The authors review the theory and phenomenology of instantons in quantum chromodynamics (QCD). After a general overview, they provide a pedagogical introduction to semiclassical methods in quantum mechanics and field theory. The main part of the review summarizes our understanding of the instanton liquid in QCD and the role of instantons in generating the spectrum of light hadrons. The authors also discuss properties of instantons at finite temperature and how instantons can provide a mechanism for the chiral phase transition. They give an overview of the role of instantons in some other models, in particular low-dimensional sigma models, electroweak theory, and supersymmetric QCD.

http://wonka.physics.ncsu.edu/~tmschaef/physics/RevModPhys_Instantons.pdf

Instantons in QCD

Recent studies of QCD Green's functions and their applications in hadronic physics are reviewed. We briefly discuss the issues of gauge fixing, BRS invariance and positivity. Evidence for the violation of positivity by quarks and transverse gluons in the covariant gauge is collected, and it is argued that this is one manifestation of confinement. 
We summarise the derivation of the Dyson-Schwinger equations (DSEs) of QED and QCD. The influence of instantons on DSEs in a 2-dimensional model is mentioned. Solutions for the Green's functions in QED in 2+1 and 3+1 dimensions provide tests of various schemes to truncate DSEs. We discuss possible extensions to QCD and their limitations. Truncation schemes for DSEs of QCD are discussed in the axial gauge and in the Landau gauge. We review the available results from a systematic non-perturbative expansion scheme established for Landau gauge QCD. Comparisons to related lattice results, where available, are presented. 
The applications of QCD Green's functions to hadron physics are summarized. Properties of ground state mesons are discussed on the basis of the Bethe-Salpeter equation for quarks and antiquarks. The Goldstone nature of pseudoscalar mesons and mechanisms of diquark confinement are reviewed. We discuss some properties of ground state baryons based on their description as Bethe-Salpeter/Faddeev bound states of quark-diquark correlations in the quantum field theory of confined quarks and gluons.

The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States

The infrared behaviour of QCD Green's functions ☆: Confinement, dynamical symmetry breaking, and hadrons as relativistic bound states

There is accumulating evidence that (fundamental) scalar fields may exist in nature. The gravitational collapse of such a boson cloud would lead to a boson star (BS) as a new type of a compact object. As with white dwarfs and neutron stars, a limiting mass exists similarly, below which a BS is stable against complete gravitational collapse to a black hole. According to the form of the self-interaction of the basic constituents and spacetime symmetry, we can distinguish mini-, axidilaton, soliton, charged, oscillating and rotating BSs. Their compactness prevents a Newtonian approximation; however, modifications of general relativity, as in the case of Jordan?Brans?Dicke theory as a low-energy limit of strings, would provide them with gravitational memory. In general, a BS is a compact, completely regular configuration with structured layers due to the anisotropy of scalar matter, an exponentially decreasing 'halo', a critical mass inversely proportional to the constituent mass, an effective radius and a large particle number. Due to the Heisenberg principle, a completely stable branch exists, and as a coherent state, it allows for rotating solutions with quantized angular momentum. In this review, we concentrate on the fascinating possibilities of detecting the various subtypes of (excited) BSs: possible signals include gravitational redshift and (micro-)lensing, emission of gravitational waves, or, in the case of a giant BS, its dark matter contribution to the rotation curves of galactic halos.

https://iopscience.iop.org/article/10.1088/0264-9381/20/20/201/pdf

General relativistic boson stars

http://cds.cern.ch/record/367814/files/9810070.pdf

Gravitating non-abelian solitons and black holes with yang-mills fields

A comprehensive review of the known classical solutions of $\mathrm{SU}(2)$ gauge theories is presented. The author follows the historical development of this subject from its beginning (the first explicit solution found was an imbedded Abelian static Coulomb solution) up to the most recent work in the field (in particular the solutions which represent monopoles, instantons, and merons). As well as being a detailed survey, this article is intended to serve as a self-contained introduction to the subject.

Classical Solutions of SU(2) Yang-Mills Theories

We discuss some properties of the (instanton—anti-instanton) solution of the SU(2) gauge theory with a massless Higgs doublet recently found by Lipatov, Bukhvostov and Malkov.

Properties of an instanton—anti-instanton solution of a Yang-Mills theory

Elliptic function methods in φ4 theory and Yang-Mills theory

The well-known connection between the SU(2) gauge theory and the massless φ
4 theory is extended to theories with nonzero mass. Elliptic solutions of these massive theories are given. These are of the ‘plane-wave’ variety, with independent variable u=p·x where p
μ is a constant four-vector. They depend on a free parameter k. Two of the solutions are generalized plane-waves while the third describes fluctuations about the vacuum solution.

Alfred Actor

Papers

Classical Solutions of SU(2) Yang-Mills Theories

Properties of an instanton—anti-instanton solution of a Yang-Mills theory

Elliptic function methods in φ4 theory and Yang-Mills theory

Periodic solutions of massive φ 4 and Yang-Mills theories

Classical solutions and the energy-momentum tensor