ADHM construction of (anti-)self-dual instantons in 4n dimensions

Abstract

Abstract:The ADHM construction is a very strong scheme to construct the instantons in four dimensions. We study an ADHM construction of instantons in 4n (n ≥ 2) dimensions by generalizing this scheme. The higher-dimensional ADHM construction generates the 4n-dimensional (anti-)self-dual instantons which satisfy the (anti-)self-dual equation in 4n dimensions: F (n) = ± * 4n F (n). Here F (n) is the nth wedge products of the gauge field strength 2-form F . We also show that our scheme reproduces the known 4n-dimensional one-instantons and there are multi-instanton solutions of the 't Hooft type in the dilute instanton gas limit. Moreover, we discuss a Harrington-Shepard type caloron in 4n dimensions and this monopole limit.

Instantons and Berry's connections on quantum graph

“…Furthermore, the constructions for the O(n) and Sp(n) instantons are known and will be applied to this system. The higher dimensional generalizations of ADHM construction are also discussed in [23,24] and higher dimensional instantons would appear as the Berry's connections.…”

Instantons and Berry’s connections on quantum graph

“…Furthermore, the constructions for the O(n) and Sp(n) instantons are known and will be applied to this system. The higher dimensional generalizations of ADHM construction are also discussed in [26][27][28] and higher dimensional instantons would appear as the Berry's connections.…”

A Unified Construction of Skyrme-type Non-linear sigma Models via The Higher Dimensional Landau Models

“…The self-dual equations of higher dimensional gauge theories were also revealed in 1980s [18,19,20,21,22,24,25,23,26]. An explicit recipe for the derivation of the Skyrmion field configuration from the Yang-Mills gauge theories was proposed by Atiyah and Manton [27,28], which stimulated recent studies about mathematical connections of topological solitons in different dimensions [29,30,31,32,33,34] and [35,36,37,38,39,40,41]. Apart from such deep mathematical structures, Skyrmions now appear ubiquitously in many branches of theoretical physics [42] and are also observed in daily nanoscale magnetic experiments (see [43] and references therein).…”