Vector-tensor fields and Euclidean spaces
We study a novel class of vector-tensor field theories with non-zero scalar and mass tensors. These theories are based on the gradient-flow equation of motion and encode vector-like mass terms. We find that the vector-tensor fields have a simple Euclidean representation in the space of non-perturbative solutions. This gives rise to class of vector-tensor algebraic vector-like solutions in the space of perturbative solutions. These solutions are derived from information in the vector field theory, in which the vector field is represented as a non-perturbative input with the derivative of the vector field. We show that these solutions have a "zoom" in the metric, i.e. they vanish at a later time and a "time" that is in general smaller than the current time. We compare this time with the current time and find that the current time is in general smaller than the time in which the "zooming" occurs.