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.     

N = 1 heterotic / M-theory duality and Joyce manifolds

We present an ansatz which enables us to construct heterotic/M-theory dual pairs in four dimensions. It is checked that this ansatz reproduces previous results and that the massless spectra of the proposed new dual pairs agree. The new dual pairs consist of M-theory compactifications on Joyce manifolds of G₂ holonomy and Calabi-Yau compactifications of heterotic strings. These results are further evidence that M-theory is consistent on orbifolds. Finally, we interpret these results in terms of M-theory geometries which are K3 fibrations and heterotic geometries which are conjectured to be T³ fibrations. Even though the new dual pairs are constructed as non-freely acting orbifolds of existing dual pairs, the adiabatic argument is apparently not violated.     

F-theory and N=1 Quivers from Polyvalent Geometry

We study four-dimensional quiver gauge models from F-theory compactified on fourfolds with hyper-K¨ahler structure.Using intersecting complex toric surfaces,we derive a class of N =1 quivers with charged fundamental matter placed on external nodes.The emphasis is on how local Calabi–Yau equations solve the corresponding physical constraints including the anomaly cancelation condition.Concretely,a linear chain of SU(N) groups with flavor symmetries has been constructed using polyvalent toric geometry.     

Superspace geometry from D = 4, N = 1 heterotic superstrings

The presence of classical κ-supersymmetry invariance is shown to be consistent with an off-shell D = 4, N = 1 conformal supergravity background in the presence of a tensor multiplet. We derive a suitable set of constraints, via super Weyl rescaling, for a heterotic superstring in such a background. Starting from the geometry of 16-16 supergravity and gauging the R-symmetry with a composite connection, we derive a geometrical structure similar to that of new minimal supergravity.     

Spinor-vector duality in heterotic string vacua

Classification of the N=1 space–time supersymmetric fermionic Z₂×Z₂ heterotic-string vacua with symmetric internal shifts, revealed a novel spinor-vector duality symmetry over the entire space of vacua, where the S_t↔V duality interchanges the spinor plus anti-spinor representations with vector representations. In this paper we demonstrate that the spinor-vector duality exists also in fermionic Z₂ heterotic string models, which preserve N=2 space–time supersymmetry. In this case the interchange is between spinorial and vectorial representations of the unbroken SO(12) GUT symmetry. We provide a general algebraic proof for the existence of the S_t↔V duality map. We present a novel basis to generate the free fermionic models in which the ten-dimensional gauge degrees of freedom are grouped into four groups of four, each generating an SO(8) modular block. In the new basis the GUT symmetries are produced by generators arising from the trivial and non-trivial sectors, and due to the triality property of the SO(8) representations. Thus, while in the new basis the appearance of GUT symmetries is more cumbersome, it may be more instrumental in revealing the duality symmetries that underly the string vacua.     

Perturbative prepotential and monodromies in N = 2 heterotic superstring

We discuss the prepotential describing the effective field theory of N = 2 heterotic superstring models. At the one loop-level the prepotential develops logarithmic singularities due to the appearance of charged massless states at particular surfaces in the moduli space of vector multiplets. These singularities modify the classical duality symmetry group which now becomes a representation of the fundamental group of the moduli space minus the singular surfaces. For the simplest two-moduli case, this fundamental group turns out to be a certain braid group and we determine the resulting full duality transformations of the prepotential, which are exact in perturbation theory.     

N=1 supergravity theories coupled to matter and duality transformations

The most general action for chiral and complex linear superfields coupled to theN=1 old minimal supergravity is given. Scalar potentials for pure complex linear and mixed cases are found. A condition for the breakdown of the duality transformation, which transforms a theory with complex linear superfields to one with chiral scalar superfields, is obtained. When this condition is satisfied, the potentials and couplings cannot be transformed, in general, into a Kähler form; examples are given. Some aspects of vanishing cosmological constant are considered in this context.     

No renormalization of the N=1 supergravity theory derived from the heterotic string

We show that one-loop string effects do not alter the form of the leading terms in the low-energy effective ten-dimensional N=1 supergravity theory derived from the heterotic string. We extend this result to the four-dimensional N=1 supergravity theory obtained after compactification, showing in particular that its Kähler potential is not renormalized by string loop effects or by the exchange of Kaluza-Klein modes. We also demonstrate that the Kähler potential and the gauge kinetic function are not renormalized by one-loop string effects in a wide class of four-dimensional formulations of superstring theories.     

Branes and N = 1 duality in string theory

We propose a construction of dual pairs in four dimensional N = 1 supersymmetric Yang-Mills theory using branes in type IIA string theory.     

Evidence for heterotic - Type I string duality

A study is made of the implications of heterotic string T-duality and extended gauge symmetry for the conjectured equivalence of heterotic and Type I superstrings. While at first sight heterotic string world-sheet dynamics appears to conflict with Type I perturbation theory, a closer look shows that Type I perturbation theory “miraculously” breaks down, in some cases via novel mechanisms, whenever the heterotic string has massless particles not present in Type I perturbation theory. This strongly suggests that the two theories actually are equivalent. As further evidence in the same direction, we show that the Dirichlet one-brane of Type I string theory has the same world-sheet structure as the heterotic string.     

F-theory,T-duality on K3 surfaces,and N = 2 supersymmetric gauge theories in four dimensions

We construct T-duality on K3 surfaces. The T-duality exchanges a 4-brane RR charge and a 0-brane RR charge. We study the action of the T-duality on the moduli space of 0-branes located at points of K3 and 4-branes wrapping it. We apply the construction to F-theory compactified on a Calabi-Yau 4-fold and study the duality of N = 2 SU(N_c) gauge theories in four dimensions. We discuss the generalization to the N = 1 duality scenario.