2022/08/21 by Berman, David S., Gherardini, Tancredi Schettini
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2208.09891
We examine a generalisation of the usual self-duality equations for Yang-Mills theory when the colour space admits a non-trivial involution. This involution allows us to construct a non-trivial twist which may be combined with the Hodge star to form a twisted self-dual curvature. We will construct a simple example of twisted self-duality for su(2) ⊕ su(2) gauge theory along with its explicit solutions and then dimensionally reduce from four dimensions to obtain families of non-trivial non-linear equations in lower dimensions. This twisted self-duality constraint will be shown to arise in E7 exceptional field theory through a Scherk-Schwarz reduction and we will show how an Eguchi-Hanson gravitational instanton also obeys the twisted self-duality condition.