Testing the violation of the equivalence principle in the electromagnetic sector and its consequences in f(T) gravity

A violation of the distance-duality relation is directly linked with a temporal variation of the electromagnetic fine-structure constant. We consider a number of well-studied $f\left(T\right)$ gravity models and we revise the theoretical prediction of their corresponding induced violation of the distance-duality relationship. We further extract constraints on the involved model parameters through fine-structure constant variation data, alongside with supernovae data, and Hubble parameter measurements. Moreover, we constrain the evolution of the effective $f\left(T\right)$ gravitational constant. Finally, we compare with revised constraints on the phenomenological parametrisations of the violation of the equivalence principle in the electromagnetic sector.