多重 M5 膜: 高階規範場論與自對偶性

Abstract

在學習自對偶場論的基本架構之後,我們建造一個在六維時空的非阿貝爾高階規範自對偶場論。此理論在緊緻化後可以變成一般的 Yang-Mills 規範場論並且在阿貝爾極限底下自洽地回到已知的羅倫茲對稱自對偶模型。此理論將預期可用來描述 M 理論中的多重五膜。 我們也討論此模型的一些推廣情形及其物理內涵。

We first review self-dual (chiral) gauge field theories by studying their Lorentz non-covariant and Lorentz covariant formulations. Then we construct a non-Abelian gauge theory of self-dual two-form potentials in six dimensions with a spatial direction compactified on a circle. We will see that this model reduces to the Yang-Mills theory in five dimensions for a small compactified radius R. This model also reduces to the Lorentz-invariant theory of Abelian self-dual two-form potentials when the gauge group is Abelian. The model is expected to describe multiple 5-branes in M-theory. We will also discuss its decompactified limit and other generalizations.