Exact solution for a traversable wormhole in a curvature-coupled antisymmetric background field

In this work, we study a traversable wormhole sourced by an ideal matter fluid with an antisymmetric 2-tensor background field coupled to gravity in a scenario of spontaneously broken Lorentz symmetry. Contrary to employed in the literature, we use a nonminimal curvature-coupling term $B^{\mu\nu}B^{\kappa\lambda}R_{\mu\nu\kappa\lambda}$ which incorporates all three kinds of Lorentz-violating coefficient for the pure-gravity sector of the minimal standard-model extension. We find that the wormhole is non-asymptotically globally flat and determine the allowed parameters of the theory, showing that the matter fluid must be necessarily anisotropic. We also analyze the energy conditions, checking their validity range and comparing them with those predicted by general relativity.