New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
Abstract
We present a broad conceptual introduction to some new ideas in non-perturbative QFT. The large-
N
orbifold-orientifold equivalence connects a natural large-
N
limit of QCD to QCD with adjoint fermions. QCD(adj) with periodic boundary conditions and double-trace deformation of Yang-Mills theory satisfy large-
N
volume independence, a type of orbifold equivalence. Certain QFTs that satisfy volume independence at
N=∞
exhibit adiabatic continuity at finite-
N
, and also become semi-classically calculable on small
R
3
×
S
1
. We discuss the role of monopole-instantons, and magnetic and neutral bion saddles in connection to mass gap, and center and chiral symmetry realizations. Neutral bions also provide a weak coupling semiclassical realization of infrared-renormalons. These considerations help motivate the necessity of complexification of path integrals (Picard-Lefschetz theory) in semi-classical analysis, and highlights the importance of hidden topological angles. Finally, we briefly review the resurgence program, which potentially provides a novel non-perturbative continuum definition of QFT. All these ideas are continuously connected.