Jean-Pierre Derendinger

On the Low Energy d = 4, N = 1 Supergravity Theory Extracted from the d = 10, N = 1 Superstring*

We extract some general features of the N = 1 supergravity, d = 4 theory which could be obtained as a low energy limit of the recently proposed anomaly-free superstring theories. One finds that after the breaking of the residual d = 4 supersymmetry the gravitino and gaugino masses are equal. Soft scalar couplings are also obtained, including trilinear terms as well as common scalar masses m ˜ m 3/2 . It is argued that a possible source of supersymmetry breaking may be the condensation of fermions in the Yang-Mills sector and we discuss this possibility in the context of the E 8 × E 8 model. Finally, we discuss some implications for the low energy supersymmetric spectrum, particularly squark and gluino masses.

On loop corrections to string effective field theories: field-dependent gauge couplings and σ-model anomalies

Abstract We show that certain one-loop corrections to superstring effective four-dimensional lagragians, involving non-harmonic field-dependent renormalization of gauge couplings, can be consistently written in a standard N = 1 supergravity form, preserving target-space duality. The preservation of target-space duality is due both to a four-dimensional Green-Schwarz mechanism and to local terms, coming from non-local chiral superfields, originated by mixed gauge-σ-model anomaly diagrams. In some models, the Green-Schwarz mechanism is sufficient to achieve complete anomaly cancellation. In more general models automorphic functions, generated by the integration over the heavy string modes, are required to preserve target-space duality.

Vector multiplets coupled to N=2 supergravity: Super-Higgs effect, flat potentials and geometric structure

We obtain general properties of N=2 gauged extended supergravity coupled to vector multiplets, which can gauge an arbitrary group. General formulas for masses and curvatures are derived. Particular attention is devoted to the scalar potential of the theory which determines the classical vacuum structure. Explicit examples are given in which the potential is identically zero, but supersymmetry is broken. It is found that these theories are symmetric under generalized duality transformations.

Anti-Su(5)

Abstract We discuss ordinary as well as supersymmetric SU(5) ×Ũ(1) models in the hope of accomodating acceptable τp and sin2θW. The ordinary SU(5) ×Ũ(1) model does not have the monopole. The supersymmetric SU(5) ×Ũ(1) model can be unified in SO(10).

Superpotentials in IIA compactifications with general fluxes

We derive the effective N = 1, D = 4 supergravity for the seven main moduli of type IIA orientifolds with D6 branes, compactified on T 6 /(Z2 × Z2) in the presence of general fluxes. We illustrate and apply a general method that relates the N = 1 �

On the Low-Energy Limit of Superstring Theories

Abstract We study some aspects of the low-energy supersymmetric d = 4 theory obtained as a limit of superstring theories. We first consider a general O(6) invariant truncation of the d = 10 supergravity + Yang-Mills theory, including bosonic as well as fermionic bilinear terms. As a particular case, one may recover the results of Wittens truncation. The Kahler potential is easily obtained from the fermionic sector of the theory. We next study the process of supersymmetry breaking and argue that only in the case where the hidden E′ 8 symmetry is badly broken on compactification may one obtain a relatively small gravitino mass. The problem of SUSY breaking in the “observable” sector is also discussed, as well as the role of the “dilations” and “axions” of the theory in connection with the strong- CP and cosmological constant problems. Finally, we classify possible low-energy phenomenological models and show how the residual gauge symmetries may be broken radiatively in a natural way. Some problems of the whole approach are pointed out.

Patterns of symmetry breaking in supersymmetric gauge theories

Abstract We give a group-theoretical analysis of the spontaneous breaking of the gauge group in supersymmetric Yang-Mills theories with unbroken supersymmetry.

All loop gauge couplings from anomaly cancellation in string effective theories

Abstract We derive, to all orders in perturbation theory, the E 8 gauge coupling and the modified dilaton-axion Kahler potential for the effective theories of a class of d = 4, N = 1 heterotic string models. The derivation relies on an extended version of the Green-Schwarz anomaly cancellation mechanism, and exploits target-space duality invariance. Although we deal with field-dependent effective gauge couplings and scales in a non-renormalizable supergravity theory, we derive for them a renormalization group equation as a relation among dynamical fields. When expectation values of these fields are considered, our results agree with those previously obtained in renormalizable theories with N = 1 global supersymmetry. We finally comment on possible generalizations of the present results.

Properties of E6 breaking and superstring theory

Abstract We consider symmetry breaking patterns of E 6 down to SU(3)×SU(2)×U(1) which may be related to superstring theories. The Higgs structure suggested by these theories leads to few possibilities compatible with the values of the strong, weak and electromagnetic coupling constants at low energies.

(Weak) G2 holonomy from self-duality, flux and supersymmetry

The aim of this paper is two-fold. First, we provide a simple and pedagogical discussion of how compactifications of M-theory or supergravity preserving some four-dimensional supersymmetry naturally lead to reduced holonomy or its generalization, reduced weak holonomy. We relate the existence of a (conformal) Killing spinor to the existence of certain closed and co-closed p-forms, and to the metric being Ricci flat or Einstein. Then, for seven-dimensional manifolds, we show that octonionic self-duality conditions on the spin connection are equivalent to G_2 holonomy and certain generalized self-duality conditions to weak G_2 holonomy. The latter lift to self-duality conditions for cohomogeneity-one spin(7) metrics. To illustrate the power of this approach, we present several examples where the self-duality condition largely simplifies the derivation of a G_2 or weak G_2 metric.