Kac-Moody Extensions of 3-Algebras and M2-branes

Understand

We study the 3-algebraic structure involved in the recently shown M2-branes worldvolume gauge theories.

• We first extend an arbitrary finite dimensional 3-algebra into an infinite dimensional 3-algebra by adding a mode number to each generator.
• A unique central charge in the algebra of gauge transformations appears naturally in this extension.
• We present an infinite dimensional extended 3-algebra with a general metric and also a different extension with a Lorentzian metric.