D-branes, Wilson Bags, and Coherent Topological Charge Structure in QCD

Abstract

Monte Carlo studies of pure glue SU(3) gauge theory using the overlap-based topological charge operator have revealed a laminar structure in the QCD vacuum consisting of extended, thin, coherent, locally 3-dimensional sheets of topological charge embedded in 4D space, with opposite sign sheets interleaved. Studies of localization properties of Dirac eigenmodes have also shown evidence for the delocalization of low-lying modes on effectively 3-dimensional surfaces. In this talk, I review some theoretical ideas which suggest the possibility of 3-dimensionally coherent topological charge structure in 4-dimensional gauge theory and provide a possible interpretation of the observed structure. I begin with Luscher's ``Wilson bag'' integral over the 3-index Chern-Simons tensor. The analogy with a Wilson loop as a charged world line in 2-dimensional $CP^{N-1}$ sigma models suggests that the Wilson bag surface represents the world volume of a physical membrane. The large-N chiral Lagrangian arguments of Witten also indicate the existence of multiple ``k-vacuum'' states with discontinuous transitions between k-vacua at $θ=$ odd multiples of $π$. The domain walls between these vacua have the properties of a Wilson bag surface. Finally, I review the AdS/CFT duality view of $θ$ dependence in QCD. The dual realtionship between topological charge in gauge theory and Ramond-Ramond charge in type IIA string theory suggests that the coherent topological charge sheets observed on the lattice are the holographic image of wrapped D6 branes.