Holographic dark energy as a source for wormholes in modified gravity

In this work, we analyze the properties of wormhole solutions in modified gravitational theory, i.e., f ( R , T ) , where R denotes the Ricci scalar and T represents the trace of the energy-momentum tensor. We develop wormhole models by employing holographic dark energy density profiles inspired by Rényi, Moradpour and Bekenstein-Hawking, expressed respectively as: ρ R = α 4 α 1 r 4 c 2 κ ln ( 1 + π α 1 r 2 ) , ρ M = α 4 π r 2 c 2 κ ( π α 1 r 2 + 1 ) , ρ B H = α 4 c 2 κ r 2 , where α and β are dimensional parameters of units L − 2 . The derived shape functions satisfy the necessary conditions for traversable wormholes. We examine the influence of parameters α and β on the equilibrium state and violation of energy conditions. Our analysis reveals that the null-energy condition (NEC) is not satisfied, thereby indicating the necessary of exotic matter. Geometric features are further explored through embedding diagrams.