Quantisation of the N = 2 String in a Real Spacetime Structure

We study the N = 2 string with a real structure on the (2, 2) spacetime, using BRST methods. Several new features emerge. In the diagonal basis, the operator exp(λ ∫ z J ), which is associated with the moduli for the U(1) gauge field on the world-sheet, is local and it relates the physical operators in the NS and R sectors. However, the picture-changing operators are non-invertible in this case, and physical operators in different pictures cannot be identified. The three-point interactions of all physical operators leads to three different types of amplitudes, which can be effectively described by the interactions of a scalar NS operator and a bosonic spinorial R operator. In the off-diagonal bases for the fermionic currents, the picture-changing operators are invertible, and hence physical operators in different pictures can be identified. However, now there is no local operator exp(λ ∫ z J ) that relates the physical operators in different sectors. The physical spectrum is thus described by one scalar NS operator and one spinorial R operator. The NS and R operators give rise to different types of three-point amplitudes, and thus cannot be identified. Supported in part by the U.S. Department of Energy, under grant DE-FG05-91-ER40633 Supported in part by the EC Human Capital and Mobility Programme, under contract number