NCGGTH · Non-Commutative Geometry, Gauge Theories and Higher Yang-Mills Theories with Nonabelian 2-Form Gauge Potential
FP6 — Marie Curie Actions (Human Resources and Mobility)
- Duration
- 2005-09-01 → 2006-08-31
- EU contribution
- €40,000
- Participants
- 1
- Scheme
- ERG
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Results in brief
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.
Data: CORDIS, © European Union
Project objective
This is a study of gravity as a gauge theory on noncommutative spaces. Seiberg-Witten map, deformation quantization, random matrix models are some of the noncommutative geometry methods used. Noncommutative geometry techniques are also applied to deform a belian gauge theories with 2-form gauge potential. Global aspects of these theories are described by bundle gerbes (these are a higher version of line bundles) . Noncommutative bundle gerbes are then applied to the noncommutative description of D-branes. Nonabelian bundle gerbes and their associated nonabelian gauge theories with 2-form gauge potential are also investigated (with recently developed differential geometry methods). Also this theory is then applied to study branes. Professional reintegration will be attained through: strict research collaboration, supervising activity (graduate students), teaching activity, co-organization of workshops, creation of new (international) research collaborations. There is a strategy for successful stable reintegra tion of the researcher in the host institution. The researcher returns to his region of origin.
Original text from CORDIS.
Participants
- UNIVERSITÀ DEGLI STUDI DEL PIEMONTE ORIENTALE AMEDEO AVOGADRO · VERCELLICoordinatorItaly
Links
Data: CORDIS, © European Union