Traversable wormholes from a smoothed string fluid in 4D Einstein–Gauss–Bonnet gravity

We investigate traversable wormhole solutions in four-dimensional Einstein-Gauss–Bonnet (EGB) gravity sourced by a smoothed string fluid. Originally proposed to model regular black holes, this energy density profile is adapted here to sustain wormhole geometries by allowing for a radially varying equation of state. We obtain zero-tidal-force solutions that satisfy all traversability criteria and remain globally regular. The Gauss–Bonnet (GB) coupling α plays a central role in shaping the throat geometry, allowing the identification of a parameter region ( α ≥ 1 , ɛ ≤ 0 . 1 ) where the null energy condition is satisfied in the vicinity of the throat, representing a significant improvement over general relativistic counterparts. The interplay between the smoothing scale a and the string density ɛ ensures finite curvature invariants while reducing the violation of energy conditions. An analysis of the volume integral quantifier and the complexity factor further shows that strong EGB coupling simultaneously suppresses gravitational complexity and the total amount of exotic matter. These results suggest a phenomenological bridge between regular black holes and traversable wormholes, showing that the same smoothed string-fluid profile can support distinct nonsingular compact geometries once higher-curvature corrections and an effective anisotropic equation of state are taken into account.