The authors construct Stueckelberg completions for massive mixed-symmetry tensor fields and derive mixed-symmetry currents and a 't Hooft anomaly for linearized gravity, but a sign error invalidates the (2,1) current as printed.
The Riemann-Lovelock Curvature Tensor
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abstract
In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \le D <4k. In D=2k+1 this identity implies that all solutions of pure kth-order Lovelock gravity are `Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle space times, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D=3, which corresponds to the k=1 case. We speculate about some possible further consequences of Riemann-Lovelock curvature.
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hep-th 1years
2024 1verdicts
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Tensor global symmetries and the Stueckelberg mechanism for tensor fields
The authors construct Stueckelberg completions for massive mixed-symmetry tensor fields and derive mixed-symmetry currents and a 't Hooft anomaly for linearized gravity, but a sign error invalidates the (2,1) current as printed.