arXiv subjects
Publications and source records attributed to M. A. Lledó.
We compute explicitly a star product on the Minkowski space whose Poisson bracket is quadratic. This star product corresponds to a deformation of the conformal spacetime, whose big cell is the Minkowski spacetime. The description of Minkowski space is made in the twistor formalism and the quantization follows by substituting the classical conformal group by a quantum group.
In this paper we study a family of algebraic deformations of regular coadjoint orbits of compact semisimple Lie groups with the Kirillov Poisson bracket. The deformations are restrictions of deformations on the dual of the Lie algebra. We prove that there are non isomorphic deformations in the family. The star products are not differential, unlike the star products considered in other approaches. We make a comparison with the differential star product canonically defined by Kontsevich's map.
We consider supersymmetry algebras in space-times with arbitrary signature and minimal number of spinor generators. The interrelation between super Poincaré and super conformal algebras is elucidated. Minimal super conformal algebras are seen to have as bosonic part a classical semimisimple algebra naturally associated to the spin group. This algebra, the Spin$(s,t)$-algebra, depends both on the dimension and on the signature of space time. We also consider maximal super conformal algebras, which are classified by the orthosymplectic algebras.
Field theories on "quantum" or deformed space-time are considered here. The Moyal-Weyl deformation breaks the Lorentz invariance of the theory, but one can still require invariance under the supertranslation algebra. We investigate some aspects of the Wess-Zumino model, super Yang-Mills theories and analyze the correspondence of the later with the supersymmetric Born-Infeld action.
We study properties of a family of algebraic star products defined on coadjoint orbits of semisimple Lie groups. We connect this description with the point of view of differentiable deformations and geometric quantization.
A method for the deformation quantization of coadjoint orbits of semisimple Lie groups is proposed. It is based on the algebraic structure of the orbit. Its relation to geometric quantization and differentiable deformations is explored.
In this paper we review some properties of BPS black holes of supergravities with n=32,16 supersymmetries. The BPS condition, a condition on the eigenvalues of the central charge matrix, can be shown to be U-duality invariant. We explicitly work out D=4, N=8 and D=5, N=4 supergravities.
We investigate some aspects of Moyal-Weyl deformations of superspace and their compatibility with supersymmetry. For the simplest case, when only bosonic coordinates are deformed, we consider a four dimensional supersymmetric field theory which is the deformation of the Wess-Zumino renormalizable theory of a chiral superfield. We then consider the deformation of a free theory of an abelian vector multiplet, which is a non commutative version of the rank one Yang-Mills theory. We finally give the supersymmetric version of the $α'\mapsto 0$ limit of the Born-Infeld action with a B-field turned on, which is believed to be related to the non commutative U(1) gauge theory.
We consider certain supersymmetric Born-Infeld couplings to the D3 brane action and show that they give rise to massless and massive KK excitations of type IIB on $AdS_5\times S_5$, in terms of singleton Yang-Mills superfields.