3 responsible for building up an expected positive delta-function contact term in the topological charge correlator [8]. The contribution of this contact term to the topological susceptibility χ$_{t}$ , (given by the integrated correlator) does not go away in the continuum limit, but in fact combines with the contribution of the negative tail at | x | > 0 to give a positive topological susceptibility which scales properly with the mass gap. (This is true for 4-dimensional SU (3) gauge theory and 2-dimensional CP $^{N}$− 1 for N > 3. The only exceptions are the CP 1 and CP 2 models, which are dominated by small instantons and do not exhibit proper scaling for χ$_{t}$ [4, 9, 10].) The laminated structure appearing at the cutoff scale is thus essential for obtaining the proper continuum physics. Among other things, the topological sandwich vacuum serves as a medium which supports the physical fluctuations of topological charge density in the vacuum, which arise from the bends, folds, phonons, and other deviations from a regular one-dimensional crystal structure. This has the notable effect of replacing locally quantized instanton fluctuations, which would exist in the perturbative vacuum, with unquantized gaussian fluctuations. (Topological charge can flow to and from infinity in a continuous way along the membranes.) The relaxation of the local quantization constraint causes the θ -dependence of the vacuum energy to change from the instanton gas prediction ∝ 1 − cos θ to FIG. 2: The two-point topological charge correlator for the 2-dimensional CP 3 sigma model. The correlation length determined from the ¯ ZZ meson mass varies by a factor of 5 over the range of β ’s plotted. -0.0004 -0.0003 -0.0002 -0.0001 0 1e-04 0.0002 0.0003 0.0004 0 1 2 3 4 5 r (lattice units) beta=0.8 beta=0.9 beta=1.0 beta=1.1 beta=1.2