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Mass-deformed BLG theory in light-cone superspace. (English) Zbl 1198.81169

Summary: Maximally supersymmetric mass deformation of the Bagger-Lambert-Gustavsson (BLG) theory corresponds to a non-central extension of the \(d=3\) \(N=8\) Poincaré superalgebra (allowed in three dimensions). We obtain its light-cone superspace formulation which has the novel feature of the dynamical supersymmetry generators being cubic in the kinematical ones. The mass deformation picks a quaternionic direction, described by \(\Omega _m ^n\), which breaks the \(SO(8) R\)-symmetry down to \(SO(4) \times SO(4)\). The Hamiltonian of the theory is shown to be a quadratic form of the dynamical supersymmetry transformations to all orders in the mass parameter \(M\) and the structure constants \(f^{abcd}\).

MSC:

81T60 Supersymmetric field theories in quantum mechanics
81T13 Yang-Mills and other gauge theories in quantum field theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
46S60 Functional analysis on superspaces (supermanifolds) or graded spaces
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References:

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