Abstract
We present a generalization of the six-dimensional (2,0) system of arXiv:1007.2982 to include a constant abelian 3-form. For vanishing 3-form this system is known to provide a variety descriptions of parallel M5-branes. For a particular choice of 3-form the system is shown to reduce to that of two M2-branes. Thus this generalised (2,0) system provides a unified description of two parallel M2-branes or M5-branes.
Highlights
The periodic array of M2-branes to a variation of five-dimensional Super-Yang-Mills as a description of M5-branes
In this paper we will generalise the six-dimensional (2,0) superalgebra construction of [11] by including a non-dynamical abelian background three-form.1. Setting this to zero reproduces the previous results which have been proposed as a description of two M5-branes
We show that turning on the background three-form allows some components of the vector to be dynamical and forces a dimensional reduction to three dimensions leading to the maximally supersymmetric field theory of two M2-branes [2, 3]
Summary
Where α, β, γ, γ′, δ are constants to be determined and a dot (·) denotes an arbitrary field. There are additional terms that one could consider the rationale behind this choice of algebra will become clear upon showing how a natural reduction to the M2-branes arises. We will show that the superalgebra closes on shell and we will derive the equations of motion and the constraints that the fields need to satisfy. Before we consider the closure of the algebra we first observe that the fermion equation of motion can be obtained by imposing self-duality of δH. We find that δHμνλ − (⋆δH)μνλ = iǫΓμνλ. Provided that γ′ = 3γ (otherwise one does not find a single expression on the right hand side). We see that the Fermion equation of motion is (3.3)
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