Heterotic Superstrings

This kind of theory involves only closed strings. Thus there are left and right sectors. The left-moving sector contains a bosonic string theory and the right-moving sector contains superstrings. This theory is supersymmetric on the right sector only, thus the theory contains ${\cal N}=1$ spacetime supersymmetry. The momentum at the left sector $P_L$ lives in 26 dimensions, while $P_R$ lives in 10 dimensions. It is natural to identify the first ten components of $P_L$ with $P_R$. Consistency of the theory tell us that the extra 16 dimensions should belong to the root lattice $E_8 \times E_8$ or a ${\bf Z}_2$-sublattice of the SO(32) weight lattice. The spectrum consists of a tachyon in the ground state of the left-moving sector. In both sectors we have the spacetime metric $G_{IJ}$, the antisymmetric tensor $B_{IJ}$, the dilaton $\phi$ and finally there are 496 gauge fields $A_I$ in the adjoint representation of the gauge group $E_8 \times E_8$ or SO$(32)$. All these Types of superstring theories do admit a low energy effective description in terms of a supergravity theory. These theories involves the corresponding background fields of their spectra. Supergravity actions of these diverse types will be constructed later to study strong/weak coupling duality in string theory. truecm