An important property of the strong interaction which is potentially observable in heavy-ion collisions is local parity violation. It manifests as a charge separation along the direction of the magnetic field, a phenomenon called the Chiral Magnetic Effect (CME). A similar effect in which the presence of a vector charge (e.g., electric charge) causes a separation of chiralities is the Chiral Separation Effect (CSE). Their coupling leads to a wave propagation of the electric charge called the Chiral Magnetic Wave (CMW), causing a charge-dependent anisotropic flow.

The charge dependence of the three-particle correlator $\gamma_{ab}$, often employed as evidence for the CME, is measured in Xe--Xe collisions at $\sqrt{s_{\rm NN}} = 5.44$ TeV. This correlator depends strongly on centrality and is similar to that in Pb--Pb collisions. This finding and the prediction of a significantly larger CME signal in Pb--Pb than Xe--Xe collisions from Monte Carlo calculations including a magnetic field due to spectators point to a large non-CME contribution to the correlator. Furthermore, it is reproduced by the Anomalous Viscous Fluid Dynamics model with values of the CME signal close to zero and by a blast wave model calculation that incorporates background effects. The charge dependence of elliptic ($v_2$) and triangular ($v_3$) flow coefficients of unidentified charged hadrons and pions are used to search for the CMW in Pb--Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV. The $v_3$ results are consistent with those of $v_2$, which suggests a significant background contribution.