Scale vs Conformal Invariance in Ultra-Relativistic Field Theory

We argue that when an ultra-relativistic field theory acquires scale invariance it is automatically endowed with conformal invariance, provided that unitarity and locality hold. Using flat space holography we also obtain a c-function for this theory which is monotonically decreasing from the UV to the IR by employing the null energy condition in the bulk. Furthermore we obtain the conformal anomaly for such a theory via the flat space holography technique.