W(E10) Symmetry, M-Theory and Painleve Equations
Shun'ya Mizoguchi, Yasuhiko Yamada
Abstract
The Weyl group symmetry W(Ek) 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(E10) 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(Ek) symmetry to the duality of M-theory on a torus is discussed on the level of string equations of motion.
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