Holographic dark energy as a source for slowly rotating wormholes: Implications for null geodesics and shadows

In this work, we explore for the first time slowly rotating traversable wormholes embedded in holographic dark energy. We focus on three representative holographic dark energy models—Rényi, mixed, and Moradpour—and construct the wormhole shape functions directly from these energy density profiles using a Teo-type rotating wormhole metric. This allows us to examine the wormhole geometry in detail, including throat structure, the flaring-out condition for safe traversal, and violations of the null energy condition. To capture the effects of different redshift behaviors, we consider three smooth hyperbolic redshift functions—Sinh, Cosh, and Tanh—and study how they influence photon motion, null geodesics, effective potentials, photon-sphere locations, and Lense-Thirring precession caused by wormhole rotation. Our analysis shows that cuspy Rényi profiles produce tighter photon orbits and stronger asymmetry, while smoother mixed and Moradpour profiles allow more circular paths and weaker frame-dragging effects. Finally, we calculate the shadows cast by these wormholes, finding that Rényi-supported wormholes generate smaller, asymmetric shadows, whereas mixed and Moradpour-supported wormholes produce larger, nearly circular silhouettes. Altogether, this study provides a detailed theoretical picture of photon dynamics, shadow morphology, and relativistic effects in slowly rotating wormholes within realistic holographic dark energy environments, offering potential guidance for observational signatures of these exotic objects.