Coset Space Dimensional Reduction Research Articles

Model building by coset space dimensional reduction scheme using eight-dimensional coset spaces

We investigate the twelve-dimensional gauge-Higgs unification models with an eight- dimensional coset space as the extra space. For each model, we apply the coset space dimensional reduction procedure and examine the particle contents of the resulting four-dimensional theory. All combinations of inputs to the procedure are exhaustively analyzed under several assumptions. As a result, some twelve-dimensional SO(18) gauge theories lead to models of the SO(10) × U(1) grand unified theory in four dimensions, where fermions of the Standard Model appear in multiple generations along with scalars that may break the electroweak symmetry. The representations of the obtained scalars and fermions are summarized.

Classification of the Vacua of the Dimensionally Reduced Low‐Energy Limit of the Heterotic String Over Nearly‐Kähler Manifolds

AbstractWe examine the vacua of the scalar potential of the effective 4‐d action, obtained after the dimensional reduction of the 10‐d heterotic supergravity coupled to an Yang‐Mills sector. The (Coset Space) dimensional reduction takes place over the three 6‐d nearly‐Kähler manifolds, namely the homogeneous 6‐d non‐symmetric coset spaces, , and . The current work consists a complete catalogue of the kinds of vacua of theories obtained after the reduction of the heterotic string over the 6‐d non‐symmetric coset spaces and, moreover, a contribution to the dialogue of the possibility to result with non‐AdS vacua in the framework of string theories.

Gauge Theories: From Kaluza–Klein to noncommutative gravity theories

First, the Coset Space Dimensional Reduction scheme and the best particle physics model so far resulting from it are reviewed. Then, a higher-dimensional theory in which the extra dimensions are fuzzy coset spaces is described and a dimensional reduction to four-dimensional theory is performed. Afterwards, another scheme including fuzzy extra dimensions is presented, but this time the starting theory is four-dimensional while the fuzzy extra dimensions are generated dynamically. The resulting theory and its particle content is discussed. Besides the particle physics models discussed above, gravity theories as gauge theories are reviewed and then, the whole methodology is modified in the case that the background spacetimes are noncommutative. For this reason, specific covariant fuzzy spaces are introduced and, eventually, the program is written for both the 3-d and 4-d cases.

Instantons in Lifshitz field theories

BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kahler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4+1 dimensions, for which we take the Chern-Simons term as the superpotential.

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 .

Nearly‐Kähler dimensional reduction of the heterotic string

AbstractThe effective action in four dimensions resulting from the ten‐dimensional 𝒩 = 1 heterotic supergravity coupled to 𝒩 = 1 supersymmetric Yang‐Mills upon dimensional reduction over nearly‐Kähler manifolds is discussed. Nearly‐Kähler manifolds are an interesting class of manifolds admitting an SU(3)‐structure and in six dimensions all homogeneous nearly‐Kähler manifolds are included in the class of the corresponding non‐symmetric coset spaces plus a group manifold. Therefore it is natural to apply the Coset Space Dimensional Reduction scheme using these coset spaces as internal manifolds in order to determine the four‐dimensional theory.

Dimensional reduction of the heterotic string over nearly-Kähler manifolds

Our aim is to derive the effective action in four dimensions resulting by reducing dimensionally the ten-dimensional = 1 heterotic supergravity coupled to = 1 super Yang-Mills over manifolds admitting a nearly-K?hler structure. Given the fact that all homogeneous six-dimensional nearly-K?hler manifolds are included in the class of the corresponding non-symmetric coset spaces plus a group manifold, our procedure amounts in applying the Coset Space Dimensional Reduction scheme using these coset spaces as internal manifolds. In our examination firstly the rules of the reduction of the theory over a general six-dimensional non-symmetric manifold are stated and subsequently a detailed case by case analysis is performed for all the three non-symmetric coset spaces. For each case the four-dimensional scalar potential is derived and the corresponding nearly-K?hler limit is obtained. Finally, we determine the corresponding supergravity description of the four-dimensional theory employing the heterotic Gukov-Vafa-Witten formula and results of the special K?hler geometry.

GAUGE-HIGGS UNIFICATION MODELS WITH COSET SPACE DIMENSIONAL REDUCTION SCHEME

We investigate the gauge-Higgs unification models within the scheme of the coset space dimensional reduction, beginning with two types of set up; fourteen-dimensional gauge theory with simple gauge groups and ten-dimensional gauge theory with direct product gauge groups. We found some phenomenologically acceptable models through an exhaustive search for the candidates of the coset spaces, the gauge group in higher dimension, and fermion representation.

Model building by coset space dimensional reduction in eight-dimensions

We investigate gauge-Higgs unification models in eight-dimensional spacetime where extra-dimensional space has the structure of a four-dimensional compact coset space. The combinations of the coset space and the gauge group in the eight-dimensional spacetime of such models are listed. After the dimensional reduction of the coset space, we identified SO(10), SO(10)×U(1) and SO(10)×U(1)×U(1) as the possible gauge groups in the four-dimensional theory that can accomodate the Standard Model and thus is phenomenologically promising. Representations for fermions and scalars for these gauge groups are tabulated.

Model building by coset space dimensional reduction in ten dimensions with direct product gauge symmetry

We investigate ten-dimensional gauge theories whose extra six-dimensional space is a compact coset space, $S/R$, and whose gauge group is a direct product of two Lie groups. We list candidates of the gauge group and embeddings of $R$ into them. After dimensional reduction of the coset space, we find fermion and scalar representations of ${G}_{\mathrm{GUT}}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ with ${G}_{\mathrm{GUT}}=\mathrm{SU}(5)$, $\mathrm{SO}(10)$ and ${E}_{6}$, which accommodate all of the standard model particles. We also discuss possibilities to generate distinct Yukawa couplings among the generations using representations with different dimensions for ${G}_{\mathrm{GUT}}=\mathrm{SO}(10)$ and ${E}_{6}$ models.

Coset space dimensional reduction and classification of semi‐realistic particle physics models

AbstractStarting from a Yang‐Mills‐Dirac theory defined in ten dimensions we classify the semi‐realistic particle physics models resulting from their Forgacs‐Manton dimensional reduction. The higher‐dimensional gauge group is chosen to be E8. This choice as well as the dimensionality of the space‐time is suggested by the heterotic string theory. Furthermore, we assume that the space‐time on which the theory is defined can be written in the compactified form M4 × B, with M4 the ordinary Minkowski spacetime and B = S/R a 6 ‐ dim homogeneous coset space. We constrain our investigation in those cases where the dimensional reduction leads in four dimensions to phenomenologically interesting and anomaly‐free GUTs such as E6, SO(10) and SU(5). However the four‐dimensional surviving scalars transform in the fundamental of the resulting gauge group are not suitable for the superstrong symmetry breaking of the Standard Model. The main objective of our work is the investigation to which extent the latter can be achieved by employing the Wilson flux breaking mechanism.

Coset space dimensional reduction of Einstein–Yang–Mills theory

AbstractIn the present contribution we extend our previous work by considering the coset space dimensional reduction of higher‐dimensional Einstein–Yang–Mills theories including scalar fluctuations as well as Kaluza–Klein excitations of the compactification metric and we describe the gravity‐modified rules for the reduction of non‐abelian gauge theories.

Model Building by Coset Space Dimensional Reduction Scheme Using Ten-Dimensional Coset Spaces

We investigate the gauge-Higgs unification models within the scheme of the coset space dimensional reduction, beginning with a gauge theory in a fourteen-dimensional spacetime where extra-dimensional space has the structure of a ten-dimensional compact coset space. We found seventeen phenomenologically acceptable models through an exhaustive search for the candidates of the coset spaces, the gauge group in fourteen dimension, and fermion representation. Of the seventeen, ten models led to $\mathrm{SO}(10) (\times \mathrm{U}(1))$ GUT-like models after dimensional reduction, three models led to $\mathrm{SU}(5) \times \mathrm{U}(1)$ GUT-like models, and four to $\mathrm{SU}(3) \times \mathrm{SU}(2) \times \mathrm{U}(1) \times \mathrm{U}(1)$ Standard-Model-like models. The combinations of the coset space, the gauge group in the fourteen-dimensional spacetime, and the representation of the fermion contents of such models are listed.

On the consistency of coset space dimensional reduction

In this Letter we consider higher-dimensional Yang–Mills theories and examine their consistent coset space dimensional reduction. Utilizing a suitable ansatz and imposing a simple set of constraints we determine the four-dimensional gauge theory obtained from the reduction of both the higher-dimensional Lagrangian and the corresponding equations of motion. The two reductions yield equivalent results and hence they constitute an example of a consistent truncation.

Unified theories from fuzzy extra dimensions

AbstractWe combine and exploit ideas from Coset Space Dimensional Reduction (CSDR) methods and Non‐commutative Geometry. We consider the dimensional reduction of gauge theories defined in high dimensions where the compact directions are a fuzzy space (matrix manifold). In the CSDR one assumes that the form of space‐time is MD = M4 × S / R with S / R a homogeneous space. Then a gauge theory with gauge group G defined on MD can be dimensionally reduced to M4 in an elegant way using the symmetries of S / R, in particular the resulting four dimensional gauge is a subgroup of G. In the present work we show that one can apply the CSDR ideas in the case where the compact part of the space‐time is a finite approximation of the homogeneous space S / R, i.e. a fuzzy coset. In particular we study the fuzzy sphere case.

Dimensional Reduction over Coset Spaces and Supersymmetry Breaking

We address the question of supersymmetry breaking of a higher dimensional supersymmetric theory due to coset space dimensional reduction. In particular we study a ten-dimensional supersymmetric $E_{8}$ gauge theory which is reduced over all six-dimensional coset spaces. We find that the original supersymmetry is completely broken in the process of dimensional reduction when the coset spaces are symmetric. On the contrary softly broken four-dimensional supersymmetric theories result when the coset spaces are non-symmetric. From our analysis two promising cases are emerging which lead to interesting GUTs with three fermion families in four dimensions, one being non-supersymmetric and the other softly broken supersymmetric.

Supersymmetry breaking by dimensional reduction over coset spaces

We study the dimensional reduction of a ten-dimensional supersymmetric E 8 gauge theory over six-dimensional coset spaces. We find that the coset space dimensional reduction over a symmetric coset space leaves the four dimensional gauge theory without any track of the original supersymmetry. On the contrary the dimensional reduction over a non-symmetric coset space leads to a softly broken supersymmetric gauge theory in four dimensions. The SO 7/ SO 6 and G 2/ SU(3) are used as representative prototypes of symmetric and non symmetric coset spaces, respectively.

Strongly-interacting fermions from a higher-dimensional unified gauge theory

The method of coset-space dimensional reduction is employed in order to proceed from a gauged E 8× E 8′ unified theory defined in 10 dimensions to 4 dimensions. The resulting theory comprises the Standard Model along with a strongly-interacting fermion sector which breaks the electroweak symmetry dynamically at the right scale.

Ten-dimensional SO(10) GUT models with dynamical symmetry breaking.

We discuss the derivation of SO(10) GUT models from higher-dimensional theories with intermediate breaking scales. We then present models based on the coset space dimensional reduction scheme with intermediate symmetry breaking induced by four fermion condensates.

A three generation unified model from coset space dimensional reduction

We present a model based on SO(16) in ten dimensions and dimensionally reduce, via the coset space dimensional reduction mechanism, to the standard model on the manifold M 4 ⊗ SU (3)/U (1) ⊗ U (1) ⊗ Z 2. Three generations of light flavour chiral fermions emerge as a consequence of the existence of an SU(3) flavour symmetry.