Hans Peter Nilles

Supersymmetry breaking and soft terms in M theory

Abstract We investigate gaugino condensation in the framework of the strongly coupled heterotic E8×E8 string (M-theory). Supersymmetry is broken in a hidden sector and gravitational interactions induce soft breaking parameters in the observable sector. The resulting soft masses are of order of the gravitino mass. The situation is similar to that in the weakly coupled E8×E8 theory with one important difference: we avoid the problem of small gaugino masses which are now comparable to the gravitino mass.

A natural solution of the μ problem with a composite axion in the hidden sector

Abstract Some superstring models with an intermediate scale hidden sector for supersymmetry breaking can provide a global symmetry which induces the needed μ-term of the supersymmetric standard model in terms of the hidden sector scale. We discuss the μ problem and its solution within the low-energy supersymmetric standard model with an intermediate scale (10 10 – 10 13 GeV) hidden sector. We also present this realization in an orbifold model with a gauge group SU(3) c ⊗ SU(2) L ⊗ U(1) ⊗ SU(5) h with possible extra U(1)s.

Gaugino condensation and duality invariance

Abstract We use space-duality invariance in order to clarify some questions concerning the incorporation of gaugino condensates in the low-energy effective action of string theories. This symmetry requires a modulus dependence of the gauge kinetic function and the gaugino condensates. The resulting effective potential becomes quite complicated and a simple cancellation of the vacuum energy by a sliding dilaton seems no longer to occur.

Duality and the role of nonperturbative effects on the world-sheet☆

Abstract An extension of R to 1 R duality transformations is given for orbifold compactifications of the heterotic string. We show that even nonperturbative effects on the world-sheet do not disturb this symmetry. As a consequence of this fact we are able to derive a classical uncertainty relation between winding and momentum numbers in such theories.

Twisted sector representations of discrete background symmetries for two-dimensional orbifolds☆

We have investigated two-dimensional orbifold compactifications of the closed bosonic string theory subject to modular transformations of the complex background parameter π. The representations of the pair of generators s(π → 1π) and t(π → π − 1), which amount to the duality and axionic shift operations respectively, have been determined for the various twisted sectors. This analysis may be performed in two different ways: either by an inspection of correlation functions of twist field ground states on the sphere (Yukawa couplings, etc.), or by deducing the finite symmetry group for fixed values of π which leaves the correlators of twist fields unaltered. The latter option is closely related to Verlindes approach providing constraints on the fusion rule algebra. Our results take a form which is familiar from world-sheet modular transformations of characters related to highest weight states in rational conformal field theories.

How to reach the correct sin2 θW and αS in string theory

Effective theories with the matter content of the minimal supersymmetric Standard Model below the string scale M_string predict a wrong value for the weak--mixing angle sin^2theta_W and strong coupling constant alpha_S at the scale M_Z. To resolve this problem one needs large threshold corrections. At the same time one would like to avoid introducing new intermediate scales that are small compared to M_string. Two requests which seem to be incompatible. We show how both requirements can be satisfied in a class of (0,2) heterotic superstring compactifications with a natural choice of the vevs of the moduli fields entering the moduli dependent string threshold corrections.

Gaugino condensation and the cosmological implications of the hidden sector

Abstract We investigate the cosmological implications of models in which the breakdown of supersymmetry proceeds via gaugino condensation in a hidden sector, only gravitationally coupled to the observable sector. Semistable particles in the hidden sector are forbidden in the range between 100 eV and a few times 1010 GeV. These constraints derived from the restrictions on energy density and nucleosynthesis are shown to have consequences for model building. As a byproduct of these investigations we point out a particularly attractive solution of the μ-problem and the strong CP-problem with a composite hidden sector axion.

Gravitational divergences as a mediator of supersymmetry breaking

Abstract Gravitational divergences associated with singlet fields in supersymmetric theories are reexamined, and their possible contributions to the low-energy effective theory are pointed out. We demonstrate that such divergences are not necessarily harmful and that Planck-scale physics could play an important role in models of low-energy supersymmetry breaking via a radiatively induced tadpole term in the scalar potential. In this case, gravitational divergences play the role of the supersymmetry breaking mediator, leading to a simple realization of the so-called messenger model. We also point out a new mechanism for the generation of mass terms for the Higgs fields in models of low-energy supersymmetry breaking, as well as a horizontal messenger mechanism in which the horizontally charged scalars are rendered heavy. Implications to the flavor problem in supersymmetric models are also discussed.

Space duality and quantized Wilson lines

Abstract We discuss space duality of the bosonic and heterotic string compactified on toroidal orbifolds, allowing for the most general modular invariant background. This includes discrete axionic background fields as well as quantized Wilson lines. The latter are known to reduce the gauge symmetry and to lead to (0,2)-models. We show that the canonical generalization of torus duality is not a transformation in moduli space. Instead in turns out to provide a map from a symmetric to an asymmetric orbifold. For duality to be a symmetry in moduli space one has to define a different transformation.

On non-minimal Higgs boson searches from Z boson decay

Abstract We compute the rate of Higgs boson production in Z decay for the process where the Higgs boson is radiated off a heavy fermion line. The importance of this reaction is pointed out for the Higgs search in models with non-minimal Higgs structure and a relatively heavy pseudoscalar.