THE EFFECT OF SPATIAL CURVATURE ON CLASSICAL AND QUANTUM STRINGS

We study the effects of spatial curvature on classical and quantum string dynamics. We find the general solution of the circular string motion in static Robertson–Walker space-times with closed or open sections. This is given closely and completely in terms of elliptic functions. The physical properties, string length, energy and pressure are computed and analyzed. We find the back-reaction effect of these strings on the space-time: the self-consistent solution to the Einstein equations is a spatially closed (K>0) space-time with a selected value of the curvature index K (the scale factor is normalized to unity). No self-consistent solutions with K≤0 exist. We semiclassically quantize the circular strings and find the mass m in each case. For K>0, the very massive strings, oscillating on the full hypersphere, have m2~Kn2(n∈N0)independent of α' and the level spacing grows with n, while the strings oscillating on one hemisphere (without crossing the equator) have m2α′~n and a finite number of states N~1/Kα′. For K<0, there are infinitely many string states with masses m log m ~ n, i.e. the level spacing grows slower than n. The stationary string solutions as well as the generic string fluctuations around the center of mass are also found and analyzed in closed form.