Weyl invariance with a nontrivial mass scale
  A theory with a mass scale and yet Weyl invariant is presented. The theory is not invariant under all diffeomorphisms but only under transverse ones. This is the reason why Weyl invariance does not imply scale invariance in a free falling frame. Physical implications of this framework are discussed. 
Enrique Alvarez, Sergio Gonz\'alez-Mart\'in
hep-th