Zurab Kakushadze

String expansion as large N expansion of gauge theories

Abstract 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 ′ → 0, the string perturbative expansion coincides with `t Hoofts large N expansion. We specifically concentrate on theories with d = 4 and N = 0, 1, 2, 4, and use world-sheet orbifold techniques to prove vanishing theorems for the field theory β-functions to all orders in perturbation theory in the large N limit. This is in accord with recent predictions.

Aspects of N = 1 type I-heterotic duality in four dimensions

Abstract 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 the perturbative heterotic description in a certain region of the moduli space. We match the perturbative type I and heterotic tree-level massless spectra by 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 the type I description onto the 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.

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 {bold Z}{sub 7} orbifold. The model has N=1 supersymmetry, a U(4){circle_times}U(4){circle_times}U(4){circle_times}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 vacuum expectation values, 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 nonrenormalizable (unlike the Z-orbifold case discussed by Kakushadze, 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 {bold Z}{sub 3} and {bold Z}{sub 7} cases to include D5-branes which would help in understanding nonperturbative five-brane dynamics on the heterotic side. {copyright} {ital 1997} {ital The American Physical Society}

Type IIB Orientifolds with NS-NS Antisymmetric Tensor Backgrounds

We consider six dimensional N=1 space-time supersymmetric type IIB orientifolds with a nonzero untwisted NS-NS sector B field. The B field is quantized due to the requirement that the type IIB spectrum be left-right symmetric. The presence of the B field results in rank reduction of both 99 and 55 open string sector gauge groups. We point out that in some of the models with a nonzero B field there are extra tensor multiplets in the {bold Z}{sub 2} twisted closed string sector, and we explain their origin in a simple example. Also, the 59 open string sector states come with a multiplicity that depends on the B field. These two facts are in accord with anomaly cancellation requirements. We point out relations between various orientifolds with and without the B field, and also discuss the F-theory duals of these models. {copyright} {ital 1998} {ital The American Physical Society}

Type IIB orientifolds, F-theory, Type I strings on orbifolds and Type I-heterotic duality

Abstract We consider six- and four-dimensional 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 N = 1 orientifolds (which are rather constrained) that satisfy these conditions. We argue that in most cases orientifolds contain nonperturbative 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 N = 1 Type I vacua which are non-perturbative from the heterotic viewpoint.

Gauge theories from orientifolds and large N limit

Extending the recent work by M. Bershadsky, Z. Kakushadze and C. Vafa (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′ → 0 limit the weak coupling string perturbative expansion maps to `t Hoofts large-N expansion. We focus on four-dimensional N = 1, 2, 4 supersymmetric theories, and also discuss possible extensions to 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 N = 4 theory. In particular, we discuss theories (which are rather constrained) with vanishing β-functions to all orders in perturbation theory in the large-N limit. We also point out that in theories with non-vanishing β-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).

FOUR-DIMENSIONAL 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 a 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 1-heterotic (tree-level) duality matching. We illustrate these issues on a particular example of Z3 ⊗ Z3 orbifold type I model (and its heterotic dual). The model has N = 1 supersymmetry, U(4)3 ⊗ 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 Z6 orbifold. The model has N = 1 supersymmetry, [U(6) ⊗ U(6) ⊗ U(4)]2 gauge group, and chiral matter. This would correspond to a non-perturbative chiral vacuum from the heterotic point of view.

Three-Family SO(10) Grand Unification in String Theory.

The construction of a supersymmetric SO(10) grand unification with 5 left-handed and 2 right-handed families in the four-dimensional heterotic string theory is presented. The model has one SO(10) adjoint Higgs field. The SO(10) current algebra is realized at level 3. {copyright} {ital 1996 The American Physical Society.}

A three-family SU(6) type I compactification

Abstract We construct a four dimensional chiral N =1 space-time supersymmetric Type I vacuum corresponding to a compactification on a toroidal Z 2 ⊗ Z 2 ⊗ 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.

Novel extension of MSSM and 'TeV scale' coupling unification

Abstract Motivated by the coupling unification problem, we propose a novel extension of the Minimal Supersymmetric Standard Model. One of the predictions of this extension is the existence of new states neutral under SU (3) c ⊗ SU (2) w but charged under U (1) y . The mass scale for these new states can be around the mass scale of the electroweak Higgs doublets. This suggests the possibility of their detection in the present or near future collider experiments. Unification of gauge couplings in this extension is as precise (at one loop) as in the MSSM, and can occur in the TeV range.