String Expansion as 't Hooft's Expansion
We briefly review some recent developments in large N gauge theories which utilize the power of string perturbation techniques.
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arXiv subjects
Zurab Kakushadze
Publications and source records attributed to Zurab Kakushadze.
A Brief Review of Three-Family Grand Unification in String Theory
We briefly review the status of three-family grand unified string models.
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A Three-Family $SU(4)_c \otimes SU(2)_w \otimes U(1)$ Type I Vacuum
We construct a four dimensional chiral N=1 space-time supersymmetric perturbative Type I vacuum corresponding to a compactification on a toroidal Z_2 X Z_2 X Z_3 orbifold with a discrete Wilson line. This model is non-perturbative from the heterotic viewpoint. It has three chiral families in the SU(4)_c X SU(2)_w X U(1) subgroup of the total gauge group. We compute the tree-level superpotential in this model. There appears to be no obvious obstruction to Higgs the gauge group down to SU(3)_c X SU(2)_w X U(1)_Y and obtain the Standard Model gauge group with three chiral families.
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A Three-Family SU(6) Type I Compactification
We construct a four dimensional chiral N=1 space-time supersymmetric Type I vacuum corresponding to a compactification on a toroidal Z_2 X Z_2 X Z_3 orbifold. Using recent results in four dimensional orientifolds, we argue that this model has a well defined world-sheet description. An interesting feature of this model is that the gauge group contains an SU(6) subgroup with three chiral generations. Moreover, this model contains D5-branes and therefore corresponds to a non-perturbative heterotic vacuum. This is the first example of a consistent chiral N=1 supersymmetric string vacuum which is non-perturbative from the heterotic viewpoint, has a perturbative description in a dual theory, and possesses some phenomenologically interesting characteristics. We also compute the tree-level superpotential in this theory
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Type IIB Orientifolds, F-theory, Type I Strings on Orbifolds and Type I - Heterotic Duality
We consider six and four dimensional ${\cal N}=1$ supersymmetric orientifolds of Type IIB compactified on orbifolds. We give the conditions under which the perturbative world-sheet orientifold approach is adequate, and list the four dimensional ${\cal N}=1$ orientifolds (which are rather constrained) that satisfy these conditions. We argue that in most cases orientifolds contain non-perturbative sectors that are missing in the world-sheet approach. These non-perturbative sectors can be thought of as arising from D-branes wrapping various collapsed 2-cycles in the orbifold. Using these observations, we explain certain ``puzzles'' in the literature on four dimensional orientifolds. In particular, in some four dimensional orientifolds the ``naive'' tadpole cancellation conditions have no solution. However, these tadpole cancellation conditions are derived using the world-sheet approach which we argue to be inadequate in these cases due to appearance of additional non-perturbative sectors. The main tools in our analyses are the map between F-theory and orientifold vacua and Type I-heterotic duality. Utilizing the consistency conditions we have found in this paper, we discuss consistent four dimensional chiral ${\cal N}=1$ Type I vacua which are non-perturbative from the heterotic viewpoint.
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Gauge Theories from Orientifolds and Large N Limit
Extending the recent work in hep-th/9803076, we consider string perturbative expansion in the presence of D-branes and orientifold planes imbedded in orbifolded space-time. In the $α'\to 0$ limit the weak coupling string perturbative expansion maps to `t Hooft's large N expansion. We focus on four dimensional ${\cal N}=1,2,4$ supersymmetric theories, and also discuss possible extensions to ${\cal N}=0$ cases. Utilizing the string theory perturbation techniques we show that computation of any M-point correlation function in these theories reduces to the corresponding computation in the parent ${\cal N}=4$ theory. In particular, we discuss theories (which are rather constrained) with vanishing beta-functions to all orders in perturbation theory in the large N limit. We also point out that in theories with non-vanishing beta-functions the gauge coupling running is suppressed in the large N limit. Introduction of orientifold planes allows to construct certain gauge theories with SO, Sp and SU gauge groups and various matter (only unitary gauge groups with bi-fundamental/adjoint matter arise in theories without orientifold planes).
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String Expansion as Large N Expansion of Gauge Theories
We consider string perturbative expansion in the presence of D-branes imbedded in orbifolded space-time. In the regime where the string coupling is weak and $α'\to 0$, the string perturbative expansion coincides with `t Hooft's large N expansion. We specifically concentrate on theories with d=4 and ${\cal N}=0,1,2,4$, and use world-sheet orbifold techniques to prove vanishing theorems for the field theory beta functions to all orders in perturbation theory in the large N limit. This is in accord with recent predictions.
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Dynamical Flavor Hierarchy and Heavy Top
In the Standard Model one of the generations is much heavier than the other two. We propose a simple mechanism where all three generations are treated on the equal footing to begin with, and one heavy and two light families emerge from supersymmetric strong dynamics. The Yukawa mass matrix is identified with vevs of the meson fields of some additional gauge theory. It is then forced to have rank one (in the leading order) by non-perturbative superpotential.
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4-D Chiral N=1 Type I Vacua With And Without D5-Branes
In this paper we consider compactifications of type I strings on Abelian orbifolds. We discuss the tadpole cancellation conditions for the general case with D9-branes only. Such compactifications have (perturbative) heterotic duals which are also realized as orbifolds (with non-standard embedding of the gauge connection). The latter have extra twisted states that become massive once orbifold singularities are blown-up. This is due to the presence of perturbative heterotic superpotential with couplings between the extra twisted states, the orbifold blow-up modes, and (sometimes) untwisted matter fields. Anomalous U(1) (generically present in such models) also plays an important role in type I-heterotic (tree-level) duality matching. We illustrate these issues on a particular example of Z_3 \otimes Z_3 orbifold type I model (and its heterotic dual). The model has N=1 supersymmetry, U(4)^3 \otimes SO(8) gauge group, and chiral matter. We also consider compactifications of type I strings on Abelian orbifolds with both D9- and D5-branes. We discuss tadpole cancellation conditions for a certain class of such models. We illustrate the model building by considering a particular example of type I theory compactified on Z_6 orbifold. The model has N=1 supersymmetry, [U(6)\otimes U(6)\otimes U(4)]^2 gauge group, and chiral matter. This would correspond to a non-perturbative chiral vacuum from the heterotic point of view.
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Aspects of N=1 Type I-Heterotic Duality in Four Dimensions
In this paper we discuss some aspects of N=1 type I-heterotic string duality in four dimensions. We consider a particular example of a (weak-weak) dual pair where on the type I side there are only D9-branes corresponding to perturbative heterotic description in a certain region of the moduli space. We match the perturbative type I and heterotic tree-level massless spectra via giving certain scalars appropriate vevs, and point out the crucial role of the perturbative superpotential (on the heterotic side) for this matching. We also discuss the role of anomalous U(1) gauge symmetry present in both type I and heterotic models. In the perturbative regime we match the (tree-level) moduli spaces of these models. Since both type I and heterotic models can be treated perturbatively, we are able to discuss a dictionary that in generic models maps type I description onto heterotic one, and vice-versa. Finally, we discuss possible directions to study perturbative quantum corrections to the moduli space, as well as outline ways to learn about the non-perturbative effects in both descriptions.
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A Review of Three-Family Grand Unified String Models
We review the construction and classification of three-family grand unified models within the framework of asymmetric orbifolds in perturbative heterotic superstring. We give a detailed survey of all such models which is organized to aid analysis of their phenomenological properties. We compute tree-level superpotentials for these models. These superpotentials are used to analyze the issues of proton stability (doublet-triplet splitting and R-parity violating terms) and Yukawa mass matrices. To have agreement with phenomenological data all these models seem to require certain degree of fine-tuning. We also analyze the possible patterns of supersymmetry breaking in these models. We find that the supersymmetry breaking scale comes out either too high to explain the electroweak hierarchy problem, or below the electroweak scale unless some degree of fine-tuning is involved. Thus, none of the models at hand seem to be phenomenologically flawless.
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A Remark on Dilaton Stabilization
Dilaton stabilization may occur in a theory based on a single asymptotically free gauge group with matter due to an interplay between quantum modification of the moduli space and tree-level superpotential. We present a toy model where such a mechanism is realized. Dilaton stabilization in this mechanism tends to occur at strong coupling values unless some unnatural adjustment of parameters is involved.
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A Chiral N=1 Type I Vacuum in Four Dimensions and Its Heterotic Dual
In this paper we consider Type I string theory compactified on a Z_7 orbifold. The model has N=1 supersymmetry, a U(4) \otimes U(4) \otimes U(4) \otimes SO(8) gauge group, and chiral matter. There are only D9-branes (for which we discuss tadpole cancellation conditions) in this model corresponding to a perturbative heterotic description in a certain region of the moduli space. We construct the heterotic dual, match the perturbative type I and heterotic tree-level massless spectra via giving certain scalars appropriate vevs, and point out the crucial role of the perturbative superpotential (on the heterotic side) for this matching. The relevant couplings in this superpotential turn out to be non-renormalizable (unlike the Z-orbifold case discussed in Ref [1], where Yukawa couplings sufficed for duality matching). We also discuss the role of the anomalous U(1) gauge symmetry present in both type I and heterotic models. In the perturbative regime we match the (tree-level) moduli spaces of these models. We point out possible generalizations of the Z_3 and Z_7 cases to include D5-branes which would help in understanding non-perturbative five-brane dynamics on the heterotic side.
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Couplings in Asymmetric Orbifolds and Grand Unified String Models
Using the bosonic supercurrent (or covariant lattice) formalism, we review how to compute scattering amplitudes in asymmetric orbifold string models. This method is particularly useful for calculating scattering of multiple asymmetrically twisted string states, where the twisted states are rewritten as ordinary momentum states. We show how to reconstruct some of the 3-family grand unified string models in this formalism, and identify the quantum numbers of the massless states in their spectra. The discrete symmetries of these models are rather intricate. The superpotentials for the 3-family E_6 model and a closely related SO(10) model are discussed in some detail. The forms of the superpotentials of the two 3-family SU(6) models (with asymptotically-free hidden sectors SU(3) and SU(2) \otimes SU(2)) are also presented.
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Three-Family Grand Unification in String Theory
We briefly discuss the status of three-family grand unified string models.
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Phenomenology of 3-Family Grand Unified String Models
In the 3-family grand unified string models constructed so far, there is only one adjoint (and no higher dimensional representation) Higgs field in the grand unified gauge group. In this preliminary analysis, we address the proton-decay problem in the 3-family E_6 and related SO(10) string models. In particular, we analyze the doublet-triplet splitting (within certain assumptions about non-perturbative dynamics). It appears that generically some fine-tuning is necessary to arrange for a pair of Higgs doublets to be light, while having color Higgs triplets superheavy. We also discuss charge-2/3 quark mass matrix that generically also seems to require some fine-tuning to have rank 1.
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A Classification of 3-Family Grand Unification in String Theory I. The SO(10) and E_6 Models
We give a classification of 3-family SO(10) and E_6 grand unification in string theory within the framework of conformal field theory and asymmetric orbifolds. We argue that the construction of such models in the heterotic string theory requires certain Z_6 asymmetric orbifolds that include a Z_3 outer-automorphism, the latter yielding a level-3 current algebra for the grand unification gauge group SO(10) or E_6. We then classify all such Z_6 asymmetric orbifolds that result in models with a non-abelian hidden sector. All models classified in this paper have only one adjoint (but no other higher representation) Higgs field in the grand unified gauge group. In addition, all of them are completely anomaly free. There are two types of such 3-family models. The first type consists of the unique SO(10) model with SU(2) X SU(2) X SU(2) as its hidden sector (which is not asymptotically-free at the string scale). This SO(10) model has 4 left-handed and 1 right-handed 16s. The second type is described by a moduli space containing 17 models (distinguished by their massless spectra). All these models have an SU(2) hidden sector, and 5 left-handed and 2 right-handed families in the grand unified gauge group. One of these models is the unique E_6 model with an asymptotically-free SU(2) hidden sector. The others are SO(10) models, 8 of them with an asymptotically free hidden sector at the string scale.
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A Classification of 3-Family Grand Unification in String Theory II. The SU(5) and SU(6) Models
Requiring that supersymmetric SU(5) and SU(6) grand unifications in the heterotic string theory must have 3 chiral families, adjoint (or higher representation) Higgs fields in the grand unifiedgauge group, and a non-abelian hidden sector, we construct such string models within the framework of conformal field theory and asymmetric orbifolds. Within this framework, we construct all such string models via Z_6 asymmetric orbifolds that include a Z_3 outer-automorphism, the latter yielding a level-3 current algebra for the grand unification gauge group SU(5) or SU(6). We then classify all such Z_6 asymmetric orbifolds that result in models with a non-abelian hidden sector. All models classified in this paper have only one adjoint (but no otherhigher representation) Higgs field in the grand unified gauge group. This Higgs field is neutral under all other gauge symmetries. The list of hidden sectors for 3-family SU(6) string models are SU(2), SU(3) and $SU(2) \otimes SU(2)$. In addition to these, 3-family SU(5) string models can also have an SU(4) hidden sector. Some of the models have an anomalous U(1).
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