Abstract:

It was recently understood that when QCD, or any vectorlike or chiral gauge theory, is compactified on a small circle, the physics responsible for confinement becomes analytically tractable via non-perturbative semi-classical methods. I will first give a qualitative review of the key players - some old and some recent - the Polyakov mechanism of confinement, the twisted ``monopole-instantons" in circle compactifications (first discovered via string theory D-branes), the role of center-stabilizing double-trace deformations, and the relevant index theorem. I will then argue that these ingredients explain confinement via novel non-self-dual topological excitations. These can be ``bions", ``triplets", ``quintets", etc., depending on the massless fermion content of the theory, somewhat at odds with conventional wisdom associating confinement with pure glue only. While the semi-classical solvability at small circle size does not apply to QCD in the decompactification limit, it allows for qualitative studies of the phase diagram of any theory with massless fermions. In particular, it helps address the question of when a theory ceases to confine and becomes conformal upon adding extra massless fermionic species. Our predictions for the ``conformal window" in QCD and other vectorlike or chiral gauge theories will be compared to those obtained by lattice simulations and other tools.