Vacuum Energies of String Compactified on Torus

N. Sakai, I. Senda
1987 Progress of theoretical physics  
Computation of. the one-loop vacuum energy is attempted for closed bosonic string compactified on various tori. Modular invariance of the one-loop vacuum energy is shown. The divergent tachyon contribution forces us to employ a subtraction prescription. For one-dimensional torus, the affine Kac-Moody algebra for 5U(2) x 5U(2) is realized at the absolute minimum of the vacuum energy. For general r-dimensional torus, the algebra for [5 U (2) x 5 U (2) 1 r is found to be an unstable saddle point.
more » ... detailed study of r=2 case shows that 5U(3) x 5U(3) has the lowest vacuum energy.
doi:10.1143/ptp.77.773 fatcat:5ipjguc2cbduvlbxhdwu6qhqlm