Chiral Condensation and Chiral Phase Diagram under Combined Rotation and Chemical Potential in Holographic QCD

We investigate the combined effects of rotation and finite quark chemical potential on inhomogeneous chiral condensation and the chiral phase diagram within the soft-wall holographic QCD model. Using the five-dimensional AdS-RN metric, we study the spatial profile of the chiral condensate and the resulting $T-\mathrm{\Omega }$ phase diagram under Neumann and Dirichlet boundary conditions. Increasing $\mathrm{\Omega }$ induces strong spatial inhomogeneity: the condensate is suppressed more strongly near the edge than at the center, and vanishes at the boundary when $\mathrm{\Omega }$ exceeds a critical value. The chemical potential $\mu$ acts as a global suppression factor, reducing the condensate magnitude without altering the spatial pattern. The $T-\mathrm{\Omega }$ phase diagrams are investigated for different chemical potentials .For the case $\mu$ = 0, they are also studied at different distances from the rotation axis. It is found that both $\mathrm{\Omega }$ and $\mu$ lower the chiral phase transition temperature, and their suppression effects are additive. In a rotating system, the critical temperature becomes position-dependent, decreasing with increasing distance from the rotation axis. These findings reveal a rich, spatially dependent phase structure in rotating QCD matter, relevant for non-central heavy-ion collisions.