D1D5 system and noncommutative geometry

D1D5 System and Noncommutative Geometry

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...

Noncommutative geometry

Noncommutative Geometry and Quantization

The purpose of these lectures is to survey several aspects of noncommutative geometry, with emphasis on its applicability to particle physics and quantum field theory. By now, it is a commonplace statement that spacetime at short length —or high energy— scales is not the Cartesian continuum of macroscopic experience, and that older methods of working with functions on manifolds must be rethough...

Noncommutative geometry and reality

We introduce the notion of real structure in our spectral geometry. This notion is motivated by Atiyah’s KR-theory and by Tomita’s involution J. It allows us to remove two unpleasant features of the “Connes-Lott” description of the standard model, namely, the use of bivector potentials and the asymmetry in the Poincare duality and in the unimodularity condition.

Noncommutative Geometry and Physics

The two existing theories which successfully encode our knowledge of space-time are : • General Relativity • The Standard Model General relativity describes space-time as far as large scales are concerned (cf. Figure 1 and [2] for many more suggestive thoughts and pictures) and is based on the geometric paradigm discovered by Riemann. It replaces the flat (pseudo) metric of Poincaré, Einstein, ...