Pauli-Villars Regularization and One-Loop Finiteness of Type-I Superstring Theory

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Abstract
In a previous paper we reanalyzed the issue of one-loop finiteness of the light-cone 4-point amplitude of the type-I SO(N) superstring theory in terms of the Pauli-Villars regularization. The same analysis is applied, in this paper, to the 5-point amplitude in the light-cone formalism as well as to the parity-conserving covariant M-point amplitude and the generality of the previous results is confirmed. Namely, the assignment of the regulator masses to the planar and nonorientable diagrams is essentially arbitarary in the present scheme. However, once a particular mass assignment is fixed, by one way or another, it is firmly established that the one-loop finiteness condition picks up the same N for an arbitrary number M of external lines. In particular, the assignment 2mP = mN renders all the one-loop amplitude finite for N = 32.

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