Antoine Van Proeyen

Fayet–Iliopoulos terms in supergravity and cosmology

We clarify the structure of N = 1 supergravity in 1+3 dimensions with constant Fayet?Iliopoulos (FI) terms. The FI terms g? induce non-vanishing R-charges for the fermions and the superpotential. Therefore the D-term inflation model in supergravity with constant FI terms has to be revisited. We present all corrections of order g?/M2P to the classical supergravity action required by local supersymmetry and provide a gauge-anomaly-free version of the model. We also investigate the case of the so-called anomalous U(1) when a chiral superfield is shifted under U(1). In such a case, in the context of string theory, the FI terms originate from the derivative of the K?hler potential and they are inevitably field dependent. This raises an issue of stabilization of the relevant field in applications to cosmology. The recently suggested equivalence between the D-term strings and D-branes of type II theory shows that brane?anti-brane systems produce the FI terms in the effective 4d theory, with the Ramond?Ramond axion shifting under the U(1) symmetry. This connection gives the possibility to interpret many unknown properties of systems in the more familiar language of 4d supergravity D-terms, and vice versa. For instance, the shift of the axion field in both cases restricts the possible forms of the moduli-stabilizing superpotential. We provide some additional consistency checks of the correspondence of D-term strings to D-branes and show that instabilities of the two are closely related. Surviving cosmic D-strings of the type II theory may be potentially observed in the form of D-term strings of 4d supergravity. We study such string solutions of supergravity with constant FI terms with one half supersymmetry unbroken and explain some of the puzzling properties of the zero modes around cosmic strings, such as the difference between the numbers of fermionic and bosonic modes.

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 Kahler 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.

Superconformal algebras in two dimensions with N=4

Abstract We discuss a one-parameter family of d =2 superconformal algebras. They have N =4 supersymmetries and satisfy all the usual requirements. There is one Virasoro algebra, the other generators have dimensions 1 2 , 1 or 3 2 and there is one central extension. A realisation is given on a linear σ-model on a group manifold.

Supersymmetry in singular spaces

Published in: J. High Energy Phys. 10 (2000) 033 citations recorded in [Science Citation Index] Abstract: We develop the concept of supersymmetry in singular spaces, apply it in an example for 3-branes in D=5 and comment on 8-branes in D=10. The new construction has an interpretation that the brane is a sink for the flux and requires adding to the standard supergravity a (D-1)-form field and a supersymmetry singlet field. This allows a consistent definition of supersymmetry on a S_1/Z_2 orbifold, the bulk and the brane actions being separately supersymmetric. Randall-Sundrum brane-worlds can be reproduced in this framework without fine tuning. For fixed scalars, the doubling of unbroken supersymmetries takes place and the negative tension brane can be pushed to infinity. In more general BPS domain walls with 1/2 of unbroken supersymmetries, the distance between branes in some cases may be restricted by the collapsing cycles of the Calabi-Yau manifold. The energy of any static x^5-dependent bosonic configuration vanishes, E=0, in analogy with the vanishing of the Hamiltonian in a closed universe.

What is special Kahler geometry

The scalars in vector multiplets of N = 2 supersymmetric theories in four dimensions exhibit ‘special Kahler 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 Kahler 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.

Superconformal symmetry, supergravity and cosmology

We introduce the general N = 1 gauge theory superconformally coupled to supergravity. The theory has local SU(2,2|1) symmetry and no dimensional parameters. The superconformal origin of the Fayet-Iliopoulos (FI) terms is clarified. The phase of this theory with spontaneously broken conformal symmetry gives various formulations of N = 1 supergravity interacting with matter, depending on the choice of the R-symmetry fixing. We have found that the locally superconformal theory is useful for describing the physics of the early universe with a conformally flat FRW metric. Few applications of superconformal theory to cosmology include the study of (a) particle production after inflation, particularly the nonconformal helicity-±½ states of gravitino, (b) the super-Higgs effect in cosmology and the derivation of the equations for the gravitino interacting with any number of chiral and vector multiplets in the gravitational background with varying scalar fields, (c) the weak-coupling limit of supergravity MP→∞ and gravitino-goldstino equivalence. This explains why gravitino production in the early universe is not suppressed in the limit of weak gravitational coupling. We discuss the possible existence of an unbroken phase of the superconformal theories, interpreted as a strong-coupling limit of supergravity MP→0.

Jordan frame supergravity and inflation in the NMSSM

We present a complete explicit N=1, d=4 supergravity action in an arbitrary Jordan frame with non-minimal scalar-curvature coupling of the form

Hypermultiplets, domain walls, and supersymmetric attractors

\Phi(z, \bar z)\, R

M 5-BRANE AND SUPERCONFORMAL (0,2) TENSOR MULTIPLET IN SIX DIMENSIONS

. The action is derived by suitably gauge-fixing the superconformal action. The theory has a modified Kaehler geometry, and it exhibits a significant dependence on the frame function

Gravitino production after inflation

\Phi (z, \bar z)