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In quantum field theory an instanton is a field configuration with a “topological twist”: not in the connected component of the trivial field configurations. Specifically for gauge fields which mathematically are represented by principal connections, an instanton is a nontrivial underlying principal bundle (or similarly non-trivial associated vector bundle).
The term derives from the special case of instantons on a sphere but modeled as field configurations on a Euclidean space constrained to vanish asymptotically. These look like solutions localized in spacetime: “at an instant”.
Instantons enter the axial anomaly/chiral anomaly in the standard model of particle physics which is thought to be a source of baryogenesis in the early universe. Generally the QCD vacuum state is argued to consist of a superposition of all possible instanton sectors, see at QCD instanton.
More generally, in string theory a brane which wraps a completely spacelike cycle in target space is called an instanton, since the worldvolume of such a brane is localized in the time-direction of target space. Under passing to the effective quantum field theory of the string theory, this reproduces many instantons in the sense of quantum field theory above.
non-perturbative effect, non-perturbative quantum field theory, non-perturbative string theory
string theory FAQ – Isn’t it fatal that the string perturbation series does not converge?
gauge field: models and components
Dan Freed, Karen Uhlenbeck, Instantons and four-manifolds, Springer-Verlag, (1991)
Nicholas Manton, Paul M. Sutcliffe, Topological solitons, Cambridge Monographs on Math. Physics, gBooks
Werner Nahm, Self-dual monopoles and calorons, in Group theoretical methods in physics (Trieste, 1983), pages 189-200. Springer, Berlin (1984) (journal)
See also literature at Yang-Mills instanton.
Yang-Mills instantons on spaces other than just spheres are explicitly discussed in
based on
Chris Isham Gabor Kunstatter, Phys. Letts. v.102B, p.417, 1981. (doi)
Chris Isham Gabor Kunstatter, J. Math. Phys. v.23, p.1668, 1982. (doi)
A generalization is discussed in
Edward Frenkel, A. Losev, Nikita Nekrasov, Instantons beyond topological theory I (arXiv:hep-th/0610149)
Edward Frenkel, A. Losev, Nikita Nekrasov, Instantons beyond topological theory II (arXiv:hep-th/0610149)
Expositions and summaries of this are in
Edward Frenkel, A. Losev, Nikita Nekrasov, Notes on instantons in topological field theory and beyond (arXiv:hep-th/0702137)
Jacques Distler, Localized (2006) (blog)
In string theory (for D-branes).
Edward Witten, World-Sheet Corrections Via D-Instantons, JHEP 0002:030, 2000 (arXiv:hep-th/9907041)
Albion Lawrence, Nikita Nekrasov, Instanton sums and five-dimensional gauge theories, Nucl.Phys. B513 (1998) 239-265 (arXiv:hep-th/9706025)
The study of M-brane instantons originates around
Specifically membrane/M2-brane instantons are further discussed in
In the context of F-theory and M5-brane instantons: