Final Activity Report Summary - NCGGTH (Non-Commutative Geometry, Gauge Theories and Higher Yang-Mills Theories with Nonabelian 2-Form Gauge Potential)
The main activity during the period funded by the European research grant was the one described in the research project, i.e. the study of symmetries of space and time in the case that space-time was described by non-commutative coordinates, in which x and y differed from y and x. This research led to the implementation of the principle of general covariance, i.e. covariance under general coordinate transformations, in the non-commutative space and time context.
The outcome was the generalisation of Einstein's theory of gravity to the case of non-commutative space-times, as well as a deep understanding of the differential geometry of twisted non-commutative manifolds.
There were many investigations following this work, concerning both exact solutions, such as the question on whether a non-commutative black hole had an essential singularity in the origin, and the dynamical treatment of non-commutativity, i.e. the identification of whether the non-commutativity parameter could be considered a field itself like the metric was.
Along the same lines, non-commutative gauge theories were revisited. In particular, twisted non-commutative gauge transformations were constructed and found to be symmetric to the usual non-commutative Yang-Mills actions.
The outcome was the generalisation of Einstein's theory of gravity to the case of non-commutative space-times, as well as a deep understanding of the differential geometry of twisted non-commutative manifolds.
There were many investigations following this work, concerning both exact solutions, such as the question on whether a non-commutative black hole had an essential singularity in the origin, and the dynamical treatment of non-commutativity, i.e. the identification of whether the non-commutativity parameter could be considered a field itself like the metric was.
Along the same lines, non-commutative gauge theories were revisited. In particular, twisted non-commutative gauge transformations were constructed and found to be symmetric to the usual non-commutative Yang-Mills actions.