Borcherds-Kac-Moody Symmetry of N=4 Dyons

Understand

We consider compactifications of heterotic string theory to four dimensions on CHL orbifolds of the type T^6 /Z_N with 16 supersymmetries.

• The exact partition functions of the quarter-BPS dyons in these models are given in terms of genus-two Siegel modular forms.
• Only the N=1,2,3 models satisfy a certain finiteness condition, and in these cases one can identify a Borcherds-Kac-Moody superalgebra underlying the symmetry structure of the dyon spectrum.
• We identify the real roots, and find that the corresponding Cartan matrices exhaust a known classification.