Adjoint Reidemeister torsions of once-punctured torus bundles

Gang, Kim and Yoon have recently proposed a conjecture on a vanishing identity of adjoint Reidemeister torsions of hyperbolic 3-manifolds with torus boundary, from the viewpoint of wrapped M5-branes. In this paper, we provide infinitely many new supporting examples and an infinite family of counterexamples to this conjecture. These families come from hyperbolic once-punctured torus bundles with tunnel number one. We also propose a modified conjecture to exclude our counterexamples and show that it holds true for all hyperbolic once-punctured torus bundles with tunnel number one.