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 $N=\infty$ exhibit adiabatic continuity at finite-$N$, and also become semi-classically calculable on small ${\mathbb{R}}^3\times S^1$. 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.

28 pages, 5 figures

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• Some remarks on Lefschetz thimbles and complex Langevin dynamics
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• Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
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• Symmetry Breaking In Twisted Eguchi-Kawai Models
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• Planar Limit of Orientifold Field Theories and Emergent Center Symmetry
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• Vacuum structure of bifundamental gauge theories at finite topological angles
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• Two-flavor adjoint QCD
• Confinement in the bulk, deconfinement on the wall: infrared equivalence between compactified QCD and quantum magnets
• Global symmetries, volume independence and continuity
• Cheshire Cat resurgence, Self-resurgence and Quasi-Exact Solvable Systems
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• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
• From 4d Yang-Mills to 2d ${\mathbb{CP}}^{N-1}$ model: IR problem and confinement at weak coupling
• Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics
• Resummation of diagrammatic series with zero convergence radius for strongly correlated fermions
• Candidate Phases for SU(2) Adjoint QCD${}_4$ with Two Flavors from $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory
• Gravitational Waves from Dark Yang-Mills Sectors
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj)
• Fractional $\theta$ angle, 't Hooft anomaly, and quantum instantons in charge-$q$ multi-flavor Schwinger model
• D-instantons, String Field Theory and Two Dimensional String Theory
• Non-Perturbative Completion of Hopf-Algebraic Dyson-Schwinger Equations
• Uniformization and Constructive Analytic Continuation of Taylor Series
• Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly Matching
• On exact-WKB analysis, resurgent structure, and quantization conditions
• Asymptotic safety with Majorana fermions and new large N equivalences
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
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• Critical Points at Infinity, Non-Gaussian Saddles, and Bions
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• Deconfinement on axion domain walls
• Existence of real time quantum path integrals
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• Instantons in Chiral Magnets
• The Myriad Uses of Instantons
• Testing the Bethe ansatz with large N renormalons
• String tensions in deformed Yang-Mills theory
• The gaugino condensate from asymmetric four-torus with twists
• Deconfinement and CP-breaking at $\theta =\pi$ in Yang-Mills theories and a novel phase for SU(2)
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• Analytic Continuation of Spin foam Models
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• Quantum oscillations in the zeroth Landau Level and the serpentine Landau fan
• Resurgence and renormalons in the one-dimensional Hubbard model
• Thermal order in large N conformal gauge theories
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• Free energy of a Holonomous Plasma
• Self-conjugate QCD
• Condensates and anomaly cascade in vector-like theories
• Semiclassical analysis of the bifundamental QCD on ${\mathbb{R}}^2\times T^2$ with 't Hooft flux
• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions
• Symmetry breaking at high temperatures in large N gauge theories
• Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow
• Non-Wilsonian ultraviolet completion via transseries
• The $1/N$ expansion for SO(N) lattice gauge theory at strong coupling
• Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons matter theories
• New nonperturbative scales and glueballs in confining supersymmetric gauge theories
• Renormalons beyond the Borel plane
• Strongly coupled QFT dynamics via TQFT coupling
• Non-Perturbative Large N Trans-series for the Gross-Witten-Wadia Beta Function
• TQFT at work for IR-renormalons, resurgence and Lefschetz decomposition
• Natural inflation, strong dynamics, and the role of generalized anomalies
• The Response Field and the Saddle Points of Quantum Mechanical Path Integrals
• Cluster expansion and resurgence in Polyakov model
• Three roads to the energy gap
• Confinement on ${\mathbb{R}}^3\times {\mathbb{S}}^1$ and Double-String Collapse
• Topological Casimir effect in a quantum LC circuit: real-time dynamics
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• Infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$
• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
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• Vacuum energy of the supersymmetric $\mathbb{C}{P}^{N-1}$ model on $\mathbb{R}\times S^1$ in the $1/N$ expansion
• Introductory Lectures on Resurgence: CERN Summer School 2024
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• Cosmological Weyl-Einsteinian-Cubic Gravity as a Gauge Theory of Gravity
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