Singular BPS saturated states and enhanced symmetries of four-dimensional N = 4 supersymmetric string vacua

A class of supersymmetric (BPS saturated), static, spherically symmetric solutions of four-dimensional effective N = 4 supersymmetric superstring vacua, which become massless at special points of moduli space, is studied in terms of the fields of the effective heterotic string theory compactified on a six-torus. Those are singular four-dimensional solutions corresponding to O(6,22,Z) orbits of dyonic configurations (with zero axion), whose left-moving as well as right-moving electric and magnetic charges are orthogonal (light-like in the O(6,22,Z) sense), while the O(6,22,Z) norms of both the electric and magnetic charges are negative. Purely electric [or purely magnetic] and dyonic configurations preserve 12 and 14 of N = 4 supersymmetry, respectively, thus belonging to the vector and the highest spin 32 supermultiplets, respectively. Purely electric [or purely magnetic] solutions (along with an infinite tower of SL(2, Z) transformed states) become massless at a point of the corresponding “one-torus”, thus may contribute to the enhancement of non-Abelian gauge symmetry, while dyonic solutions become simultaneously massless at a point of the corresponding two-torus, and thus may in addition contribute to the enhancement of the local supersymmetry there.