In this paper, we give an explicit expression for a star product on the super-Minkowski space wri... more In this paper, we give an explicit expression for a star product on the super-Minkowski space written in the supertwistor formalism. The big cell of the super-Grassmannian Gr(2|0,4|1) is identified with the chiral, super-Minkowski space. The super-Grassmannian is a homogeneous space under the action of the complexification SL(4|1) of SU(2,2|1), the superconformal group in dimension 4, signature (1,3), and supersymmetry N=1. The quantization is done by substituting the groups and homogeneous spaces by their quantum deformed counterparts. The calculations are done in Manin’s formalism. When we restrict to the big cell, we can explicitly compute an expression for the super-star product in the Minkowski superspace associated to this deformation and the choice of a certain basis of monomials.
We consider the contraction of some non linear σ-models which appear in effective supergravity th... more We consider the contraction of some non linear σ-models which appear in effective supergravity theories. In particular we consider the contractions of maximally symmetric spaces corresponding to N = 1 and N = 2 theories, as they appear in certain low energy effective supergravity actions with mass deformations. The contraction procedure is shown to describe the integrating out of massive modes in the presence of interactions, as it happens in many supergravity models after spontaneous supersymmetry breaking.
We consider supersymmetry algebras in space–times with arbitrary signature and minimal number of ... more 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 semisimple algebra naturally associated to the spin group. This algebra, the Spin(s,t)-algebra, depends both on the dimension and on the signature
We interpret superfields in a functorial formalism that explains the properties that are assumed ... more We interpret superfields in a functorial formalism that explains the properties that are assumed for them in the physical applications. We study the non-trivial relation of scalar superfields with the defining sheaf of the supermanifold of super spacetime. We also investigate in the present work some constraints that are imposed on the superfields, which allow for non-trivial solutions. They give rise to superschemes that, generically, are not regular, that is they do not define a standard supermanifold.
We analyze $N=2,1,0$ vacua of type IIB string theory on $K3\times T^2/Z_2$ in presence of three-f... more We analyze $N=2,1,0$ vacua of type IIB string theory on $K3\times T^2/Z_2$ in presence of three-form fluxes from a four dimensional supergravity viewpoint. The quaternionic geometry of the $K3$ moduli space together with the special geometry of the NS and R-R dilatons and of the $T^2$-complex structure moduli play a crucial role in the analysis. The introduction of fluxes corresponds to a particular gauging of N=2, D=4 supergravity. Our results agree with a recent work of Tripathy and Trivedi. The present formulation shows the power of supergravity in the study of effective theories with broken supersymmetry.
We define complex super Minkowski space time in 4 dimensions as the big cell inside a complex sup... more We define complex super Minkowski space time in 4 dimensions as the big cell inside a complex super flag manifold. The complex superconformal group acts naturally on this super flag, allowing us to interpret it as the conformal compactification of complex super Minkowski space time. We then consider real super Minkowski space time as a suitable real form of the
In this paper, we give an explicit expression for a star product on the super-Minkowski space wri... more In this paper, we give an explicit expression for a star product on the super-Minkowski space written in the supertwistor formalism. The big cell of the super-Grassmannian Gr(2|0,4|1) is identified with the chiral, super-Minkowski space. The super-Grassmannian is a homogeneous space under the action of the complexification SL(4|1) of SU(2,2|1), the superconformal group in dimension 4, signature (1,3), and supersymmetry N=1. The quantization is done by substituting the groups and homogeneous spaces by their quantum deformed counterparts. The calculations are done in Manin’s formalism. When we restrict to the big cell, we can explicitly compute an expression for the super-star product in the Minkowski superspace associated to this deformation and the choice of a certain basis of monomials.
We consider the contraction of some non linear σ-models which appear in effective supergravity th... more We consider the contraction of some non linear σ-models which appear in effective supergravity theories. In particular we consider the contractions of maximally symmetric spaces corresponding to N = 1 and N = 2 theories, as they appear in certain low energy effective supergravity actions with mass deformations. The contraction procedure is shown to describe the integrating out of massive modes in the presence of interactions, as it happens in many supergravity models after spontaneous supersymmetry breaking.
We consider supersymmetry algebras in space–times with arbitrary signature and minimal number of ... more 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 semisimple algebra naturally associated to the spin group. This algebra, the Spin(s,t)-algebra, depends both on the dimension and on the signature
We interpret superfields in a functorial formalism that explains the properties that are assumed ... more We interpret superfields in a functorial formalism that explains the properties that are assumed for them in the physical applications. We study the non-trivial relation of scalar superfields with the defining sheaf of the supermanifold of super spacetime. We also investigate in the present work some constraints that are imposed on the superfields, which allow for non-trivial solutions. They give rise to superschemes that, generically, are not regular, that is they do not define a standard supermanifold.
We analyze $N=2,1,0$ vacua of type IIB string theory on $K3\times T^2/Z_2$ in presence of three-f... more We analyze $N=2,1,0$ vacua of type IIB string theory on $K3\times T^2/Z_2$ in presence of three-form fluxes from a four dimensional supergravity viewpoint. The quaternionic geometry of the $K3$ moduli space together with the special geometry of the NS and R-R dilatons and of the $T^2$-complex structure moduli play a crucial role in the analysis. The introduction of fluxes corresponds to a particular gauging of N=2, D=4 supergravity. Our results agree with a recent work of Tripathy and Trivedi. The present formulation shows the power of supergravity in the study of effective theories with broken supersymmetry.
We define complex super Minkowski space time in 4 dimensions as the big cell inside a complex sup... more We define complex super Minkowski space time in 4 dimensions as the big cell inside a complex super flag manifold. The complex superconformal group acts naturally on this super flag, allowing us to interpret it as the conformal compactification of complex super Minkowski space time. We then consider real super Minkowski space time as a suitable real form of the
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Papers by Maria A Lledo