Searcharxiv⌕ Search

arXiv subjects

A. Van Proeyen

Publications and source records attributed to A. Van Proeyen.

At least 19 recordsLinked to original sources
arXiv2010

Special geometry for arbitrary signatures

In this paper we generalize special geometry to arbitrary signatures in target space. We formulate the definitions in a precise mathematical setting and give a translation to the coordinate formalism used in physics. For the projective case, we first discuss in detail projective Kaehler manifolds, appearing in N=1 supergravity. We develop a new point of view based on the intrinsic construction of the line bundle. The topological properties are then derived and the Levi-Civita connection in the projective manifold is obtained as a particular projection of a Levi-Civita connection in a `mother' manifold with one extra complex dimension. The origin of this approach is in the superconformal formalism of physics, which is also explained in detail. Finally, we specialize these results to projective special Kaehler manifolds and provide explicit examples with different choices of signature.

hep-th↗
arXiv2003

Wess-Zumino sigma models with non-Kahlerian geometry

Supersymmetry of the Wess-Zumino (N=1, D=4) multiplet allows field equations that determine a larger class of geometries than the familiar Kahler manifolds, in which covariantly holomorphic vectors rather than a scalar superpotential determine the forces. Indeed, relaxing the requirement that the field equations be derivable from an action leads to complex flat geometry. The Batalin-Vilkovisky formalism is used to show that if one requires that the field equations be derivable from an action, we once again recover the restriction to Kahler geometry, with forces derived from a scalar superpotential.

hep-th↗
arXiv2001

Brane plus Bulk Supersymmetry in Ten Dimensions

We discuss a generalized form of IIA/IIB supergravity depending on all R-R potentials C^(p) (p=0,1,...,9) as the effective field theory of Type IIA/IIB superstring theory. For the IIA case we explicitly break this R-R democracy to either p<=3 or p>=5 which allows us to write a new bulk action that can be coupled to N=1 supersymmetric brane actions. The case of 8-branes is studied in detail using the new bulk & brane action. The supersymmetric negative tension branes without matter excitations can be viewed as orientifolds in the effective action. These D8-branes and O8-planes are fundamental in Type I' string theory. A BPS 8-brane solution is given which satisfies the jump conditions on the wall. As an application of our results we derive a quantization of the mass parameter and the cosmological constant in string units.

hep-th↗
arXiv2001

New Formulations of D=10 Supersymmetry and D8-O8 Domain Walls

We discuss a generalized form of IIA/IIB supergravity depending on all R-R potentials C^(p) (p=0,1,...,9) as the effective field theory of Type IIA/IIB superstring theory. For the IIA case we explicitly break this R-R democracy to either p<=3 or p>=5 which allows us to write a new bulk action that can be coupled to N=1 supersymmetric brane actions. The case of 8-branes is studied in detail using the new bulk & brane action. The supersymmetric negative tension branes without matter excitations can be viewed as orientifolds in the effective action. These D8-branes and O8-planes are fundamental in Type I' string theory. A BPS 8-brane solution is given which satisfies the jump conditions on the wall. It implies a quantization of the mass parameter in string units. Also we find a maximal distance between the two walls, depending on the string coupling and the mass parameter. We derive the same results via supersymmetric flow equations.

hep-th↗
arXiv2000

Embedding Branes in Flat Two-time Spaces

We show how non-near horizon, non-dilatonic $p$-brane theories can be obtained from two embedding constraints in a flat higher dimensional space with 2 time directions. In particular this includes the construction of D3 branes from a flat 12-dimensional action, and M2 and M5 branes from 13 dimensions. The worldvolume actions are found in terms of fields defined in the embedding space, with the constraints enforced by Lagrange multipliers.

hep-th↗
arXiv1998

Black Holes and Superconformal Mechanics

The dynamics of a (super)particle near the horizon of an extreme Reissner-Nordstrom black hole is shown to be governed by an action that reduces to a (super)conformal mechanics model in the limit of large black hole mass.

hep-th↗
arXiv1998

Conformal Theory of M2, D3, M5 and `D1+D5' Branes

The bosonic actions for M2, D3 and M5 branes in their own d-dimensional near-horizon background are given in a manifestly SO(p+1,2) x SO(d-p-1) invariant form (p=2,3,5). These symmetries result from a breakdown of ISO(d,2) (with d=10 for D3 and d=11 for M2 and M5) symmetry by the Wess-Zumino term and constraints. The new brane actions, reduce after gauge-fixing and solving constraints to (p+1) dimensional interacting field theories with a non-linearly realized SO(p+1,2) conformal invariance. We also present an interacting two-dimensional conformal field theory on a D-string in the near-horizon geometry of a D1+D5 configuration.

hep-th↗
arXiv1998

Duality in N=2 nonlinear sigma-models

We consider N=2 supersymmetric nonlinear sigma-models in two dimensions defined in terms of the nonminimal scalar multiplet. We compute in superspace the one-loop beta function and show that the classical duality between these models and the standard ones defined in terms of chiral superfields is maintained at the quantum one-loop level. Our result provides an explicit application of the recently proposed quantization of the nonminimal scalar multiplet via the Batalin-Vilkovisky procedure.

hep-th↗
arXiv1997

What is Special Kähler Geometry ?

The scalars in vector multiplets of N=2 supersymmetric theories in 4 dimensions exhibit `special Kaehler geometry', related to duality symmetries, due to their coupling to the vectors. In the literature there is some confusion on the definition of special geometry. We show equivalences of some definitions and give examples which show that earlier definitions are not equivalent, and are not sufficient to restrict the Kaehler metric to one that occurs in N=2 supersymmetry. We treat the rigid as well as the local supersymmetry case. The connection is made to moduli spaces of Riemann surfaces and Calabi-Yau 3-folds. The conditions for the existence of a prepotential translate to a condition on the choice of canonical basis of cycles.

hep-th↗
arXiv1997

Isometries of special manifolds

We describe special Kahler geometry, special quaternionic manifolds, and very special real manifolds and analyze the structure of their isometries. The classification of the homogeneous manifolds of these types is presented.

hep-th↗
arXiv1997

Quantization of the complex linear superfield

The quantization of the complex linear superfield requires an infinite tower of ghosts. We use the Batalin-Vilkovisky method to obtain a gauge-fixed action. In superspace, the method brings in some novel features.

hep-th↗
arXiv1996

A Search for Non-Perturbative Dualities of Local $N=2$ Yang--Mills Theories from Calabi--Yau Threefolds

The generalisation of the rigid special geometry of the vector multiplet quantum moduli space to the case of supergravity is discussed through the notion of a dynamical Calabi--Yau threefold. Duality symmetries of this manifold are connected with the analogous dualities associated with the dynamical Riemann surface of the rigid theory. N=2 rigid gauge theories are reviewed in a framework ready for comparison with the local case. As a byproduct we give in general the full duality group (quantum monodromy) for an arbitrary rigid $SU(r+1)$ gauge theory, extending previous explicit constructions for the $r=1,2$ cases. In the coupling to gravity, R--symmetry and monodromy groups of the dynamical Riemann surface, whose structure we discuss in detail, are embedded into the symplectic duality group $Γ_D$ associated with the moduli space of the dynamical Calabi--Yau threefold.

hep-th↗
arXiv1995

Special geometry and symplectic transformations

Special Kahler manifolds are defined by coupling of vector multiplets to $N=2$ supergravity. The coupling in rigid supersymmetry exhibits similar features. These models contain $n$ vectors in rigid supersymmetry and $n+1$ in supergravity, and $n$ complex scalars. Apart from exceptional cases they are defined by a holomorphic function of the scalars. For supergravity this function is homogeneous of second degree in an $(n+1)$-dimensional projective space. Another formulation exists which does not start from this function, but from a symplectic $(2n)$- or $(2n+2)$-dimensional complex space. Symplectic transformations lead either to isometries on the manifold or to symplectic reparametrizations. Finally we touch on the connection with special quaternionic and very special real manifolds, and the classification of homogeneous special manifolds.

hep-th↗
arXiv1995

R-Symmetry and the Topological Twist of N=2 Effective Supergravities of Heterotic Strings

We discuss R-symmetries in locally supersymmetric N=2 gauge theories coupled to hypermultiplets which can be thought of as effective theories of heterotic superstring models. In this type of supergravities a suitable R-symmetry exists and can be used to topologically twist the theory: the vector multiplet containing the dilaton-axion field has different R-charge assignments with respect to the other vector multiplets. Correspondingly a system of coupled instanton equations emerges, mixing gravitational and Yang--Mills instantons with triholomorphic hyperinstantons and axion-instantons. For the tree-level classical special manifolds $ST(n)=SU(1,1)/U(1)\times SO(2,n)/(SO(2)$ $\times SO(n))$ R-symmetry with the specified properties is a continuous symmetry, but for the quantum corrected manifolds ${\hat {ST}}(n)$ a discrete R--group of electric--magnetic duality rotations is sufficient and we argue that it exists.

hep-th↗
arXiv1995

Pseudo-Duality

Proper symmetries act on fields while pseudo-symmetries act on both fields and coupling constants. We identify the pseudo-duality groups that act as symmetries of the equations of motion of general systems of scalar and vector fields and apply our results to $N=2,4$ and $8$ supergravity theories. We present evidence that the pseudo-duality group for both the heterotic and type II strings toroidally compactified to four dimensions is $Sp(56;\Z)\times D$, where $D$ is a certain subgroup of the diffeomorphism group of the scalar field target space. This contains the conjectured heterotic $S\times T$ or type II $U$ proper duality group as a subgroup.

hep-th↗
arXiv1995

Duality Transformations in Supersymmetric Yang-Mills Theories coupled to Supergravity,

We consider duality transformations in N=2, d=4 Yang--Mills theory coupled to N=2 supergravity. A symplectic and coordinate covariant framework is established, which allows one to discuss stringy `classical and quantum duality symmetries' (monodromies), incorporating T and S dualities. In particular, we shall be able to study theories (like N=2 heterotic strings) which are formulated in symplectic basis where a `holomorphic prepotential' F does not exist, and yet give general expressions for all relevant physical quantities. Duality transformations and symmetries for the N=1 matter coupled Yang--Mills supergravity system are also exhibited. The implications of duality symmetry on all N>2 extended supergravities are briefly mentioned. We finally give the general form of the central charge and the N=2 semiclassical spectrum of the dyonic BPS saturated states (as it comes by truncation of the N=4 spectrum).

hep-th↗
arXiv1995

On Electromagnetic Duality in Locally Supersymmetric N=2 Yang--Mills Theory

We consider duality transformations in N=2 Yang--Mills theory coupled to N=2 supergravity, in a manifestly symplectic and coordinate covariant setting. We give the essential of the geometrical framework which allows one to discuss stringy classical and quantum monodromies, the form of the spectrum of BPS saturated states and the Picard--Fuchs identities encoded in the special geometry of N=2 supergravity theories.

hep-th↗