String Theory Journal Club

The counting of BPS black hole microstates has been an important development in string theory. Subsequently a degeneracy formula for 1/4-BPS dyons for 4d black holes has also been derived. This takes the form of an integral over the Weyl denominator of a Borcherds-Kac-Moody algebra. 1/4-BPS dyons can decay into pairs of electric and magnetic 1/2-BPS states at walls of marginal stability given by Weyl chamber boundaries associated to the algebra. We construct an analogous Lie algebraic counting function for 4d N=2 theories including Seiberg-Witten theory using subalgebras from the N=4 theory. This counting function also corresponds to the Weyl denominator of a Lie algebra and therefore encodes the walls and chambers in the theory including both BPS walls and walls of marginal stability. It subsequently counts the number of BPS states existing within each chamber.