Tachyonic crystals and the laminar instability of the perturbative vacuum in asymptotically free gauge theory H. B. Thacker Department of Physics, University of Virginia, P.O. Box 400714 Charlottesville, VA 22901-4714 I. INTRODUCTION (Dated: August 10, 2018) Lattice Monte Carlo studies in SU (3) gauge theory have shown that the topological charge distribution in the vacuum is dominated by thin coherent membranes of codimension one arranged in a layered, alternating-sign sandwich. A similar lamination of topological charge occurs in the 2D CP N$_{−}$ 1 model. In holographic QCD, the observed topological charge sheets are naturally interpreted as D 6 branes wrapped around an S 4 .. With this interpretation, the laminated array of topological charge membranes observed on the lattice can be identified as a “tachyonic crystal,” a regular, alternating-sign array of D 6 and ¯ D 6 branes that arises as the final state of the decay of a non-BPS D 7 brane via the tachyonic mode of the attached string. In the gauge theory, the homogeneous, space-filling D 7 brane represents the perturbative gauge vacuum, which is unstable toward lamination associated with a marginal tachyonic boundary perturbation ∝ cos( $_{X/}$√$_{2}$$_{α}$ ′ ). For the CP N$_{−}$ 1 model, the cutoff field theory can be cast as the low energy limit of an open string theory in background gauge and tachyon fields A$_{µ}$ ( x ) and λ ( x ). This allows a detailed comparison with large N field theory results and provides strong support for the tachyonic crystal interpretation of the gauge theory vacuum. Monte Carlo studies of 4-dimensional SU(3) gauge theory [1, 2] and parallel studies of 2- dimensional CP $^{N}$− 1 models [3–5] have shown that the topological charge density in the vacuum of these theories is dominated by extended coherent codimension-one sheets. These results point to a new paradigm for the physical vacuum of asymptotically free gauge theories. The vacuum appears to be a laminated “topological sandwich” consisting of densely packed, alternating sign membranes of topological charge. The possible interpretation of these topological charge membranes as the holographic dual of D6 branes in Witten’s type IIa string theory formulation of holographic QCD [6] has been discussed in [3, 7]. Locally, the membranes are flat, parallel, alternating in sign, and arXiv:1001.4215v1 [hep-th] 24 Jan 2010