Compactification on non-symmetric six dimensional coset spaces with torsion

The equations of motion of a ten dimensional model based on the Chapline-Manton lagrangian, modified by higher derivative terms, are solved using six dimensional coset spaces with torsion. Minkowski space, anti-de Sitter, de Sitter and Einstein static cosmology with negative curvature are possible four dimensional cosmologies. In all case symmetry breaking schemesE ₈×E ₈→E ₈×E ₆ with chiral 27's ofE ₆ can be obtained.     

Compactification over coset spaces with torsion and vanishing cosmological constant

We consider the compactification of ten-dimensional Einstein-Yang-Mills theories over non-symmetric, six-dimensional homogeneous coset spaces with torsion. We examine the Einstein-Yang-Mills equations of motion requiring vanishing cosmological constant at ten and four dimensions and we present examples of compactictifying solutions. It appears that the introduction of more than one radii in the coset space, when possible, may be mandatory for the existence of compactifying solutions.     

Spontaneous compactification to non-symmetric spaces

We investigate the spontaneous compactification of 4+d dimensions toM ₄ ×K/H whereK/H is ad-dimensional non-symmetric space. We present a formula giving the complete massless spinor spectrum for allK/H spaces. We discuss in detail all six-dimensional non-symmetric spacesK/H withK being simple.     

A non-singular homogeneous universe with torsion

The Raychaudhuri equation and other relations for a spinning fluid in the framework of the Einstein-Cartan theory are obtained. It is shown that non-singular cosmological models of the Bianchi types I÷VIII are possible. As an example, a class of solutions for the I and the V type is presented.     

Symmetries of coset spaces and Kaluza-Klein supergravity

Known theorems about the isometry group of a general coset space $\text{G}\text{H}$ are reviewed. The Killing vectors on $\text{G}\text{H}$ are explicitly constructed. Rescalings of the coset vielbeins are discussed, and a simple criterion to find which rescalings preserve the isometry group is given. A general expression for the Riemann and Ricci tensors in terms of the rescaled vielbeins and the group structure constants is derived. These results have useful applications in Kaluza-Klein theories. As an example, the round and the squashed seven-spheres that have been used to compactify d = 11 supergravity are discussed, and it is shown that they can be identified with two appropriately rescaled coset spaces $\text{SO(5)}\text{SO(3)}$.     

Exceptional coset spaces and unification in six dimensions

The coset spaces E₈/SO(10)×H_F allow complex structures which can account for three quark–lepton generations including right-handed neutrinos. We show that in the context of supersymmetric SO(10) gauge theories in 6 dimensions they also provide the Higgs fields which are needed to break the electroweak and B−L gauge symmetries, and to generate small neutrino masses via the seesaw mechanism.     

Heterotic strings on homogeneous spaces

We construct heterotic string backgrounds corresponding to families of homogeneous spaces as exact conformal field theories. They contain left cosets of compact groups by their maximal tori supported by NS‐NS 2‐forms and gauge field fluxes. We give the general formalism and modular‐invariant partition functions, then we consider some examples such as SU (2)/U (1) ~ S² (already described in a previous paper) and the SU (3)/U(1)² flag space. As an application we construct new supersymmetric string vacua with magnetic fluxes and a linear dilaton.     

A generalized positive energy theorem for spaces with asymptotic SUSY compactification

In this short note, we prove a generalized positive energy theorem for spaces with asymptotic SUSY compactification involving non-symmetric data. This work is motivated by the work of Dai [A positive mass theorem for spaces with asymptotic SUSY compactification, Comm. Math. Phys. 244 (2004) 335–345; A note on positive energy theorem for spaces with asymptotic SUSY compactification, 2004. arXiv:math-ph/0406006], Hertog–Horowitz–Maeda [Negative energy density in Calabi–Yau compactifications, JHEP 0305 (2003) 060], and Zhang [Angular momentum and positive mass theorem, Comm. Math. Phys. 206 (1999) 137–155].     

Compactification of ten-dimensional superstring theories over Ricci-flat coset spaces

In this paper the compactification of ten-dimensional superstring theories over homogeneous coset spaces S/R is analyzed. We construct explicitly the Ricci-flattening spin connection with torsion for the non-symmetric spaces G₂/SU(3), SU(3)/U(1) × U(1) and Sp(4)/SU(2) × U(1). These spaces provide a solution to the classical field equations with vanishing energy-momentum tensor and therefore one might expect that the conformal invariance of the string theory is preserved. We discuss the two-dimensional non-linear σ-model with Wess-Zumino term corresponding to the homogeneous spaces S/R. In addition, we investigate the constraints for the compactification coming from the requirement of unbroken supersymmetry and anomaly cancellation and give explicit examples of consistent compactification with S and R being embedded into the ten-dimensional gauge group E₈.     

Abelian gauge theories on homogeneous spaces

An algebraic technique of separation of gauge modes in Abelian gauge theories on homogeneous spaces is proposed. An effective potential for the Maxwell-Chern-Simons theory on S ³ is calculated. A generalization of the Chern-Simons action is suggested and analyzed with the example of SU(3)/U(1) X U(1).     

Orbifold compactification and solutions of M-theory from Milne spaces

In this paper, we consider solutions and spectral functions of M-theory from Milne spaces with extra free dimensions. Conformal deformations to the metric associated with real hyperbolic space forms are derived. For the three-dimensional case, the orbifold identifications , where Id is the identity matrix, is analyzed in detail. The spectrum of an eleven-dimensional field theory can be obtained with the help of the theory of harmonic functions in the fundamental domain of this group and it is associated with the cusp forms and the Eisenstein series. The supersymmetry surviving for supergravity solutions involving real hyperbolic space factors is briefly discussed.Received: 30 November 2004, Published online: 25 January 2005     

Free vector field in a homogeneous space with torsion

The effect of torsion of space-time, induced by the spin of a vector field, upon the physical properties of the field is studied within the framework of Einstein-Cartan gravitational theory. It is shown that the torsion leads to the appearance of nonlinearities in the vector field, as a consequence of which soliton solutions are possible under certain conditions. A cosmological model without singularities is constructed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 26–29, September, 1979.     

Higher‐Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions

We first review the Coset Space Dimensional Reduction (CSDR) programme and present the best model constructed so far based on the , 10‐dimensional E₈ gauge theory reduced over the nearly‐Kähler manifold with the additional use of the Wilson flux mechanism. Then we present the corresponding programme in the case that the extra dimensions are considered to be fuzzy coset spaces and the best model that has been constructed in this framework too. In both cases the best model appears to be the trinification GUT .     

Correlators of matrix models on homogeneous spaces

We investigate the correlators of TrA_μA_ν in matrix models on homogeneous spaces: S² and S²×S². Their expectation value is a good order parameter to measure the geometry of the space on which non-commutative gauge theory is realized. They also serve as the Wilson lines which carry the minimum momentum. We develop an efficient procedure to calculate them through 1PI diagrams. We determine the large N scaling behavior of the correlators. The order parameter shows that fuzzy S²×S² acquires a 4-dimensional fractal structure in contrast to fuzzy S². We also find that the two point functions exhibit logarithmic scaling violations.     

Canonical distributions on Riemannian homogeneous k-symmetric spaces

It is known that distributions generated by almost product structures are applicable, in particular, to some problems in the theory of Monge–Ampère equations. In this paper, we characterize canonical distributions defined by canonical almost product structures on Riemannian homogeneous $k$-symmetric spaces in the sense of types AF (anti-foliation), F (foliation), TGF (totally geodesic foliation). Algebraic criteria for all these types on $k$-symmetric spaces of orders $k=4,5,6$ were obtained. Note that canonical distributions on homogeneous $k$-symmetric spaces are closely related to special canonical almost complex structures and $f$-structures, which were recently applied by I. Khemar to studying elliptic integrable systems.     

Naturally reductive homogeneous Randers spaces

In this paper, we study naturally reductive Randers metrics on homogeneous manifolds. We first prove that naturally reductive Randers metrics are of Berwald type. We then give an explicit formula for the flag curvature of naturally reductive Randers metrics. Finally a necessary and sufficient condition for invariant Randers metrics on homogeneous manifolds being naturally reductive is given.