SUPERSYMMETRY IN DIMENSIONS BEYOND 11

Spacetime superalgebras with 64 or less number of real supercharges, c ontaining the type IIB Poincare superalgebra in (9, 1) dimensions and the N = 1 Poincare superalgebra in (10, 1) are considered. The restric tion D less than or equal to 14, and two distinct possibilities arise: The N = (1, 0) superalgebra in (11, 3) dimensions, and the N = (2, 0) superalgebra in (10, 2) dimensions. Emphasizing the former, we descri be superparticle and super Yang-Mills systems in (11, 3) dimensions. W e also propose an N = (2, 1) superstring theory in (n, n) dimensions a s a possible origin of super Yang-Mills in (8 + n, n) dimensions.