Carroll z-scale invariance of Carroll-invariant scalar and vector field theories

In this thesis, we determine the Carroll z-scale invariance of Carroll(-invariant) scalar and vector field theories where z is an anisotropy parameter of Lifschitz type and z = 1 describes the isotropic (or “standard”) scale. We mainly focus on Carroll swiftons, namely the bi-scalar, multi-scalar, electromagnetic and 2d dilaton gravity swifton model, recently introduced in the preprint [1] where we determine the scaling exponents for the scalar and vector fields, interaction terms, possible potentials and coupling functions of the field theories. We see that the bi-scalar, multi-scalar and electromagnetic model introduce the same restriction on the scale z which makes it possible to combine different interaction terms as well as spin- 0 and spin- 1 Carroll field theories. Furthermore, we show that the Carroll swifton scalar field action cannot be extended to the Carroll extremal surface if one wants Carrol z-scale invariance.