Conformal invariance in noncommutative geometry and mutually interacting Snyder particles

Conformal Structures in Noncommutative Geometry

It is well-known that a compact Riemannian spin manifold (M, g) can be reconstructed from its canonical spectral triple (C∞(M), L2(M,ΣM),D) where ΣM denotes the spinor bundle and D the Dirac operator. We show that g can be reconstructed up to conformal equivalence from (C∞(M), L2(M,ΣM), sign(D)).

Mm Obius Transformations in Noncommutative Conformal Geometry

We study the projective linear group PGL 2 (A) associated with an arbitrary algebra A and its subgroups from the point of view of their action on the space of involutions in A. This action formally resembles M obius transformations known from complex geometry. By specifying A to be an algebra of bounded operators in a Hilbert space H, we rediscover the Mobius group ev (M) de ned by Connes and...

Möbius Transformations in Noncommutative Conformal Geometry

We study the projective linear group PGL2(A) associated with an arbitrary algebra A, and its subgroups from the point of view of their action on the space of involutions in A. This action formally resembles Möbius transformations known from complex geometry. By specifying A to be an algebra of bounded operators in a Hilbert space H, we rediscover the Möbius group μev(M) defined by Connes and st...

Conformal Geometry and Elementary Particles.

Entanglement entropy , conformal invariance and extrinsic geometry

We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface Σ that separates two subsystems of quantum strongly coupled N = 4 SU(N) superconformal gauge theory. We extend this result and calculate entanglement entropy of a generic 4d conformal field theory. As a byproduct, we obtain a clos...