南部-泊松M5膜世界體理論及賽伯格威騰映射

Abstract

M-theory is hoped to unify five superstring theories. In M-theory, there exists two fundamental extensive objects, M2- and M5-branes. They can relate to fundamental strings and D-branes by compactifying some directions of M-branes on a nontrivial submanifold. Recently, BLG model is proposed by manipulating Lie 3-algebra to construct multiple coincident M2-branes theory, which is a superconformal non-abelian gauge theory. Furthermore, manipulating a specific kind of Lie 3-algebra 'Nambu-Poisson bracket,' a single M5-brane theory is realized from the BLG M2-branes theory. Using double dimensional reduction, this theory can be reduced to the first order in coupling constant g of the noncommutative U(1) gauge theory on a D4-brane world-volume. But the Nambu-Poisson M5-brane theory cannot be deformed such that it reduces to the higher order terms of the Moyal bracket of the D4-brane theory. Therefore, we provide a no-go theorem describing that it is impossible to construct the higher order terms to match these two theories, at least perturbatively and in large C field background. A second order solution of Seiberg-Witten map of the theory is given, there appears an ambiguity for gauge transformation. An exact solution is also given without any free parameter.