A Geometric Derivation of the Dyon Wall-Crossing Group

TL;DR

This paper provides a geometric derivation of the hyperbolic reflection group governing wall-crossing phenomena of BPS dyons in N=4, d=4 theories, linking it to supersymmetric five-brane networks and M-theory geometry.

Contribution

It offers a new geometric understanding of the wall-crossing group through supersymmetry and M-theory brane configurations, extending previous supergravity results.

Findings

Identifies the hyperbolic reflection group as arising from supersymmetric (p,q) five-brane networks.

Connects the wall-crossing structure to the holomorphicity of M5-brane wrapped Riemann surfaces.

Provides a geometric interpretation consistent with decoupled four-dimensional gravity.

Abstract

Recently, using supergravity analysis, a hyperbolic reflection group was found to underlie the structure of wall-crossing, or the discontinuous moduli dependence of the supersymmetric index due to the presence of walls of marginal stability, of the BPS dyons in the N=4, d=4 compactification. In this paper we work in the regime where four-dimensional gravity decouples and we show how the presence of such a group structure can be easily understood as a consequence of the supersymmetry of a system of (p,q) five-brane network, or equivalently the holomorphicity of the Riemann surface wrapped by the appropriate M5 branes in the Euclidean M-theory frame.