The heterotic string
Katrin Becker, Melanie Becker, John H. Schwarz · Cambridge University Press eBooks · 2006
The preceding chapters have described bosonic strings as well as type I and type II superstrings. In the case of the bosonic string, one was led to 26-dimensional Minkowski space-time by the requirement of cancellation of the conformal anomaly of the world-sheet theory. Similar reasoning led to the conclusion that the type I and type II superstring theories should have D = 10. In all of these theories the world-sheet degrees of freedom can be divided into left-movers and right-movers, though in the case of open strings these are required to combine so as to give standing waves. In the case of the type II superstring theories, the left-moving and right-moving modes introduce independent conserved supersymmetry charges, each of which is a Majorana–Weyl spinor with 16 real components. Thus, the type II superstring theories have two such conserved charges, or N = 2 supersymmetry, which means that they have 32 conserved supercharges. The type IIA and type IIB theories are distinguished by whether the two Majorana–Weyl spinors have the same (IIB) or opposite (IIA) chirality. In the case of the type I theory, as well as related theories whose construction involves an orientifold projection, the only conserved supercharge that survives the projection is the sum of the left-moving and right-moving supercharges of the type IIB theory. Thus these theories have N = 1 supersymmetry in ten dimensions.