arXiv subjects

Antoine Van Proeyen

Publications and source records attributed to Antoine Van Proeyen.

At least 55 records · Page 3Linked to original sources

arXiv2008

Vector Supersymmetry: Casimir operators and contraction from OSp(3,2|2)

We study some algebraic properties of the 'vector supersymmetry' (VSUSY) algebra, a graded extension of the four-dimensional Poincare' algebra with two odd generators, a vector and a scalar, and two central charges. The anticommutator between the two odd generators gives the four-momentum operator, from which the name vector supersymmetry. We construct the Casimir operators for this algebra and we show how both algebra and Casimirs can be derived by contraction from the simple orthosymplectic algebra OSp(3,2|2). In particular, we construct the analogue of superspin for vector supersymmetry and we show that, due to the algebraic structure of the Casimirs, the multiplets are either doublets of spin (s,s+1) or two spin 1/2 states. Finally, we identify an odd operator, which is an invariant in a subclass of representations where a BPS-like algebraic relation between the mass and the values of the central charges is satisfied.

hep-th↗

arXiv2008

Real forms of very extended Kac-Moody algebras and theories with eight supersymmetries

We consider all theories with eight supersymmetries whose reduction to three dimensions gives rise to scalars that parametrise symmetric manifolds. We conjecture that these theories are non-linear realisations of very-extended Kac-Moody algebras for suitable choices of real forms. We show for the most interesting cases that the bosonic sector of the supersymmetric theory is precisely reproduced by the corresponding non-linear realisation.

hep-th↗

arXiv2008

Effective action for the field equations of charged black holes

In this article, we consistently reduce the equations of motion for the bosonic N = 2 supergravity action, using a multi-centered black hole ansatz for the metric. This reduction is done in a general, non-supersymmetric setup, in which we extend concepts of BPS black hole technology. First of all we obtain a more general form of the black hole potential, as part of an effective action for both the scalars and the vectors in the supergravity theory. Furthermore, we show that there are extra constraints specifying the solution, which we calculate explicitly. In the literature, these constraints have already been studied in the one-center case. We also show that the effective action we obtain for non-static metrics, can be linked to the "entropy function" for the spherically symmetric case, as defined by Sen and Cardoso et al.

hep-th↗

arXiv2007

Symplectic structure of N=1 supergravity with anomalies and Chern-Simons terms

The general actions of matter-coupled N=1 supergravity have Peccei-Quinn terms that may violate gauge and supersymmetry invariance. In addition, N=1 supergravity with vector multiplets may also contain generalized Chern-Simons terms. These have often been neglected in the literature despite their importance for gauge and supersymmetry invariance. We clarify the interplay of Peccei-Quinn terms, generalized Chern-Simons terms and quantum anomalies in the context of N=1 supergravity and exhibit conditions that have to be satisfied for their mutual consistency. This extension of the previously known N=1 matter-coupled supergravity actions follows naturally from the embedding of the gauge group into the group of symplectic duality transformations. Our results regarding this extension provide the supersymmetric framework for studies of string compactifications with axionic shift symmetries, generalized Chern-Simons terms and quantum anomalies.

hep-th↗

arXiv2007

Domain-wall/Cosmology correspondence in adS/dS supergravity

We realize the domain-wall/cosmology correspondence for (pseudo)supersymmetric domain walls (cosmologies) in the context of four-dimensional supergravity. The OSp(2|4)-invariant anti-de Sitter (adS) vacuum of a particular N=2 Maxwell-Einstein supergravity theory is shown to correspond to the OSp(2^*|2,2)-invariant de Sitter (dS) vacuum of a particular pseudo-supergravity model, with `twisted' reality conditions on spinors. More generally, supersymmetric domain walls of the former model correspond to pseudo-supersymmetric cosmologies of the latter model, with time-dependent pseudo-Killing spinors that we give explicitly.

hep-th↗

arXiv2007

Tits-Satake projections of homogeneous special geometries

We organize the homogeneous special geometries, describing as well the couplings of D=6, 5, 4 and 3 supergravities with 8 supercharges, in a small number of universality classes. This relates manifolds on which similar types of dynamical solutions can exist. The mathematical ingredient is the Tits-Satake projection of real simple Lie algebras, which we extend to all solvable Lie algebras occurring in these homogeneous special geometries. Apart from some exotic cases all the other, 'very special', homogeneous manifolds can be grouped in seven universality classes. The organization of these classes, which capture the essential features of their basic dynamics, commutes with the r- and c-map. Different members are distinguished by different choices of the paint group, a notion discovered in the context of cosmic billiard dynamics of non maximally supersymmetric supergravities. We comment on the usefulness of this organization in universality classes both in relation with cosmic billiard dynamics and with configurations of branes and orbifolds defining special geometry backgrounds.

hep-th↗

arXiv2007

The energy and stability of D-term strings

Cosmic strings derived from string theory, supergravity or any theory of choice should be stable if we hope to observe them. In this paper we consider D-term strings in D=4, N=1 supergravity with a constant Fayet-Iliopoulos term. We show that the positive deficit angle supersymmetric D-term string is non-perturbatively stable by using standard Witten-Nester techniques to prove a positive energy theorem. Particular attention is paid to the negative deficit angle D-term string, which is known to violate the dominant energy condition. Within the class of string solutions we consider, this violation implies that the negative deficit angle D-term string must have a naked pathology and therefore the positive energy theorem we prove does not apply to it. As an interesting aside, we show that the Witten-Nester charge calculates the total gravitational energy of the D-term string without the need for a cut-off, which may not have been expected.

hep-th↗

arXiv2007

The Stability of D-term Cosmic Strings

In this note, which is based on hep-th/0611111, we review the stability of the static, positive deficit angle D-term string solutions of D=4, N=1 supergravity with a constant Fayet-Iliopoulos term. We prove the semi-classical stability of this class of solutions using standard positive energy theorem techniques. In particular, we discuss how the negative deficit angle D-term string, which also solves the Killing spinor equations, violates the dominant energy condition and so is excluded from our arguments.

hep-th↗

arXiv2006

Gaugino Condensates and D-terms from D7-branes

We investigate, at the microscopic level, the compatibility between D-term potentials from world-volume fluxes on D7-branes and non-perturbative superpotentials arising from gaugino condensation on a different stack of D7-branes. This is motivated by attempts to construct metastable de Sitter vacua in type IIB string theory via D-term uplifts. We find a condition under which the Kaehler modulus, T, of a Calabi-Yau 4-cycle gets charged under the anomalous U(1) on the branes with flux. If in addition this 4-cycle is wrapped by a stack of D7-branes on which gaugino condensation takes place, the question of U(1)-gauge invariance of the (T-dependent) non-perturbative superpotential arises. In this case an index theorem guarantees that strings, stretching between the two stacks, yield additional charged chiral fields which also appear in the superpotential from gaugino condensation. We check that the charges work out to make this superpotential gauge invariant, and we argue that the mechanism survives the inclusion of higher curvature corrections to the D7-brane action.

hep-th↗

arXiv2006

The map between conformal hypercomplex/hyper-Kaehler and quaternionic(-Kaehler) geometry

We review the general properties of target spaces of hypermultiplets, which are quaternionic-like manifolds, and discuss the relations between these manifolds and their symmetry generators. We explicitly construct a one-to-one map between conformal hypercomplex manifolds (i.e. those that have a closed homothetic Killing vector) and quaternionic manifolds of one quaternionic dimension less. An important role is played by 'ξ-transformations', relating complex structures on conformal hypercomplex manifolds and connections on quaternionic manifolds. In this map, the subclass of conformal hyper-Kaehler manifolds is mapped to quaternionic-Kaehler manifolds. We relate the curvatures of the corresponding manifolds and furthermore map the symmetries of these manifolds to each other.

hep-th↗

arXiv2006

Superconformal N=2, D=5 matter with and without actions

We investigate N=2, D=5 supersymmetry and matter-coupled supergravity theories in a superconformal context. In a first stage we do not require the existence of a Lagrangian. Under this assumption, we already find at the level of rigid supersymmetry, i.e. before coupling to conformal supergravity, more general matter couplings than have been considered in the literature. For instance, we construct new vector-tensor multiplet couplings, theories with an odd number of tensor multiplets, and hypermultiplets whose scalar manifold geometry is not hyperkaehler. Next, we construct rigid superconformal Lagrangians. This requires some extra ingredients that are not available for all dynamical systems. However, for the generalizations with tensor multiplets mentioned above, we find corresponding new actions and scalar potentials. Finally, we extend the supersymmetry to local superconformal symmetry, making use of the Weyl multiplet. Throughout the paper, we will indicate the various geometrical concepts that arise, and as an application we compute the non-vanishing components of the Ricci tensor of hypercomplex group manifolds. Our results can be used as a starting point to obtain more general matter-couplings to Poincare supergravity.

hep-th↗

arXiv2006

N=2 supergravity in five dimensions revisited

We construct matter-coupled N=2 supergravity in five dimensions, using the superconformal approach. For the matter sector we take an arbitrary number of vector-, tensor- and hyper-multiplets. By allowing off-diagonal vector-tensor couplings we find more general results than currently known in the literature. Our results provide the appropriate starting point for a systematic search for BPS solutions, and for applications of M-theory compactifications on Calabi-Yau manifolds with fluxes.

hep-th↗

arXiv2006

Effective supergravity descriptions of superstring cosmology

This text is a review of aspects of supergravity theories that are relevant in superstring cosmology. In particular, it considers the possibilities and restrictions for `uplifting terms', i.e. methods to produce de Sitter vacua. We concentrate on N=1 and N=2 supergravities, and the tools of superconformal methods, which clarify the structure of these theories. Cosmic strings and embeddings of target manifolds of supergravity theories in others are discussed in short at the end.

hep-th↗

arXiv2005

D-term cosmic strings from N=2 Supergravity

We describe new half-BPS cosmic string solutions in N=2, d=4 supergravity coupled to one vector multiplet and one hypermultiplet. They are closely related to D-term strings in N=1 supergravity. Fields of the N=2 theory that are frozen in the solution contribute to the triplet moment map of the quaternionic isometries and leave their trace in N=1 as a constant Fayet-Iliopoulos term. The choice of U(1) gauging and of special geometry are crucial. The construction gives rise to a non-minimal Kaehler potential and can be generalized to higher dimensional quaternionic-Kaehler manifolds.

hep-th↗

arXiv2005

The identification of conformal hypercomplex and quaternionic manifolds

We review the map between hypercomplex manifolds that admit a closed homothetic Killing vector (i.e. `conformal hypercomplex' manifolds) and quaternionic manifolds of 1 dimension less. This map is related to a method for constructing supergravity theories using superconformal techniques. An explicit relation between the structure of these manifolds is presented, including curvatures and symmetries. An important role is played by `ξtransformations', relating connections on quaternionic manifolds, and a new type `\hatξtransformations' relating complex structures on conformal hypercomplex manifolds. In this map, the subclass of conformal hyper-Kaehler manifolds is mapped to quaternionic-Kaehler manifolds.

math.DG↗

arXiv2005

Non Relativistic Dp Branes

We construct a kappa-symmetric and diffeomorphism-invariant non-relativistic Dp-brane action as a non-relativistic limit of a relativistic Dp-brane action in flat space. In a suitable gauge the world-volume theory is given by a supersymmetric free field theory in flat spacetime in p+1 dimensions of bosons, fermions and gauge fields.

hep-th↗

arXiv2005

Dirac actions for D-branes on backgrounds with fluxes

The understanding of the fermionic sector of the worldvolume D-brane dynamics on a general background with fluxes is crucial in several branches of string theory, like for example the study of nonperturbative effects or the construction of realistic models living on D-branes. In this paper we derive a new simple Dirac-like form for the bilinear fermionic action for any Dp-brane in any supergravity background, which generalizes the usual Dirac action valid in absence of fluxes. A nonzero world-volume field strength deforms the usual Dirac operator in the action to a generalized non-canonical one. We show how the canonical form can be re-established by a redefinition of the world-volume geometry.

hep-th↗

arXiv2004

Hypermultiplets and hypercomplex geometry from 6 to 3 dimensions

The formulation of hypermultiplets that has been developed for 5-dimensional matter multiplets is by dimensional reductions translated into the appropriate spinor language for 6 and 4 dimensions. We also treat the theories without actions that have the geometrical structure of hypercomplex geometry. The latter is the generalization of hyper-Kaehler geometry that does not require a Hermitian metric and hence corresponds to field equations without action. The translation tables of this paper allow the direct application of superconformal tensor calculus for the hypermultiplets using the available Weyl multiplets in 6 and 4 dimensions. Furthermore, the hypermultiplets in 3 dimensions that result from reduction of vector multiplets in 4 dimensions are considered, leading to a superconformal formulation of the c-map and an expression for the main geometric quantities of the hyper-Kaehler manifolds in the image of this map.

hep-th↗