Geometric quantization of strings and reparametrization invariance

The structure of the phase space of closed bosonic strings in $R^{d-1,1}$ and its geometric quantization are investigated. It is shown that the critical dimension $d=26$ for bosonic strings arises as a condition of integrability of the quantum connection on the fibers of a bundle of complex structures over a loop space. The connection with BRST (Becchi–Rouet–Stora–Tyutin) string quantization is considered.