Lie 3-Algebra Non-Abelian (2,0) Theory in Loop Space

Details Lie 3-Algebra Non-Abelian (2,0) Theory in Loop Space Lie 3-Algebra Non-Abelian (2,0) Theory in Loop Space

2010-08-23

arxiv.org/abs/1008.3834v2

Physics

High Energy Physics

High Energy Physics - Theory

Latex 18 pages, typos corrected, Detail several calculations

Scientific paper

It is believed that the multiple M5-branes are described by the non-abelian (2,0) theory and have the non-local structure. In this note we investigate the non-abelian (2,0) theory in loop space which incorporates the non-local property. All fields will be formulated as loop fields and the two-form potential becomes a part of connection. We make an ansatz for field supersymmetry transformation with a help of Lie 3-algebra and examine the closure condition of the transformation to find the field equations. However, the closure conditions lead to several complex terms and we have not yet found a simple form for some constrain field equations. In particular, we present the clear scheme and several detailed calculations in each step. Many useful $\Gamma$ matrix algebras are derived in the appendix.

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