Stefan Forste

Supersymmetric ZN×ZM orientifolds in 4D with D-branes at angles

We construct orientifolds of type IIA string theory. The theory is compactified on a T 6 /ZN × ZM orbifold. In addition worldsheet parity in combination with a reflection of three compact directions is modded out. Tadpole cancellation requires to add D-6-branes at angles. The resulting four dimensional theories are N = 1 supersymmetric and non-chiral.

A comment on self-tuning and vanishing cosmological constant in the brane world

Abstract In this note we elaborate on various five dimensional contributions to the effective 4D cosmological constant in brane systems. In solutions with vanishing 5D cosmological constant we describe a non-local mechanism of cancellation of vacuum energy between the brane and the singularities. We comment on a hidden fine tuning which is implied by this observation.

The cosmological constant problem from a brane-world perspective

We point out several subtleties arising in brane-world scenarios of cosmological constant cancellation. We show that solutions with curvature singularities are inconsistent, unless the contribution to the effective four-dimentional cosmological constant of the physics that resolves the singularities is fine-tuned. This holds for both flat and curved branes. Irrespective of this problem, we then study an isolated class of flat solutions in models where a bulk scalar field with a vanishing potential couples to a 3-brane. We give an example where the introduction of a bulk scalar potential results in a non-zero cosmological constant. Finally we comment on the stability of classical solutions of the brane system with respect to quantum corrections.

Orientifolds with branes at angles

We present supersymmetry breaking four-dimensional orientifolds of type-IIA strings. The compact space is a torus times a four-dimensional orbifold. The orientifold group reflects one direction in each torus. RR tadpoles are cancelled by D6-branes intersecting at angles in the torus and in the orbifold. The angles are chosen such that supersymmetry is broken. The resulting four-dimensional theories contain chiral fermions. The tadpole cancellation conditions imply that there are no non-abelian gauge anomalies. The models also contain anomaly-free U(1) factors.

Strings, Branes and Extra Dimensions

This review is devoted to strings and branes. Firstly, perturbative string theory is introduced. The appearance of various types of branes is discussed. These include orbifold fixed planes, D-branes and orientifold planes. The connection to BPS vacua of supergravity is presented afterwards. As applications, we outline the role of branes in string dualities, field theory dualities, the AdS/CFT correspondence and scenarios where the string scale is at a TeV. Some issues of warped compactifications are also addressed. These comprise corrections to gravitational interactions as well as the cosmological constant problem.This review is devoted to strings and branes. Firstly, perturbative string theory is introduced. The appearance of various types of branes is discussed. These include orbifold fixed planes, D-branes and orientifold planes. The connection to BPS vacua of supergravity is presented afterwards. As applications, we outline the role of branes in string dualities, field theory dualities, the AdS/CFT correspondence and scenarios where the string scale is at a TeV. Some issues of warped compactifications are also addressed. These comprise corrections to gravitational interactions as well as the cosmological constant problem.

Scattering amplitudes in strongly coupled N = 4 SYM from semiclassical strings in AdS

Very recently in [1] Alday and Maldacena gave a string theory prescription for computing (all) planar amplitudes in = 4 supersymmetric gauge theory at strong coupling using the AdS/CFT correspondence. These amplitudes are determined by a classical string solution and contain a universal exponential factor involving the action of the classical string. On the gauge theory side, expressions for perturbative amplitudes at strong coupling were previously proposed only for specific helicities of external particles — the maximally helicity violating or MHV amplitudes. These follow from the exponential ansatz of Bern, Dixon and Smirnov [2] for MHV amplitudes in = 4 SYM. In this paper we examine the amplitudes dependence on helicities and particle-types of external states. We consider the prefactor of string amplitudes and give arguments suggesting that the prefactor at strong coupling should be the same as the Yang-Mills tree-level amplitude for the same process. This implies that scattering amplitudes in = 4 SYM simplify dramatically in the strong coupling limit. It follows from our proposal that in this limit all (MHV and non-MHV) n-point amplitudes are given by the (known) tree-level Yang-Mills result times the helicity-independent (and particle-type-independent) universal exponential.

Gauging flavour in meta-stable susy breaking models

We modify the first ISS model [1] by gauging a diagonal flavour symmetry. We add additional multiplets transforming as fundamentals and anti-fundamentals under the gauged flavour group. Their number is chosen such that the microscopic theory is asymptotically free whereas in the Seiberg dual (w.r.t. the colour group) an additional adjoint changes it to an infrared free or conformal theory. Non perturbative effects within the flavour group correct the location of the supersymmetric vacuum. Statements about meta-stability of the susy breaking vacuum would require a two loop calculation. For general couplings, the question whether gauging flavour destabilises susy breaking remains open.

Z(2)x Z(2)heterotic orbifold models of non factorisable six dimensional toroidal manifolds

We discuss heterotic strings on 2 × 2 orbifolds of non factorisable six-tori. Although the number of fixed tori is reduced as compared to the factorisable case, Wilson lines are still needed for the construction of three generation models. An essential new feature is the straightforward appearance of three generation models with one generation per twisted sector. We illustrate our general arguments for the occurrence of that property by an explicit example. Our findings give further support for the conjecture that four dimensional heterotic strings formulated at the free fermionic point are related to 2 × 2 orbifolds.

Current-current deformations of conformal field theories, and WZW models

Moduli spaces of conformal field theories corresponding to current-current deformations are discussed. For WZW models, CFT and sigma model considerations are compared. It is shown that current-current deformed WZW models have WZW-like sigma model descriptions with non-bi-invariant metrics, additional B-fields and a non-trivial dilaton.

Geometry of rank reduction

We show how one can obtain geometric scaling properties from the Balitsky-Kovchegov (BK) equation. We start by explaining how, this property arises for the b-independent BK equation. We show that it is possible to extend this model to the full BK equation including momentum transfer. The saturation scale behaves like max(q, QT) where q is the momentum transfer and QT a typical scale of the target. Geometric scaling 1 expresses the fact that the DIS HERA data depend of the virtuality Q 2 and the rapidity Y = log(1/x) only through the ratio Q/Q s (Y) where Q s is an energy-dependent scale. On another side, a lot of research have been done during the last ten years to obtain a description of the saturation effects in the high-energy limit of QCD, leading to the Balitsky-Kovchegov equation 2. This equation supplements the BFKL 3 equation in including the contributions from fan diagrams. It has recently been shown in the framework of the impact-parameter independent BK equation that one can infer geometric scaling from the asymptotic solutions of the evolution equation. We shall explain how we have extended these properties of geometric scaling to the case of the full BK equation. Our analysis is performed in momentum space where we also introduce a new form of the BK equation. We shall discuss the properties of the saturation scale and its momentum-transfer dependence. Let us thus start our analysis by considering the case of the impact-parameter independent BK equation: N (x, y) = N (|x−y|). If we go to momentum space using ˜ N (k) = 1 2π d 2 r r 2 e ik.r N (r) = ∞ 0 dr r J 0 (kr)N (r), a On leave from the fundamental theoretical physics group of the University ofLì ege.We introduce continuous Wilson lines to reduce the rank of the gauge group in orbifold constructions. In situations where the orbifold twist can be realized as a rotation in the root lattice of a grand unified group we derive an appealing geometric picture of the symmetry breakdown. This symmetry breakdown is smooth and corresponds to a standard field theory Higgs mechanism. The embedding into heterotic string theory is discussed.