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In the generalized topological quantum field theory constructed by Andersenand Kashaev, invariants of 3-manifolds are defined given the combinatorialstructure of a tetrahedral decomposition. Furthermore, a variant of the volumeconjecture has been proposed in which the hyperbolic volume can be extractedfrom this invariant of the complementary space of the hyperbolic knot in anoriented $3$-dimensional closed manifold. We prove that the reformulated volumeconjecture holds for the complementary space of the hyperbolic knot $7_3$ in$S^3$, given a specific tetrahedral decomposition.

A proof of the Teichm\"{u}ller TQFT volume conjecture for $7_3$ knot