N = 8 Superconformal Algebra and the Superstring

The superstring in D=3; 4 and 6 is invariant under an N=D\Gamma2 superconformal algebra based on d S D\Gamma3 . There is a direct relationship between this (world-sheet) symmetry and the super-Poincar'e (target space) symmetry. We establish this relationship using the light-cone gauge, show how the statement generalizes to D= 10 and examine the properties of the N = 8 superconformal algebra and the possible implications of its existence. Published in Phys.Lett. 311B (1993) 76. In order to understand the physics of a certain model, we need to find its symmetries. The crucial step in the Veneziano model [1] was the discovery of the Virasoro algebra [2], the infinite-dimensional conformal symmetry. It led to the no-ghost theorem, and in the modern era it has been used e.g. to construct string field theory. It was also the extension of this symmetry to the superconformal one by Ramond [3] that led to the Ramond-Neveu-Schwarz model [3,4] we use today. However, in this formalism global ..