Five-brane superpotentials and heterotic/F-theory duality

Under heterotic/F-theory duality it was argued that a wide class of heterotic five-branes is mapped into the geometry of an F-theory compactification manifold. In four-dimensional compactifications this identifies a five-brane wrapped on a curve in the base of an elliptically fibered Calabi–Yau threefold with a specific F-theory Calabi–Yau fourfold containing the blow-up of the five-brane curve. We argue that this duality can be reformulated by first constructing a non-Calabi–Yau heterotic threefold by blowing up the curve of the five-brane into a divisor with five-brane flux. Employing heterotic/F-theory duality this leads us to the construction of a Calabi–Yau fourfold and four-form flux. Moreover, we obtain an explicit map between the five-brane superpotential and an F-theory flux superpotential. The map of the open–closed deformation problem of a five-brane in a compact Calabi–Yau threefold into a deformation problem of complex structures on a dual Calabi–Yau fourfold with four-form flux provides a powerful tool to explicitly compute the five-brane superpotential.     

Compactifications of F-theory on Calabi-Yau threefolds (II)

We continue our study of compactifications of F-theory on Calabi-Yau threefolds. We gain more insight into F-theory duals of heterotic strings and provide a recipe for building F-theory duals for arbitrary heterotic compactifications on elliptically fibered manifolds. As a byproduct we find that string/string duality in six dimensions gets mapped to fiber/base exchange in F-theory. We also construct a number of new N = 1, d = 6 examples of F-theory vacua and study transitions among them. We find that some of these transition points correspond upon further compactification to 4 dimensions to transitions through analogues of Argyres-Douglas points of N = 2 moduli. A key idea in these transitions is the notion of classifying (0,4) fivebranes of heterotic strings.     

Four-dimensional N = 2 superstring constructions and their (non-) perturbative duality connections

We investigate the connections between four-dimensional, N = 2 M-theory vacua constructed as orbifolds of type II, heterotic, and type I strings. All these models have the same massless spectrum, which contains an equal number of vector multiplets and hypermultiplets, with a gauge group of the maximal rank allowed in a perturbative heterotic string construction. We find evidence for duality between two type I compactifications recently proposed and a new heterotic construction that we present here. This duality allows us to gain insight into the non-perturbative properties of these models. In particular we consider gravitational corrections to the effective action.     

Vector Bundles and F Theory

To understand in detail duality between heterotic string and F theory compactifications, it is important to understand the construction of holomorphic G bundles over elliptic Calabi-Yau manifolds, for various groups G. In this paper, we develop techniques to describe these bundles, and make several detailed comparisons between the heterotic string and F theory. Received: 6 February 1997 / Accepted: 29 May 1997     

Four-dimensional heterotic strings-orbifolds and covariant lattices

Two - so far unrelated - constructions of four-dimensional heterotic string theories are discussed within a common framework. We show that four-dimensional heterotic string theories which are based on covariant self-dual lattices are equivalent to a wide class of asymmetric orbifolds. This equivalence provides an explicit realization of twist fields and allows the straight-forward calculation of scattering amplitudes of various massless fields. “Topological” properties of the orbifolds, like the number of fixed points, are related to group theoretical features of the covariant lattices. Two explicit examples illustrate our conclusions.     

Solutions of the Strominger System via Stable Bundles on Calabi-Yau Threefolds

We prove that a given Calabi-Yau threefold with a stable holomorphic vector bundle can be perturbed to a solution of the Strominger system provided that the second Chern class of the vector bundle is equal to the second Chern class of the tangent bundle. If the Calabi-Yau threefold has strict SU(3) holonomy then the equations of motion derived from the heterotic string effective action are also satisfied by the solutions we obtain.     

Four-dimensional heterotic string models with third-integral twists

The massless string states are constructed for a four-dimensional heterotic string model with the U(5) gauge group in the untwisted sector. The complete observable gauge group, quark and lepton generations, Higgs scalar structure, quark and lepton mass matrix, couplings to colour triplet scalars, and gauge symmetry breaking are studied for this model.     

Curvature-corrected dilatonic black holes and black hole—string transition

We investigate extremal charged black hole solutions in the four-dimensional string frame Gauss-Bonnet gravity with the Maxwell field and the dilaton. Without curvature corrections, the extremal electrically charged dilatonic black holes have singular horizon and zero Bekenstein entropy. When the Gauss-Bonnet term is switched on, the horizon radius expands to a finite value provided curvature corrections are strong enough. Below a certain threshold value of the Gauss-Bonnet coupling the extremal black hole solutions cease to exist. Since decreasing Gauss-Bonnet coupling corresponds to decreasing string coupling g _s , the situation can tentatively be interpreted as classical indication on the black hole—string transition. Previously the extremal dilaton black holes were studied in the Einstein-frame version of the Gauss-Bonnet gravity. Here we work in the string frame version of the theory with the S-duality symmetric dilaton function as required by the heterotic string theory. The article is published in the original.     

Brane Cosmology From Heterotic String Theory

We consider brane cosmologies within the context of five-dimensional effective actions with higher curvature corrections. The actions are compatible with bulk string amplitude calculations from heterotic string theory. We find wrapped solutions that satisfy the field equations in an approximate but acceptable manner given their complexity, where the internal, four-dimensional, scale factor is naturally inflating, having an exponential De-Sitter form. The temporal dependence of the metric components is nontrivial so that this metric cannot be factored as in a conformally flat case. The effective Planck mass is finite and the brane solutions can localize four-dimensional gravity while the four-dimensional gravitational constant varies with time. The Hubble constant can be freely specified through the initial value of the scalar field, to conform with recent data.     

Heterotic and Type I string dynamics from eleven dimensions

We propose that the ten-dimensional E₈ × E₈ heterotic string is related to an eleven-dimensional theory on the orbifold in the same way that the Type IIA string in ten dimensions is related to . This in particular determines the strong coupling behavior of the ten-dimensional E₈ × E₈ theory. It also leads to a plausible scenario whereby duality between SO(32) heterotic and Type I superstrings follows from the classical symmetries of the eleven-dimensional world, just as the duality of the ten-dimensional Type IIB theory follows from eleven-dimensional diffeomorphism invariance.     

Duality symmetry group of two dimensional heterotic string theory

The equations of motion of the massless sector of the two dimensional string theory, obtained by compactifying the heterotic string theory on an eight dimensional torus, is known to have an affine o(8,24) symmetry algebra generating an O(8,24) loop group. In this paper we study how various known discrete S- and T- duality symmetries of the theory are embedded in this loop group. This allows us to identify the generators of the discrete duality symmetry group of the two dimensional string theory.     

Momentum lattice for CHL string

We propose some analogue of the Narain lattice for CHL string. The symmetries of this lattice are the symmetries of the perturbative spectrum. We explain in this language the known results about the possible gauge groups in compactified theory. For the four-dimensional theory, we explicitly describe the action of S-duality on the background fields. We show that the moduli spaces of the six-, seven- and eight-dimensional compactifications coincide with the moduli spaces of the conjectured type IIA, M-theory and F-theory duals. We classify the rational components of the boundary of the moduli space in seven, eight and nine dimensions.     

Four-dimensional heterotic string models with SU(5) and SO(10) grand unification

The gauge group, quark and lepton generations, Higgs scalar structure, couplings of quarks and leptons to Higgs scalars and to colour triplet scalars, and the gauge symmetry breaking are studied for a class of four-dimensional heterotic string models whose boundary conditions include third-integral twists.     

A-twisted heterotic Landau–Ginzburg models

In this paper, we apply the methods developed in recent work for constructing A-twisted (2, 2) Landau–Ginzburg models to analogous (0, 2) models. In particular, we study (0, 2) Landau–Ginzburg models on topologically non-trivial spaces away from large-radius limits, where one expects to find correlation function contributions akin to (2, 2) curve corrections. Such heterotic theories admit A- and B-model twists, and exhibit a duality that simultaneously exchanges the twists and dualizes the gauge bundle. We explore how this duality operates in heterotic Landau–Ginzburg models, as well as other properties of these theories, using examples which renormalization-group flow to heterotic nonlinear sigma models as checks on our methods.     

Ward identities in four-dimensional string theory

A four-dimensional heterotic string theory is envisaged in the background of its massless gauge Ward identities are derived. The spontaneous generating functional is constructed in the hamiltonian phase space and gauge Ward identities are derived. The spontaneous breaking of gauge symmetry is discussed in this approach.     

Exact monodromy group of N = 2 heterotic superstring

We describe an N = 2 heterotic superstring model of rank 3 which is dual to the type II string compactified on a Calabi-Yau manifold with Betti numbers b_1,1 = 2 and b_1,2 = 86. We show that the exact duality symmetry found from the type II realization contains the perturbative duality group of the heterotic model, as well as the exact quantum monodromies of the rigid SU(2) super-Yang-Mills theory. Moreover, it contains a non-perturbative monodromy which is stringy in origin and corresponds roughly to an exchange of the string coupling with the compactification radius.