1998/12/31 by Oliver DeWolfe, Tamas Hauer, Amer Iqbal +1
Physics and Astronomy · #hep-th
published as Adv.Theor.Math.Phys. 3 (1999) 1785-1833 · 32 pages LaTeX, 4 eps figures. A relation between the trace of the monodromy and the determinant of the Cartan matrix is established. The role of the asymptotic charge constraint is clarified
arxiv created 1999/08/06 · arxiv updated 2009/11/30
We begin a classification of the symmetry algebras arising on configurations of type IIB [p,q] 7-branes. These include not just the Kodaira symmetries that occur when branes coalesce into a singularity, but also algebras associated to other physically interesting brane configurations that cannot be collapsed. We demonstrate how the monodromy around the 7-branes essentially determines the algebra, and thus 7-brane gauge symmetries are classified by conjugacy classes of the modular group SL(2,Z). Through a classic map between the modular group and binary quadratic forms, the monodromy fixes the asymptotic charge form which determines the representations of the various (p,q) dyons in probe D3-brane theories. This quadratic form also controls the change in the algebra during transitions between different brane configurations. We give a unified description of the brane configurations extending the DN, EN and Argyres-Douglas HN series beyond the Kodaira cases. We anticipate the appearance of affine and indefinite infinite-dimensional algebras, which we explore in a sequel paper.