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Borcherds-Kac-Moody Symmetry of N=4 Dyons
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. 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.Comment: 44 pages, 1 figur
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