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Basis tensor gauge theory (BTGT) is a vierbein analog reformulation of ordinary gauge theories in which the vierbein field describes a Wilson line. One of its interesting properties is the increased degree of locality compared to a Wilson line. A BTGT formulation consistent with phenomenology and perturbative stability requires an introduction of a new lower dimensional continuous symmetry. I will review BTGT (1609.03679, 1712.10118, 1905.08363, 2001.03845) in both Abelian and non-Abelian contexts.