Nonabelian Orbifolds Research Articles

Gauging discrete symmetries of TN-theories in five dimensions

We study the gauging of a discrete ℤ3 symmetry in the five-dimensional superconformal TN theories. We argue that this leads to an infinite sequence of five-dimensional superconformal theories with either E6× SU(N) or SU(3) × SU(N) global symmetry group. In the M-theory realisation of TN theories as residing at the origin in the Calabi-Yau orbifolds frac{{mathbb{C}}^3}{{mathbb{Z}}_Ntimes {mathbb{Z}}_N} we identify the ℤ3 symmetry geometrically and the new theories arise from M-theory on the non-Abelian orbifolds left(frac{{mathbb{C}}^3}{{mathbb{Z}}_Ntimes {mathbb{Z}}_N}right)/{mathbb{Z}}_3 . On the other hand, in the (p, q) 5-brane web description in Type IIB theory, the symmetry combines the U-duality symmetry with a rotation in space, defining a so-called U-fold background, where the E6 symmetry is manifest.

Non-abelian orbifolds of lattice vertex operator algebras

We construct orbifolds of holomorphic lattice vertex operator algebras for non-abelian finite automorphism groups G. To this end, we construct twisted modules for automorphisms g together with the projective representation of the centralizer of g on the twisted module. This allows us to extract the irreducible modules of the fixed-point VOA VG, and to compute their characters and modular transformation properties. We then construct holomorphic VOAs by adjoining such modules to VG. Applying these methods to extremal lattices in d=48 and d=72, we construct more than fifty new holomorphic VOAs of central charge 48 and 72, many of which have a very small number of light states.

Discrete gauging in Coulomb branches of three dimensional mathcal{N}=4 supersymmetric gauge theories

This paper tests a conjecture on discrete non-Abelian gauging of 3d mathcal{N}=4 supersymmetric quiver gauge theories. Given a parent quiver with a bouquet of n nodes of rank 1, invariant under a discrete Sn global symmetry, one can construct a daughter quiver where the bouquet is substituted by a single adjoint n node. Based on the main conjecture in this paper, the daughter quiver corresponds to a theory where the Sn discrete global symmetry is gauged and the new Coulomb branch is a non-Abelian orbifold of the parent Coulomb branch. We demonstrate and test the conjecture for three simply laced families of bouquet quivers and a non-simply laced bouquet quiver with C2 factor in the global symmetry.

Heterotic non-abelian orbifolds

Abstract We perform the first systematic analysis of particle spectra obtained from heterotic string compactifications on non-Abelian toroidal orbifolds. After developing a new technique to compute the particle spectrum in the case of standard embedding based on higher dimensional supersymmetry, we compute the Hodge numbers for all recently classified 331 non-Abelian orbifold geometries which yield $ \mathcal{N}=1 $ supersymmetry for heterotic compactifications. Surprisingly, most Hodge numbers follow the empiric pattern h (1,1) − h (2,1) = 0 mod 6, which might be related to the number of three standard model generations. Furthermore, we study the fundamental groups in order to identify the possibilities for non-local gauge symmetry breaking. Three examples are discussed in detail: the simplest non-Abelian orbifold S 3 and two more elaborate examples, T 7 and Δ(27), which have only one untwisted Kähler and no untwisted complex structure modulus. Such models might be especially interesting in the context of no-scale supergravity. Finally, we briefly discuss the case of orbifolds with vanishing Euler numbers in the context of enhanced (spontaneously broken) supersymmetry.

Aspects of ABJM orbifolds

We study abelian and non-abelian orbifolds of the ABJM model. We compute the precise moduli space of these models by analyzing the classical BPS equations for the theory on the cylinder, which include classical solutions of magnetic monopole operators. These determine the chiral ring of the theory, and thus they provide the complete set of order parameters determining the classical vacua of the theory. We show that the proper quantization of these semiclassical solutions gives us the topology of moduli space, including the additional quotient information due to the Chern-Simons levels. In general, we find that in the dual M-theory setup, the M-theory fiber is divided by the product of the Chern-Simons level times the order of the orbifold group, even in the non-abelian case. This depends non-trivially on how the different Chern-Simons terms have different levels in these constructions. We also see a direct relation in this setup between the Chern-Simons levels of the different groups and fluxes for fractional brane cycles. We also show that the problem of the moduli space can be much more easily analyzed by using the method of images and representation theory of crossed product algebras rather than dealing only with the quiver theory data.

MSSM parameters from supergravity backgrounds

We find the parameters of the MSSM in terms of bulk supergravity fields for the D-brane model of Berenstein, Jejjala and Leigh (hep-ph/0105042). The model consists of a D3-brane at the singularity of a non-abelian orbifold \Delta_{27}, which gives the particles of the Supersymmetric Standard Model. We compute the action for the D-brane fields in the presence of both supersymmetric and supersymmetry breaking background fluxes. We get quark, lepton, gaugino, Higgsino, scalar partners and Higgs masses, as well as soft trilinear couplings, as functions of the background fields. This work develops a framework for connecting MSSM phenomenology to brane compactifications.

Metrics building of pp-wave orbifold geometries

We study strings on orbifolds of AdS×S5 by SU(2) discrete groups in the Penrose limit. We derive the degenerate metrics of pp wave of AdS×S5/Γ using ordinary ADE and affine ADE singularities of complex surfaces and results on N=4 CFT4's. We also give explicit metric moduli dependences for both Abelian and non-Abelian orbifolds.

Classification of conformality models based on non-Abelian orbifolds

A systematic analysis is presented of compactifications of the type IIB superstring on ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}/\ensuremath{\Gamma}$ where $\ensuremath{\Gamma}$ is a non-Abelian discrete group. Every possible $\ensuremath{\Gamma}$ with order $g<~31$ is considered. 45 such groups exist but a majority cannot yield chiral fermions due to a certain theorem that is proved. The lowest order to embrace the non-SUSY standard $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}U(1)$ model with three chiral families is $\ensuremath{\Gamma}{=D}_{4}\ifmmode\times\else\texttimes\fi{}{Z}_{3},$ with $g=24;$ this is the only successful model found in the search. The consequent uniqueness of the successful model arises primarily from the scalar sector, prescribed by the construction, being sufficient to allow the correct symmetry breakdown.

AdS/CFT DUALITY AND CONFORMALITY FOR NON-ABELIAN ORBIFOLD

An outline of conformality approach to the gauge hierarchy is given including the use of non-abelian orbifolds to give unified model of the left-right type.

Finite N AdS/CFT correspondence for Abelian and non-Abelian orbifolds, and gauge coupling unification

Although the AdS/CFT correspondence is rigorous only for an infinite N→∞ stack of D3-branes, it can be fruitfully studied for finite N as a source of gauge structures and choices for chiral fermions and complex scalars which solve the hierarchy problem by a conformal fixed point. We emphasize orbifolds AdS5×S5/Γ where the resulting GFT has 𝒩=0 supersymmetry. The fact that the complex scalars are prescribed by the construction limits the possible spontaneous symmetry breaking. Both Abelian and non-Abelian Γ are illustrated by simple examples. An accurate sin2 θ in electroweak unification can be obtained, suggesting that this approach merits further study.

Discrete torsion, non-abelian orbifolds and the Schur multiplier

Armed with the explicit computation of Schur Multipliers, we offer a classification of SU(n) orbifolds for n = 2,3,4 which permit the turning on of discrete torsion. This is in response to the host of activity lately in vogue on the application of discrete torsion to D-brane orbifold theories. As a by-product, we find a hitherto unknown class of N = 1 orbifolds with non-cyclic discrete torsion group. Furthermore, we supplement the status quo ante by investigating a first example of a non-Abelian orbifold admitting discrete torsion, namely the ordinary dihedral group as a subgroup of SU(3). A comparison of the quiver theory thereof with that of its covering group, the binary dihedral group, without discrete torsion, is also performed.

Classification of conformality models based on non-Abelian orbifolds

Classification of conformality models based on non-Abelian orbifolds

Torsion D-branes in nongeometrical phases

In a geometrical background, D-brane charge is classified by topological K-theory. The corresponding classification of D-brane charge in an arbitrary, nongeometrical, compactification is still a mystery. We study D-branes on non-simply-connected Calabi-Yau 3-folds, with particular interest in the D-branes whose charges are torsion elements of the K-theory. We argue that we can follow the D-brane charge through the nongeometrical regions of the Kahler moduli space and, as evidence, explicitly construct torsion D-branes at the Gepner point in some examples. In one of our examples, the Gepner theory is a nonabelian orbifold of a tensor product of minimal models, and this somewhat exotic situation seems to be essential to the physics. Work supported in part DOE Grant DE-FG02-96ER40959. Work supported in part by NSF Grant PHY0071512 and the Robert A. Welch Foundation.

Chiral fermions and AdS/CFT duality for a nonabelian orbifold

We present what we believe is the minimal three-family AdS/CFT model compactified on a nonabelian orbifold S 5/( Q× Z 3). Nontrivial irreps of the discrete nonabelian group Q× Z 3 are identified with the 4 of SU(4) R symmetry to break all supersymmetries, and the scalar content of the model is sufficient to break the gauge symmetry to the standard model. According to the conformality hypothesis the progenitor SU(4) 3× SU(2) 12 theory becomes conformally invariant at an infra-red fixed point of the renormalization group.

Brane cube realization of three-dimensional nonabelian orbifolds

We study D-branes on three-dimensional orbifolds ${\bf C}^3/\Gamma$ where $\Gamma$ are finite subgroups of SU(3). The quiver diagram of $\ZnZn \in SU(3)$ can be expressed in three-dimensional form. According to the correspondence between quiver diagrams and brane configurations, we construct a brane configuration for ${\bf C}^3/\ZnZn$ which has essentially three-dimensional structrue. Brane configurations for nonabelian orbifolds $\C^3/\Delta(3n^2)$ and $\C^3/\Delta(6n^2)$ are obtained from that for $\C^3/\ZnZn$ by certain quotienting procedure.

Brane Configurations for Three-dimensional Nonabelian Orbifolds

Brane Configurations for Three-dimensional Nonabelian Orbifolds

Chiral fermions and AdS/CFT duality for a nonabelian orbifold

Chiral fermions and AdS/CFT duality for a nonabelian orbifold

D-branes on three-dimensional nonabelian orbifolds

We study D-branes on a three complex dimensional nonabelian orbifold ${\bf C}^3/\Gamma$ with $\Gamma$ a finite subgroup of SU(3). We present general formulae necessary to obtain quiver diagrams which represent the gauge group and the spectrum of the D-brane worldvolume theory for dihedral-like subgroups $\Delta(3n^2)$ and $\Delta(6n^2)$. It is found that the quiver diagrams have a similar structure to webs of branes.

On four-dimensional N = 1 Type I compactifications

We consider four-dimensional N = 1 supersymmetric Type I compactifications on toroidal orbifolds T 6/ Γ. In particular, we focus on the Type I vacua which are perturbative from the orientifold viewpoint, that is, on the compactifications with well-defined world-sheet expansion. The number of such models is rather constrained. This allows us to study all such vacua. This, in particular, involves considering compactifications with non-trivial NS-NS antisymmetric tensor backgrounds. We derive massless spectra for these models, and also compute superpotentials. We review the reasons responsible for such a limited number of perturbative Type I compactifications on toroidal orbifolds (which include Abelian as well as non-Abelian cases). As an aside, we generalize the recent work on large N gauge theories from orientifolds to include a non-Abelian orbifold. This also provides an important independent check for perturbative consistency of the corresponding Type I compactification.

Asymmetric non-Abelian orbifolds and model building.

The rules for the free fermionic string model construction are extended to include general non-abelian orbifold constructions that go beyond the real fermionic approach. This generalization is also applied to the asymmetric orbifold rules recently introduced. These non-abelian orbifold rules are quite easy to use. Examples are given to illustrate their applications.