Generalised Chern-Simons Theory and G₂-Instantons over Associative Fibrations

Abstract

Abstract. Adjusting conventional Chern-Simons theory to G 2 -manifolds, one describes G 2 -instantons on bundles over a certain class of 7-dimensional flat tori which fiber nontrivially over T 4 , by a pullback argument. Moreover, if c 2 = 0, any (generic) deformation of the G 2 -structure away from such a fibred structure causes all instantons to vanish. A brief investigation in the general context of (conformally compatible) associative fibrations f : Y 7 → X 4 relates G 2 -instantons on pullback bundles f * E → Y and self-dual connections on the bundle E → X over the base, a fact which may be of independent interest.

Deformations of Nearly Kähler Instantons

“…Although instantons were first introduced in dimension four, the study of instantons on manifolds of dimension greater than four has a long history [1,6,7,13,14,16,17,[19][20][21]30,33,34,[36][37][38]40,41,43,[46][47][48][49][50][51][52][53][54][55][56][57][58][59] (not to mention the long and fruitful study of Hermitian-Yang-Mills connections). In favourable circumstances instantons solve the Yang-Mills equation; for this reason and others the study of instantons informs string theory, supergravity, and theoretical physics.…”

The Infinitesimal Moduli Space of Heterotic G 2 Systems

“…Furthermore, the geometric moduli for G 2 holonomy manifolds have been determined by Joyce [17,18], and explored further in the references [19][20][21][22][23][24][25][26]. Finally, deformations of G 2 instanton bundles have been studied [27][28][29][30][31].…”

Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

“…Deformations of instanton bundles over G 2 manifolds have been studied before, see e.g. [34][35][36][37][38], and deformation studies of G structures with instantons also appeared recently in [39][40][41].…”