The open-string zero-point constant is

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model · Beyond the Standard Model

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

Problem

The open-string zero-point constant is a=(D−2)/24a = (D-2)/24, obtained before fixing the number of spacetime dimensions DD. The N=1N=1 states α−1I∣p⟩\alpha^I_{-1}|p\rangle number D−2D-2. ((a)) Compute aa for D=4D=4, D=10D=10 and D=26D=26. ((b)) The N=1N=1 states have mass-squared M2=(1−a)/α′M^2=(1-a)/\alpha'. For each DD, decide whether these D−2D-2 states can form a vector consistent with Lorentz invariance, using the number of states a massive vector and a massless vector each need in DD dimensions, and hence identify which DD is free of inconsistency.

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