New Nonperturbative Methods in Quantum Field Theory: From Large-NOrbifold 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.Keywords: large-N orbifold and orientifold equivalence, volume independence, double-trace deformations, adiabatic continuity, semi-classical calculability, magnetic and neutral bions, Picard-Lefschetz theory of path integration, and resurgence arXiv:1601.03414v1 [hep-th]

Asymptotic safety with Majorana fermions and new large N equivalences

“…2 after rescaling. Phase diagrams and RG trajectories in these theories are also identical up to (11), and given by Figs. 1 and 2.…”

“…3 and 5). Based on the underlying structure, many more large N equivalences arise in gauge theories with matter and Yukawa interactions, also offering new directions for orbifold reductions [11,49].…”

“…Equivalences or dualities between seemingly different theories can provide valuable insights into the dynamics of quantum fields at weak and strong coupling. Wellknown examples include equivalences between SU , SO, and Sp gauge theories in the limit where the rank of the gauge group is large [1], electric-magnetic duality in supersymmetric theories [2], the seminal AdS/CFT conjecture [3], or equivalences between theories related by orbifold/orientifold projections [4][5][6][7][8][9] where parent and child theories achieve coinciding perturbative expansions in the planar limit, and, under some conditions, nonperturbative equivalence [10,11]. Large N equivalences have also seen many applications in QCD-like theories including on the lattice [12][13][14].…”

From 4d Yang-Mills to 2d ℂℙN − 1 model: IR problem and confinement at weak coupling

“…It was considered in physics independently and later combined with the mathematical idea of resurgence: see e.g., [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. (See also literature on large N twisted Eguchi-Kawai model [35][36][37]).…”

Deconstructing zero: resurgence, supersymmetry and complex saddles

“…It is well-known that in SUSY theories, either quantum field theory (QFT) or quantum mechanics (QM), the ground state energy is zero to all orders in perturbation theory [1,2]: At face value, this appears to be a counter-example to the resurgence idea that perturbative data may be used to deduce non-perturbative saddles, and even the fluctuations around them [3]. In this case, the perturbative (1.1) and non-perturbative data (1.2) appear to be unrelated.…”