Topics in superstring theory

The author discusses two specific issues in superstring theory as follows: regularization of open superstring from oriented closed surface and worldsheet supersymmetry. Regarding the first issue, the author discusses a technical issue occurring in the open superstring which allows introduction of a multiplicative Chan-Paton factor. For O(N) groups the adjoint representation is the antisymmetric part of N x N and this simple property is lacking in the exceptional groups. The author discusses how for superstrings there are two relevant kinds of supersymmetry: spacetime supersymmetry in d = 10 spacetime dimensions and worldsheet supersymmetry in d = 2 worldsheet dimensions. Until a few months ago, all known superstrings possessed both: at least N = 1 spacetime supersymmetry and at lest (1,0) worldsheet supersymmetry. Recently, however, an 0(16) x 0(16) superstring was proposed with no spacetime supersymmetry; the model has infrared problems on flat M10 but these problems might be cured by compactification. This motivates one to study the restrictions on the six-dimensional compact manifold for the case without spacetime supersymmetry. The author finds that (2,2) worldsheet supersymmetry and quantum conformal invariance of the two-dimensional field theory lead to equally strong restrictions as does the assumption of preserving a spacetime supersymmetry