ER = EPR from Distortion Gravity: Traversable Wormholes from Metric-Affine Geometry with Spontaneous Symmetry Breaking

We demonstrate that Distortion Gravity—a metric-affine extension of General Relativity where the affine connection carries independent dynamics—admits traversable wormhole solutions without requiring exotic matter. The wormhole is sustained by two massive vector fields, Vµ (trace non-metricity) and aµ (axial torsion), which un dergo spontaneous symmetry breaking in the high-curvature region near the throat. The negative energy density required to violate the Null Energy Condition is pro vided by the symmetry-broken phase of Vµ, while the axial torsion aµ generates a quantized flux through the throat that modulates the entanglement entropy of quantum fields across the two mouths. We introduce a modified metric ansatz ds2 = −e2Φdt2+H(r)e−2Φ(1−b(r)/r)−1dr2+r2dΩ2, where H(r) = 1+λ(r)(e2Φ−1) and λ(r) is a double Gaussian localized at the throat, and perform an extensive numerical exploration of the 13-dimensional parameter space. Over 57% of the 7,600 tested configurations yield wormholes that are simultaneously stable, open, and traversable. The entanglement entropy across the wormhole is computed via the Ryu-Takayanagi formula modified by the effective Newton constant of Distor tion Gravity. We show that the wormhole connectivity (ER) and the entanglement (EPR) are both mediated by the same axial torsion field aµ, providing a concrete geometric realization of the ER = EPR conjecture.