Supersymmetric Gauged Scale Covariance in Ten and Lower Dimensions

We present globally supersymmetric models of gauged scale covariance in ten, six, and four-dimensions. This is an application of a recent similar gauging in three-dimensions for a massive self-dual vector multiplet. In ten-dimensions, we couple a single vector multiplet to another vector multiplet, where the latter gauges the scale covariance of the former. Due to scale covariance, the system does not have a lagrangian formulation, but has only a set of field equations, like Type IIB supergravity in ten-dimensions. As by-products, we construct similar models in six-dimensions with N=(2,0) supersymmetry, and four-dimensions with N=1 supersymmetry. We finally get a similar model with N=4 supersymmetry in four-dimensions with consistent interactions that have never been known before. We expect a series of descendant theories in dimensions lower than ten by dimensional reductions. This result also indicates that similar mechanisms will work for other vector and scalar multiplets in space-time lower than ten-dimensions.