We consider a class of heterotic N=2→0 super no-scale Z2 -orbifold models. An appropriate stringy Scherk–Schwarz supersymmetry breaking induces tree level masses to all massless bosons of the twisted hypermultiplets and therefore stabilizes all twisted moduli. At high supersymmetry breaking scale, the tachyons that occur in the N=4→0 parent theories are projected out, and no Hagedorn-like instability takes place in the N=2→0 models (for small enough marginal deformations). At low supersymmetry breaking scale, the stability of the untwisted moduli is studied at the quantum level by taking into account both untwisted and twisted contributions to the 1-loop effective potential. The latter depends on the specific branch of the gauge theory along which the background can be deformed. We derive its expression in terms of all classical marginal deformations in the pure Coulomb phase, and in some mixed Coulomb/Higgs phases. In this class of models, the super no-scale condition requires having at the massless level equal numbers of untwisted bosonic and twisted fermionic degrees of freedom. Finally, we show that N=1→0 super no-scale models are obtained by implementing a second Z2 orbifold twist on N=2→0 super no-scale Z2 -orbifold models.

France

Costas Kounnas

Hervé Partouche

N=2→0 super no-scale models and moduli quantum stability

We consider “super no-scale models” in the framework of the heterotic string, where the N=4,2,1→0 spontaneous breaking of supersymmetry is induced by geometrical fluxes realizing a stringy Scherk–Schwarz perturbative mechanism. Classically, these backgrounds are characterized by a boson/fermion degeneracy at the massless level, even if supersymmetry is broken. At the 1-loop level, the vacuum energy is exponentially suppressed, provided the supersymmetry breaking scale is small, m3/2≪Mstring . We show that the “super no-scale string models” under consideration are free of Hagedorn-like tachyonic singularities, even when the supersymmetry breaking scale is large, m3/2≃Mstring . The vacuum energy decreases monotonically and converges exponentially to zero, when m3/2 varies from Mstring to 0. We also show that all Wilson lines associated to asymptotically free gauge symmetries are dynamically stabilized by the 1-loop effective potential, while those corresponding to non-asymptotically free gauge groups lead to instabilities and condense. The Wilson lines of the conformal gauge symmetries remain massless. When stable, the stringy super no-scale models admit low energy effective actions, where decoupling gravity yields theories in flat spacetime, with softly broken supersymmetry.

Super no-scale models in string theory

We study heterotic ground states in which supersymmetry is broken by coupling the momentum and winding charges of two large extra dimensions to the R-charges of the supersymmetry generators. The large dimensions give rise to towers of heavy string thresholds that contribute to the running of the gauge couplings. In the general case, these contributions are proportional to the volume of the two large dimensions and invalidate the perturbative string expansion. The problem is evaded if the susy breaking sectors arise as a spontaneously broken phase of N=4→N=2→N=0 supersymmetry, provided that N=4 supersymmetry is restored on the boundary of the moduli space. We discuss the mechanism in the case of Z2×Z2 orbifolds, which requires that the twisted sector that contains the large extra dimensions has no fixed points. We analyze the full string partition function and show that the twisted sectors distribute themselves in non-aligned N=2 orbits, hence preserving the solution to the string decompactification problem. Remarkably, we find that the contribution to the vacuum energy from the N=2→N=0 sectors is suppressed, and the only substantial contribution arises from the breaking of the N=4 sector to N=0 .

United Kingdom

Alon E. Faraggi

Large volume susy breaking with a solution to the decompactification problem

We find static spherically symmetric solutions of scale invariant R 2 gravity. The latter has been shown to be equivalent to General Relativity with a positive cosmological constant and a scalar mode. Therefore, one expects that solutions of the R 2 theory will be identical to that of Einstein theory. Indeed, we find that the solutions of R 2 gravity are in one-to-one correspondence with solutions of General Relativity in the case of non-vanishing Ricci scalar. However, scalar-flat R = 0 solutions are global minima of the R 2 action and they cannot in general be mapped to solutions of the Einstein theory. As we will discuss, the R = 0 solutions arise in Einstein gravity as solutions in the tensionless, strong coupling limit M P → 0. As a further result, there is no corresponding Birkhoff theorem and the Schwarzschild black hole is by no means unique in this framework. In fact, R 2 gravity has a rich structure of vacuum static spherically symmetric solutions partially uncovered here. We also find charged static spherically symmetric backgrounds coupled to a U(1) field. Finally, we provide the entropy and energy formulas for the R 2 theory and we find that entropy and energy vanish for scalar-flat backgrounds.

Greece

Switzerland

Alex Kehagias

Germany

CERN

Dieter Lüst

Antonio Riotto

Black hole solutions in R 2 gravity

Space-filling S-branes can mediate a transition between a contracting and an expanding universe in the Einstein frame. Following up on previous work that uncovered such bouncing solutions in the context of weakly coupled thermal configurations of a certain class of type II superstrings, we set up here the formalism in which we can study the evolution of metric fluctuations across such an S-brane. Our work shows that the specific nature of the S-brane, which is sourced by non-trivial massless thermal string states and appears when the universe reaches a maximal critical temperature, allows for a scale invariant spectrum of curvature fluctuations to manifest at late times via a stringy realization of the matter bounce scenario. The finite energy density at the transition from contraction to expansion provides calculational control over the propagation of the curvature perturbations through the bounce, furnishing a working proof of concept that such a stringy universe can result in viable late time cosmology.