Anna Pachol

Quantum deformations of the flat space superstring

We discuss a quantum deformation of the Green-Schwarz superstring on flat space, arising as a contraction limit of the corresponding deformation of AdS_5 x S^5. This contraction limit turns out to be equivalent to a previously studied limit that yields the so-called mirror model - the model obtained from the light cone gauge fixed AdS_5 x S^5 string by a double Wick rotation. Reversing this logic, the AdS_5 x S^5 superstring is the double Wick rotation of a quantum deformation of the flat space superstring. This quantum deformed flat space string realizes symmetries of timelike kappa-Poincare type, and is T dual to dS_5 x H^5, indicating interesting relations between symmetry algebras under T duality. Our results directly extend to AdS_2 x S^2 x T^6 and AdS_3 x S^3 x T^4, and beyond string theory to many (semi)symmetric space coset sigma models, such as for example a deformation of the four dimensional Minkowski sigma model with timelike kappa-Poincare symmetry. We also discuss possible null and spacelike deformations.

Different realizations ofκ-momentum space

We consider different realizations for the momentum sector of kappa-Poincare Hopf algebra, which is associated with a curved momentum space. We show that the notion of the particle mass as introduced recently by Amelino-Camelia et al. in the context of relative-locality is realization independent for a wide class of realizations, up to linear order in deformation parameter l. On the other hand, the time delay formula clearly shows a dependence on the choice of realization.

κ-Minkowski star product in any dimension from symplectic realization

We derive an explicit expression for the star product reproducing the κ-Minkowski Lie algebra in any dimension n. The result is obtained by suitably reducing the Wick-Voros star product defined on C d with n = d + 1. It is thus shown that the new star product can be obtained from a Jordanian twist.

Observables and dispersion relations in κ-Minkowski spacetime

A bstractWe revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator.This general noncommutative geometry construction is then exemplified in the case of κ-Minkowski spacetime. The corresponding quantum Poincaré-Weyl Lie algebra of in-finitesimal translations, rotations and dilatations is obtained. The d’Alembert wave operator coincides with the quadratic Casimir of quantum translations and it is deformed as in Deformed Special Relativity theories. Also momenta (infinitesimal quantum translations) are deformed, and correspondingly the Einstein-Planck relation and the de Broglie one. The energy-momentum relations (dispersion relations) are consequently deduced. These results complement those of the phenomenological literature on the subject.

κ-Deformations and Extended κ-Minkowski Spacetimes

We extend our previous study of Hopf-algebraic

Remarks on simple interpolation between Jordanian twists

\kappa

Twisted conformal algebra related to -Minkowski space

-deformations of all inhomogeneous orthogonal Lie algebras

Twisted bialgebroids versus bialgebroids from a Drinfeld twist

{\rm iso}(g)

Central tetrads and quantum spacetimes

as written in a tensorial and unified form. Such deformations are determined by a vector

Classification of digital affine noncommutative geometries

\tau