On world-volume supersymmetry of supermembrane action in static gauge
Authors
Arkady A. Tseytlin, Zihan Wang
Categories
Abstract
We review and elaborate on the issue of 3d world volume supersymmetry that appears as a residual part of global target space supersymmetry in the BST supermembrane action. While there is no direct ``spinning membrane'' analog of the world-volume supersymmetric spinning string action that could be obtained by coupling $D$ copies of 3d scalar multiplet to 3d supergravity, we discuss how one may construct an $N=1$ 3d supersymmetric analog of the derivative expansion of the bosonic membrane action in static gauge. We compare the resulting $N=1$ supersymmetric action for eight 3d scalar multiplets to the $N=8$ 3d supersymmetric action describing the $D=11$ supermembrane in the static gauge. The two actions are not equivalent which is related to the fact that the full $N=8$ supersymmetry of the static-gauge $D=11$ supermembrane action can be realised only if the fermions are described by an $SO(8)$ spinor rather than vector. The two actions are still directly related in special dimensions $D=4$ and 5. We also compute the one-loop world-volume scattering amplitudes for the two theories, finding that they indeed agree for $D=4,5$ but disagree for $D=11$.
On world-volume supersymmetry of supermembrane action in static gauge
Categories
Abstract
We review and elaborate on the issue of 3d world volume supersymmetry that appears as a residual part of global target space supersymmetry in the BST supermembrane action. While there is no direct ``spinning membrane'' analog of the world-volume supersymmetric spinning string action that could be obtained by coupling $D$ copies of 3d scalar multiplet to 3d supergravity, we discuss how one may construct an $N=1$ 3d supersymmetric analog of the derivative expansion of the bosonic membrane action in static gauge. We compare the resulting $N=1$ supersymmetric action for eight 3d scalar multiplets to the $N=8$ 3d supersymmetric action describing the $D=11$ supermembrane in the static gauge. The two actions are not equivalent which is related to the fact that the full $N=8$ supersymmetry of the static-gauge $D=11$ supermembrane action can be realised only if the fermions are described by an $SO(8)$ spinor rather than vector. The two actions are still directly related in special dimensions $D=4$ and 5. We also compute the one-loop world-volume scattering amplitudes for the two theories, finding that they indeed agree for $D=4,5$ but disagree for $D=11$.
Authors
Arkady A. Tseytlin, Zihan Wang
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