String propagation on non-compact group manifolds is studied as an exactly solvable example of propagation on more general curved spacetimes. It is shown that for the only viable group SU(1, 1) × Gc string propagation is consistent classically but not quantum mechanically (unitarity is violated). This shows that conformal invariance of the corresponding σ-model (vanishing of the β-functions) is not sufficient to guarantee unitarity.
ASJC Scopus subject areas
- Nuclear and High Energy Physics