Evidence for heterotic - Type I string duality

A study is made of the implications of heterotic string T-duality and extended gauge symmetry for the conjectured equivalence of heterotic and Type I superstrings. While at first sight heterotic string world-sheet dynamics appears to conflict with Type I perturbation theory, a closer look shows that Type I perturbation theory “miraculously” breaks down, in some cases via novel mechanisms, whenever the heterotic string has massless particles not present in Type I perturbation theory. This strongly suggests that the two theories actually are equivalent. As further evidence in the same direction, we show that the Dirichlet one-brane of Type I string theory has the same world-sheet structure as the heterotic string.     

What we learn on the heterotic string vacua from anomaly-free supergravity

The recently constructed D = 10 anomaly-free supergravity (AFS) has been argued to contain the full effective theory of the heterotic string. The solutions of the effective theory must be solutions of AFS, while the converse is not necessarily true since string theory might specify the boundary conditions for the AFS torsion equation. We show that Calabi-Yau spaces are exact solutions of AFS, while compact group and coset manifolds are not. This is due to a positivity argument, which is the extension to anomaly-free supergravity of the “ten into four won't go” theorem of Freedman, Gibbons and West for the Chapline-Manton theory.     

On heterotic vacua with fermionic expectation values

We study heterotic backgrounds with non‐trivial H‐flux and non‐vanishing expectation values of fermionic bilinears, often referred to as gaugino condensates. The gaugini appear in the low energy action via the gauge‐invariant three‐form bilinear . For Calabi‐Yau compactifications to four dimensions, the gaugino condensate corresponds to an internal three‐form that must be a singlet of the holonomy group. This condition does not hold anymore when an internal H‐flux is turned on and effects are included. In this paper we study flux compactifications to three and four‐dimensions on G‐structure manifolds. We derive the generic conditions for supersymmetric solutions. We use integrability conditions and Lichnerowicz type arguments to derive a set of constraints whose solution, together with supersymmetry, is sufficient for finding backgrounds with gaugino condensate.     

On the effective field theory of heterotic vacua

The effective field theory of heterotic vacua that realise Open image in new window preserving \(\mathcal {N}{=}1\) supersymmetry is studied. The vacua in question admit large radius limits taking the form Open image in new window , with Open image in new window a smooth threefold with vanishing first Chern class and a stable holomorphic gauge bundle Open image in new window . In a previous paper we calculated the kinetic terms for moduli, deducing the moduli metric and Kähler potential. In this paper, we compute the remaining couplings in the effective field theory, correct to first order in \({\alpha ^{\backprime }\,}\). In particular, we compute the contribution of the matter sector to the Kähler potential and derive the Yukawa couplings and other quadratic fermionic couplings. From this we write down a Kähler potential Open image in new window and superpotential Open image in new window .     

Gravitational waves as string vacua I

Recent results on the role of gravitational waves in string theory are reviwed. Motivations for the research and an organic view of the topic are furnished. Short exposition of the elements of string theory in the Polyakov formalism is provided, with particular emphasis on the evaluation of the Weyl and super-Weyl anomalies. Relevant results on the plane wave solutions of the Einstein equations are listed and a way of solving a quantum field theory in such backgrounds is presented. The results obtained for theS-matrix of the field theory and (singular) expectation values of its energy momentum tensor will be linked to string physics in subsequent parts of this review.This review article is based on the PhD thesis of the author defended in 1989 at SISSA, Trieste. It is divided into three parts with independent abstracts and tables of contents.     

Gravitational waves as string vacua III

We describe perturbative construction of in and out scalar vertex operators in nonlinear-models corresponding to gravitational plane wave backgrounds. The calculation is performed to all loops in the weak field limit and up to three loops in the usual perturbation expansion. The closed expressions for the vertex operators are given. They exhibit peculiar singularities in the target space which are closely related to the focusing phenomena in such backgrounds described in the previous parts of this review. Then the appendix is provided in which finite planar shell shock waves are studied. The review ends up with conclusions and a short list of related results, published since it was written.This is the third part of the review based on the PhD thesis of the author defended in 1989 at SISSA, Trieste.     

Gravitational waves as string vacua II

Classical propagation of (super)strings through gravitational shock waves is analyzed. The exact classical solutions are used for quantization and for the identification of the exact quantumS-matrix describing string scattering by the wave. ThisS-matrix coincides with theS-matrix of the string-string scattering in theflat space-time for particular profile of the shock wave! This is interpreted as the generation of curved geometry from the flat space-time string theory. The quantum consistence of (super)string motion in gravitational plane wave backgrounds is then studied. It turns out that for the standard dimensionsD=26 (D=10) the vanishing of the Ricci tensor for the plane wave is sufficient condition for vanishing of the Weyl (superWeyl) anomaly. Thus, plane wave solutions of the Einstein equations are automatically the classical (super)string vacua. For particular plane waves the anomaly can be evaluated even nonperturbatively.This is the second part of the review based on the PhD thesis of the author defended in 1989 at SISSA, Trieste.     

Minimal standard heterotic string models

Three generation heterotic string vacua in the free fermionic formulation gave rise to models with solely the MSSM states in the observable standard model charged sector. The relation of these models to Z₂×Z₂ orbifold compactifications dictates that they produce three pairs of untwisted Higgs multiplets. The reduction to one pair relies on the analysis of supersymmetric flat directions, which give a superheavy mass to the dispensable Higgs states. We explore the removal of the extra Higgs representations by using the free fermion boundary conditions, and hence we work directly at the string level, rather than in the effective low energy field theory. We present a general mechanism that achieves this reduction by using asymmetric boundary conditions between the left- and right-moving internal fermions. We incorporate this mechanism in explicit string models containing three twisted generations and a single untwisted Higgs doublet pair. We further demonstrate that an additional effect of the asymmetric boundary conditions is to substantially reduce the supersymmetric moduli space.     

The heterotic string is a soliton

It is shown that the Type IIA superstring compactified on K3 has a smooth string soliton with the same zero mode structure as the heterotic string compactified on a four-torus, thus providing new evidence for a conjectured exact duality between the two six-dimensional string theories. The chiral worldsheet bosons arise as zero modes of Ramond-Ramond fields of the IIA string theory and live on a signature (20,4) even, self-dual lattice. Stable, finite loops of soliton string provide the charged Ramond-Ramond states necessary for enhanced gauge symmetries at degeneration points of the K3 surface. It is also shown that Type IIB strings toroidally compactified to six dimensions have a multiplet of string solutions with Type II worldsheets.     

Orbifold compactification of heterotic string theories

The internal degrees of freedom of twisted heterotic strings are discussed using the theory of Kac-Moody algebras.     

Spacetime supersymmetry breaking in heterotic string theory

A simple mechanism for spacetime supersymmetry breaking in the ten-dimensional heterotic string theory is proposed. We present a heterotic string model with a hidden two-dimensional sigma-model sector which can induce desirably small supersymmetry breaking, without upsetting the zero value of the cosmological constant, through a topological instanton effect due to an abelian gauge field on the string world sheet. We find that the consistency condition of the gravitino field equation is satisfied for some configurations even after supersymmetry breaking.     

R parity from the heterotic string

In T-duality invariant effective supergravity with gaugino condensation as the mechanism for supersymmetry breaking, there is a residual discrete symmetry that could play the role of R parity in supersymmetric extensions of the standard model.     

Seesaw neutrinos from the heterotic string

We study the possibility of realizing the neutrino seesaw mechanism in the E(8) x E(8) heterotic string. In particular, we consider its Z6 orbifold compactifications leading to the supersymmetric standard model gauge group and matter content. We find that these models possess all the necessary ingredients for the seesaw mechanism, including the required Dirac Yukawa couplings and large Majorana mass terms. We argue that this situation is quite common in heterotic orbifolds. In contrast with the conventional seesaw of grand unified theories (GUTs), no large GUT representations are needed to generate the Majorana mass terms. The total number of right-handed neutrinos can be very large, up to O(100).     

Five-brane superpotentials and heterotic/F-theory duality

Under heterotic/F-theory duality it was argued that a wide class of heterotic five-branes is mapped into the geometry of an F-theory compactification manifold. In four-dimensional compactifications this identifies a five-brane wrapped on a curve in the base of an elliptically fibered Calabi–Yau threefold with a specific F-theory Calabi–Yau fourfold containing the blow-up of the five-brane curve. We argue that this duality can be reformulated by first constructing a non-Calabi–Yau heterotic threefold by blowing up the curve of the five-brane into a divisor with five-brane flux. Employing heterotic/F-theory duality this leads us to the construction of a Calabi–Yau fourfold and four-form flux. Moreover, we obtain an explicit map between the five-brane superpotential and an F-theory flux superpotential. The map of the open–closed deformation problem of a five-brane in a compact Calabi–Yau threefold into a deformation problem of complex structures on a dual Calabi–Yau fourfold with four-form flux provides a powerful tool to explicitly compute the five-brane superpotential.