Abstract:
This thesis studies the problem of counting dyons in certain supersymmetric string theory models and the infinite dimensional Lie algebras that underlie the dyonic degeneracies. The counting of 1/4 BPS states in N = 4 supersymmetric four-dimensional string theories can be carried out in a mathematically precise and rigorous fashion due to the fact that the spectrum of these BPS states can be generated by genus-two modular forms[1,2]. The same modular form also occurs in the context of Borcherds-Kac-Mody(BKM) Lie super algebras[3,4] in their dominator identities. The surprising mathematical structure underlying the spectrum of these states is the idea that is developed in this thesis.
