DIMENSIONAL REDUCTION AND THE TCP THEOREM IN THE SUPERSTRING THEORY

Abstract

Previously, we have shown that the Kasner solution [Formula: see text] to the D = (M+N+1)-dimensional vacuum Einstein theory [Formula: see text], where dx2 and dy2 are flat spaces of dimensionality M and N, respectively, exists only for (M - N)2 = M + N, that is D = 2+4K(K + 1), 1 + 4L2. The first three quantum numbers K = 0, 1, 2 for even D correspond to the three superstring dimensionalities D = 2, 10, 26 and are also given by the condition D = 2 mod 8 for the existence of Majorana–Weyl fermions. Here, we explain this result in terms of world-sheet symmetry and the TCP theorem applied to the superstring theory, the no-scale metric exhibiting T non-invariance which compensates the CP non-invariance due to the fermions, whose chirality thus gives the cosmological arrow of time its sense of direction.