Type I-heterotic Duality Research Articles

TYPE I ON (GENERALIZED) VOISIN–BORCEA ORBIFOLDS AND NONPERTURBATIVE ORIENTIFOLDS

We consider nonperturbative four-dimensional [Formula: see text] space–time supersymmetric orientifolds corresponding to Type I compactifications on (generalized) Voisin–Borcea orbifolds. Some states in such compactifications arise in "twisted" open string sectors which lack world sheet description in terms of D-branes. Using Type I-heterotic duality as well as the map between Type IIB orientifolds and F theory we are able to obtain the massless spectra of such orientifolds. The four-dimensional compactifications we discuss in this context are examples of chiral [Formula: see text] supersymmetric string vacua which are nonperturbative from both orientifold and heterotic points of view. In particular, they contain both D9- and D5-branes as well as nonperturbative "twisted" open string sector states. We also explain the origins of various inconsistencies arising in such compactifications for certain choices of the gauge bundle.

Heterotic little string theories and holography

It has been conjectured that Little String Theories in six dimensions are holographic to critical string theory in a linear dilaton background. We test this conjecture for theories arising on the worldvolume of heterotic fivebranes. We compute the spectrum of chiral primaries in these theories and compare with results following from Type I-heterotic duality and the AdS/CFT correspondence. We also construct holographic duals for heterotic fivebranes near orbifold singularities. Finally we find several new Little String Theories which have Spin(32)/Z_2 or E_8 \times E_8 global symmetry but do not have a simple interpretation either in heterotic or M-theory.

Non-perturbative orientifolds

We consider non-perturbative six and four dimensional N=1 space-time supersymmetric orientifolds. Some states in such compactifications arise in “twisted” open string sectors which lack world-sheet description in terms of D-branes. Using Type I-heterotic duality we are able to obtain the massless spectra for some of such orientifolds. The four dimensional compactification we discus in this context is an example of a chiral N=1 supersymmetric string vacuum which is non-perturbative in both orientifold and heterotic pictures. In particular, it contains both D9- and D5-branes plus non-perturbative “twisted” open string sector states as well.

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

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.

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 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.

Duality of N = 2 heterotic-type I compactifications in four dimensions

We discuss type I-heterotic duality in four-dimensional models obtained as a Coulomb phase of the six-dimensional U(16) orientifold model compactified on T 2 with arbitrary SU(16) Wilson lines. We show that Kähler potentials, gauge threshold corrections and the infinite tower of higher derivative F-terms agree in the limit that corresponds to weak coupling, large T 2 heterotic compactifications. On the type I side, all these quantities are completely determined by the spectrum of N = 2 BPS states that originate from D = 6 massless superstring modes.

N = 2 Type I-heterotic duality and higher derivative F-terms

We test the conjectured Type I-heterotic duality in four dimensions by analyzing a given class of higher derivative F-terms of the form F g W 2 g , with W the N = 2 gravitational superfield. We study a particular dual pair of theories, the O(2,2) heterotic model and a type I model based on the K3 Z 2 orbifold theory constructed by Gimon and Polchinski, further compactified on a torus. The F g couplings appear at 1-loop on both theories; because of the weak-weak nature of this duality in four dimensions, it is meaningful to compare the heterotic F g 's with the corresponding type 1 couplings perturbatively. We compute the F g 's in type I, showing that they receive contributions only from N = 2 BPS states and that in the appropriate limit they coincide with the heterotic coupling, in agreement with the given duality.