Strong gravitational lensing by a quantum loop black hole with a cloud of strings in a homogeneous plasma

We investigate strong gravitational lensing by a quantum loop black hole with a cloud of strings (CoS), surrounded by homogeneous plasma. The deflection angle is analytically obtained by evaluating the strong-deflection-limit coefficients [Formula: see text] and [Formula: see text], incorporating the combined effects of the cloud-of-strings parameter and plasma parameter.We numerically compute lensing observables, including angular image positions, angular image separations, the flux ratio between the outermost and remaining images, and the time delay between the first and second relativistic images, for the supermassive black holes M87* and Sgr A*. Our results show that the photon-sphere radius and the strong-deflection coefficient [Formula: see text] increase with the CoS and plasma parameters, whereas [Formula: see text] exhibits weakly non-monotonic, parameter-dependent behavior, thereby significantly modifying the lensing observables. In particular, the cloud-of-strings parameter produces more pronounced deviations than the quantum correction and plasma parameters. Furthermore, by comparing the theoretical shadow angular diameter with observational data from the Event Horizon Telescope (EHT), we obtain approximate constraints on the quantum correction parameter [Formula: see text] in the presence of homogeneous plasma and a cloud of strings. The allowed range of [Formula: see text] decreases as the plasma parameter increases, indicating a strong interplay between the plasma parameter and quantum-gravitational corrections.