• DOI:10.4310/CNTP.2009.V3.N1.A2
• Corpus ID: 15377278

Borcherds-Kac-Moody Symmetry of N=4 Dyons

@article{Cheng2008BorcherdsKacMoodySO,
  title={Borcherds-Kac-Moody Symmetry of N=4 Dyons},
  author={Miranda C N Cheng and Atish Dabholkar},
  journal={Communications in Number Theory and Physics},
  year={2008},
  volume={3},
  pages={59-110}
}

• Miranda C N Cheng, A. Dabholkar
• Published 25 September 2008
• Mathematics
• Communications in Number Theory and Physics

We consider compactifications of heterotic string theory to four dimensions on CHL (Chaudhuri-Hockney-Lykken) orbifolds of the type T /ZN with N = 4 supersymmetry. The exact partition functions of the quarter-BPS (Bogomol’nyi-Prasad-Sommerfeld) 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. We show that the Siegel modular form satisfies the Weyl denominator identity of the algebra, which enables the determination of all root multiplicities. Furthermore, the Weyl group determines the structure of wall-crossings and the attractor flows of the theory. For N > 4, no such interpretation appears to be possible.