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arXiv · hep-th/0202152

W(E_10) Symmetry, M-Theory and Painleve Equations

Shun'ya Mizoguchi·Yasuhiko Yamada
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Abstract

The Weyl group symmetry W(E_k) is studied from the points of view of the E-strings, Painleve equations and U-duality. We give a simple reformulation of the elliptic Painleve equation in such a way that the hidden symmetry W(E_10) is manifestly realized. This reformulation is based on the birational geometry of the del Pezzo surface and closely related to Seiberg-Witten curves describing the E-strings. The relation of the W(E_k) symmetry to the duality of M-theory on a torus is discussed on the level of string equations of motion.

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Shun'ya Mizoguchi, Yasuhiko Yamada. 2002-03-04. W(E_10) Symmetry, M-Theory and Painleve Equations. https://doi.org/10.1016/s0370-2693(02)01870-1

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