Modern physical approach to non(anti)commutative geometry lies on the concept of "effective field theory". In the main framework of String Theory, quantum field theories defined on such deformed structures appear in the low energy limits of particular configurations of D-branes, preserving different amount of supersymmetry, according with the deformation involved.
Therefore besides the mathematical aspects of these space-time deformations, a phenomenological perspective is needed and powerful algebraic and geometric methods can open new interpretation of physics of Standard Model and beyond that. The proposal is to pursue the study of non(anti)commutative geometry from this point of view, by focusing on the compelling problem of supersymmetry breaking.
Since low energy supersymmetry is the first natural step for physics beyond the Standard Model at TeV scale, one of the central questions is to understand the mechanism of its breaking. In particular, most phenomenological issues of these models, like cosmological constant, R-parity violation, leptonic and barionic number conservation, are determined by soft terms, those which avoid new harmful divergences.
Supersymmetric models defined on a manifold with deformed geometry have been recently shown to produce such a soft breaking. A deeper study of the different possibilities given by deforming the structure of the space-time is allowed in the natural setup of superspace, where suitable techniques allow for a simpler analysis of both classical and quantum properties.
Fields of science
- natural sciencesphysical sciencestheoretical physicsparticle physics
- natural sciencesphysical sciencestheoretical physicsstring theory
- natural sciencesphysical scienceselectromagnetism and electronicselectromagnetism
- natural sciencesmathematicspure mathematicsgeometry
- natural sciencesphysical sciencesquantum physicsquantum field theory
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