Tachyonic crystals and the laminar instability of the perturbative vacuum in asymptotically free gauge theories

Abstract

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 $D6$ 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 $D6$ and $\bar{D6}$ branes that arises as the final state of the decay of a non-BPS $D7$ brane via the tachyonic mode of the attached string. In the gauge theory, the homogeneous, space-filling $D7$ brane represents the perturbative gauge vacuum, which is unstable toward lamination associated with a marginal tachyonic boundary perturbation $\propto \cos(X/\sqrt{2\alpha'})$. 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 $A_{\mu}(x)$ and $\lambda(x)$. 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.