Using the theory of noncommutative geometry in a braided monoidal category, we improve upon a previous construction of noncommutative families of instantons of arbitrary charge on the deformed sphere S θ . We formulate a notion of noncommutative parameter spaces for families of instantons and we explore what it means for such families to be gauge equivalent, as well as showing how to remove gau...

In this letter we investigate some aspects of the noncommutative differential geometry based on derivations of the algebra of endomorphisms of an oriented complex hermitian vector bundle. We relate it, in a natural way, to the geometry of the underlying principal bundle and compute the cohomology of its complex of noncommutative differential forms. L.P.T.H.E.-ORSAY 98/14 Laboratoire associé au ...

Supergravity on AdS3×S×T has dual description as a conformal sigma-model with the target space the moduli space of instantons on the noncommutative torus. We derive the precise relation between the parameters of this noncommutative torus and the parameters of the near-horizon geometry. We show that the low energy dynamics of the system of D1D5 branes wrapped on the torus of finite size is descr...

Possible effects of noncommutative geometry on weak CP violation and unitarity triangles are discussed by taking account of a simple version of the momentum-dependent quark mixing matrix in the noncommutative standard model. In particular, we calculate nine rephasing invariants of CP violation and illustrate the noncommutative CP -violating effect in a couple of charged D-meson decays. We also ...

Exponential regularization of orthogonal and Anti-de Sitter (AdS) space is presented based on noncommutative geometry. We show that an adequately adopted noncommutative deformation of geometry makes the holography of higher dimensional quantum theory of gravity and lower dimensional theory possible. Detail counting for observable degrees of freedom of quantum system of gravity in the bulk of no...

Noncommutative geometry is a modern field of mathematics begun by Alain Connes in the early 1980s. It provides powerful tools to treat spaces that are essentially of a quantum nature. Unlike the case of ordinary spaces, their algebraof coordinates is noncommutative, reflecting phenomena like the Heisenberg uncertainty principle in quantum mechanics. What is especially interesting is the fact th...

Groupoids generalize groups, spaces, group actions, and equivalence relations. This last aspect dominates in noncommutative geometry, where groupoids provide the basic tool to desingularize pathological quotient spaces. In physics, however, the main role of groupoids is to provide a unified description of internal and external symmetries. What is shared by noncommutative geometry and physics is...

We review some aspects of the implementation of spacetime symmetries in noncommutative field theories, emphasizing their origin in string theory and how they may be used to construct theories of gravitation. The geometry of canonical noncommutative gauge transformations is analysed in detail and it is shown how noncommutative Yang-Mills theory can be related to a gravity theory. The constructio...

The possible role of gravity in a noncommutative geometry is investigated. Due to the Moyal *-product of fields in noncommutative geometry, it is necessary to complexify the metric tensor of gravity. We first consider the possibility of a complex Hermitian, nonsymmetric gμν and discuss the problems associated with such a theory. We then introduce a complex symmetric (non-Hermitian) metric, with...