem

The number of open-string states at level

N=2

D

spacetime dimensions is

(D-2) + \tfrac12(D-2)(D-1)

, from the states

\alpha^I_{-2}|p\rangle

and

\alpha^I_{-1}\alpha^J_{-1}|p\rangle

. ((a)) Evaluate this count for

D=4

D=10

and

D=26

. ((b)) Taking

D=26

as the value fixed by requiring the

N=1

states to form a massless vector (so

a=1

), and using a Regge slope

\alpha'=0.92\,\mathrm{GeV^{-2}}

, find

M^2

of the

N=2

level in

\mathrm{GeV^2}