Uncovering infinite symmetries on [p, q] 7-branes: Kac-Moody algebras and beyond
Dec, 199844 pages
Published in:
- Adv.Theor.Math.Phys. 3 (1999) 1835-1891
e-Print:
- hep-th/9812209 [hep-th]
Report number:
- MIT-CTP-2808
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Abstract:
In a previous paper we explored how conjugacy classes of the modular group classify the symmetry algebras that arise on type IIB [p,q] 7-branes. The Kodaira list of finite Lie algebras completely fills the elliptic classes as well as some parabolic classes. Loop algebras of E_N fill additional parabolic classes, and exotic finite algebras, hyperbolic extensions of E_N and more general indefinite Lie algebras fill the hyperbolic classes. Since they correspond to brane configurations that cannot be made into strict singularities, these non-Kodaira algebras are spectrum generating and organize towers of massive BPS states into representations. The smallest brane configuration with unit monodromy gives rise to the loop algebra \hat{E}_9 which plays a central role in the theory. We elucidate the patterns of enhancement relating E_8, E_9, \hat{E}_9 and E_10. We examine configurations of 24 7-branes relevant to type IIB compactifications on a two-sphere, or F-theory on K3. A particularly symmetric configuration separates the 7-branes into two groups of twelve branes and the massive BPS spectrum is organized by E_10 + E_10.- membrane model
- algebra: Kac-Moody
- algebra: affine
- loop space
- spectrum: BPS
- monodromy
- string model
- compactification
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