Lectures on instantons

Abstract

This is a self-contained set of lecture notes on instantons in (super) Yang-Mills theory in four dimensions and in quantum mechanics. First the basics are derived from scratch: the regular and singular one-instanton solutions for Yang-Mills theories with gauge groups SU(2) and SU(N), their bosonic and fermionic zero modes, the path integral instanton measure, and supersymmetric Yang-Mills theories in Euclidean space. Then we discuss applications: the θ-angle of QCD, the solution of the U(1) problem, the way Higgs fields solve the large-instanton problem, and tunneling and phase transitions in quantum mechanics and in nonabelian gauge theories. These lecture notes are an extension of a review on Yang-Mills and D-instantons written in 2000 by both authors and A.Belitsky

118 pages, 11 figures

References in corpus (19)

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• Instantons in QCD
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• Instantons in supersymmetric Yang-Mills and D-instantons in IIB superstring theory
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• Euclidean SYM Theories by Time Reduction and Special Holonomy Manifolds
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• The anomaly in the central charge of the supersymmetric kink from dimensional regularization and reduction
• Instantons, Euclidean supersymmetry and Wick rotations
• Instanton-induced Yang-Mills correlation functions at large N and their AdS_5xS^5 duals
• Instantons in $\mathcal{N}=2$ $Sp(N)$ Superconformal Gauge Theories and the AdS/CFT Correspondence
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• Explicit construction of constrained instantons
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Cited by in corpus (31)

• Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry
• Les Houches Lectures on Constructing String Vacua
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• Singular values of the Dirac operator in dense QCD-like theories
• (2,0) Supersymmetry and the Light-Cone Description of M5-branes
• (S)QCD on R^3 x S^1: Screening of Polyakov loop by fundamental quarks and the demise of semi-classics
• $N^3$ entropy of M5 branes from dielectric effect
• Nonperturbative quark-antiquark interactions in mesonic form factors
• Instanton solutions mediating tunneling between the degenerate vacua in curved space
• Oscillating instanton solutions in curved space
• Gravitational Instantons and Euclidean Supersymmetry
• Fractionalized Non-Self-Dual Solutions in the CP(N-1) Model
• Gluon Green functions free of Quantum fluctuations
• Resolution of SU(2) monopole singularities by oxidation
• Chiral symmetry breaking with no bilinear condensate revisited
• Dynamical gluon mass in the instanton vacuum model
• Boundary conditions for SU(2) Yang-Mills on $Ad{S}_4$
• Para-Complex Geometry and Gravitational Instantons
• Two-loop corrections to false vacuum decay in scalar field theory
• The holographic dual to supergravity instantons in $\mathrm{Ad}{\mathrm{S}}_5\times {\mathrm{S}}^5/{\mathbb{Z}}_{\mathrm{k}}$
• Radiative corrections to false vacuum decay in quantum mechanics
• Gravitational and Yang-Mills instantons in holographic RG flows
• $N^2$ entropy of 4D N=4 SYM
• Multiple M-branes and 3-algebras
• Instanton corrections to the effective action of N=4 SYM
• The mixed $0$-form/$1$-form anomaly in Hilbert space: pouring new wine into old bottles
• Non-perturbative Treatments of the Bosonic String and the Axion with Cosmological Implications
• D-instantons and Dualities in String Theory
• Holographic RG flows in N=4 SCFTs from half-maximal gauged supergravity
• Holographic backgrounds from D-brane probes
• Supersymmetric generalization of the maximal Abelian gauge