W(E_10) Symmetry, M-Theory and Painleve Equations
High Energy Physics - Theory
2009-11-07 v2
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.
Keywords
Cite
@article{arxiv.hep-th/0202152,
title = {W(E_10) Symmetry, M-Theory and Painleve Equations},
author = {Shun'ya Mizoguchi and Yasuhiko Yamada},
journal= {arXiv preprint arXiv:hep-th/0202152},
year = {2009}
}
Comments
14 pages, dedicated to the memory of Sung-Kil Yang, references added