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

Abstract

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.

Latex 18 pages, typos corrected, Detail several calculations

References in corpus (7)

• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Covariant Action for the Super-Five-Brane of M-Theory
• Covariant Action for a D=11 Five-Brane with the Chiral Field
• World-Volume Action of the M Theory Five-Brane
• A Noncommutative M-Theory Five-brane
• The non-Abelian tensor multiplet in loop space

Cited by in corpus (2)

• Non-Abelian Chiral 2-Form and M5-Branes
• Hopf-Wess-Zumino term in the effective action of the 6d, (2, 0) field theory revisted