Impact of conformal motion on static symmetric perfect fluid spacetimes in f(Q) gravity

In this paper, we study static plane symmetric (SPS) perfect fluid spacetimes via conformal motion within the framework of coincident [Formula: see text] gravity, where [Formula: see text] is a function of the nonmetricity scalar [Formula: see text] For this, first, we derive the field equations of SPS spacetimes in [Formula: see text] gravity considering perfect fluid as a source of energy momentum tensor (EMT). We solve the formulated equations for some important [Formula: see text] gravity models. The models include linear form of [Formula: see text], which acts as a simple modification to gravity, power law [Formula: see text] gravity which accounts for nonlinear curvature effects, the exponential model which is useful in inflationary cosmology and a logarithmic model which is relevant to the late-time cosmic evolution which offers a solution to cosmological constant problem. We also give a graphical analysis of the aforementioned models to illustrate their behavior across different curvature regimes. These models further allow us to obtain a variety of solutions to the field equations. As an application, we investigate the CVFs of the obtained solutions. The CVFs occupy a rich amount of geometric as well as physical structure as they link generators of conformal symmetry algebra to the conservation laws of Physics. Our key findings include some cases where the spacetimes become conformally flat. In such cases, the spacetimes admit fifteen CVFs. In most cases, the spacetimes admit five-dimensional CVFs. In one case, there exist four-dimensional CVFs. The overall dimension of CVFs for the obtained SPS perfect fluid spacetimes in [Formula: see text] gravity turns out to be 4, 5, and 15.