the large N prediction ∝ θ 2 [5]. The Monte Carlo evidence suggests that, with a finite cutoff, the perturbative vacuum of an asymptotically free confining gauge theory has an instability toward lamination along some di- rection, and that this lamination characterizes the transition from the perturbative vacuum to the physical, confining vacuum. In this paper I will explore the remarkable similarity between the layered, alternating-sign topological sandwich structure observed in the Monte Carlo studies and a well-known but somewhat mysterious structure in string theory called a “tachyonic crystal” [11]. This is a layered, alternating sign, one-dimensional array of codimension-one Dp branes, which arises from the tachyonic decay of an unstable D ( p + 1) brane. In the IIa formulation of holographic QCD, the topological sandwich of D6 branes can be intepreted as the stable tachyonic crystal which arises from the decay of a single spacetime filling D 7 brane. (Both the D 6 branes and the D 7 brane are wrapped around a compact S$_{4}$ and thus appear as 3- and 4-dimensional objects, respectively, in 4-dimensional spacetime.) In this framework, the homogeneous but unstable D 7 brane embodies the axial U (1) symmetry associated with the θ -parameter of the gauge theory. Its decay to an array of D 6 branes breaks this symmetry, thus implementing the axial U (1) anomaly and producing a physical vacuum with nonzero topological susceptibility. The boundary confor- mal field theory (BCFT) methods which provide the framework for our understanding of unstable brane decay [12] should thus be directly applicable to the description of the physical vacuum in asymptotically free gauge theories. In order to gain a clearer understanding of the formation and properties of the topological sandwich vacuum, we will explore these issues in the 2-dimensional CP $^{N}$− 1 model, where we already have some understanding of the physical vacuum based on large N analysis. Since they were first introduced, the CP $^{N}$− 1 models have served as an instructive example of topological charge structure which is in many ways quite similar to 4-dimensional SU ( N ) gauge theory. The study of topological charge distributions in Monte Carlo generated CP $^{N}$− 1 gauge configurations has revealed a topological sandwich structure of extended coherent codimension-one objects [3], completely analogous to the structure found in QCD. The CP $^{N}$− 1 model may be formulated as a theory of N complex scalar fields Z$_{i}$ ( x ) , i = 1 ,... ,N , interacting with an auxiliary U (1) gauge field A$_{µ}$ ( x ) and a scalar Lagrange multiplier field λ ( x ) (which incorporates the constraint Z † Z = 1). In the large N approximation (with a momentum space cutoff), the λ field acquires a VEV, which gives a mass to the Z particles. With massive Z ’s, the one loop effective action for the gauge field acquires an ( F$_{µν}$ ) 2 term, producing a linear Coulomb potential which confines U (1) charge. We will show, by writing the Z-particle propagator in a proper time representation, that the CP $^{N}$− 1 model 4