Density correlations under global and local charge conservation

This work presents a formalism to compute spatial $n$-point correlations of a conserved charge density in a large thermal system in the canonical ensemble, with explicit results presented up to 4th order. The resulting correlators contain local and balancing terms expressed through the grand-canonical susceptibilities for any equation of state. The new formalism is used to introduce a Gaussian local baryon number conservation in (spatial) rapidity in heavy-ion collisions at LHC conditions through a modulation of the balancing term. Connection to the conservation volume $V_c$ approach is established, indicating that the latter is appropriate for observables within a limited range around midrapidity. Quantitative analysis of the experimental data of the ALICE Collaboration on net proton cumulants in central Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV shows significant evidence for local baryon conservation.