We compute the massless spectra of a set of flux vacua of the heterotic string. The vacua we study include well-known non-Kahler T^2-fibrations over K3 with SU(3) structure and intrinsic torsion. Following gauged linear sigma models of these vacua into phases governed by asymmetric Landau-Ginzburg orbifolds allows us to compute the spectrum using generalizations of familiar LG-orbifold techniques. We study several four- and six-dimensional examples with N=2 spacetime supersymmetry in detail.
The problem of the stabilization of moduli is discussed within the context of compactified strongly coupled heterotic string theory. It is shown that all geometric, vector bundle and five-brane moduli are completely fixed, within a phenomenologically acceptable range, by non-perturbative physics. This result requires, in addition to the full space of moduli, non-vanishing Neveu-Schwarz flux, gaugino condensation with threshold corrections and the explicit form of the Pfaffians in string instanton superpotentials. The stable vacuum presented here has a negative cosmological constant. The possib…
We show that the formal alpha' expansion for heterotic flux vacua is only sensible when flux quantization and the appearance of string scale cycles in the geometry are carefully taken into account. We summarize a number of properties of solutions with N=1 and N=2 space-time supersymmetry.
Moduli stabilisation is explored in the context of low-energy heterotic $M$-theory to show that a small value of the cosmological constant can result from a balance between the negative potential energy left over from stabilising the moduli and a positive Casimir energy from the higher dimensions. Supersymmetry breaking is induced by the fermion boundary conditions on the two branes in the theory. An explicit calculation of the Casimir energy for the gravitino reveals that the energy has the correct sign, although the size of the contribution is close to the edge of the parameter range for whi…
We study four-dimensional heterotic flux vacua with N=2 spacetime supersymmetry. A worldsheet perspective is used to clarify quantization conditions associated to the fluxes and the constraints these place on the moduli spaces of resulting compactifications. We propose that these vacua fit naturally in the context of heterotic/IIA duality as heterotic duals to compactifications on K3-fibered but not elliptically fibered Calabi-Yau three-folds. We present some examples of such potential dual pairs.
We discuss the use of gauge fields to stabilize complex structure moduli in Calabi-Yau three-fold compactifications of heterotic string and M-theory. The requirement that the gauge fields in such models preserve supersymmetry leads to a complicated landscape of vacua in complex structure moduli space. We develop methods to systematically map out this multi-branched vacuum space, in a computable and explicit manner. In analyzing the resulting vacua, it is found that the associated Calabi-Yau three-folds are sometimes stabilized at a value of complex structure resulting in a singular compactific…
We study the effect of flux-induced isometry gauging of the scalar manifold in N=2 heterotic string compactification with gauge fluxes. We show that a vanishing theorem by Witten provides the protection mechanism. The other ungauged isometries in hyper moduli space could also be protected, depending on the gauge bundle structure. We also discuss the related issue in IIB setting
The compactification from the 11-dimensional Horava-Witten orbifold to 5-dimensional heterotic M-theory on a Schoen Calabi-Yau threefold is reviewed, as is the specific $SU(4)$ vector bundle leading to the "heterotic standard model" in the observable sector. A generic formalism for a consistent hidden sector gauge bundle, within the context of strongly coupled heterotic M-theory, is presented. Anomaly cancellation and the associated bulk space 5-branes are discussed in this context. The further compactification to a 4-dimensional effective field theory on a linearized BPS double domain wall is…
We study the non-linear sigma model realization of a heterotic vacuum with N=2 space-time supersymmetry. We examine the requirements of (0,2) + (0,4) world-sheet supersymmetry and show that a geometric vacuum must be described by a principal two-torus bundle over a K3 manifold.
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 …
We give an indirect argument for the matching $G^2=-π_* γ^2$ of four-flux and discrete twist in the duality between N=1 heterotic string and $F$-theory. This treats in detail the Euler number computation for the physically relevant case of a Calabi-Yau fourfold with singularities.
We construct hybrid linear models in which the chiral anomaly of a gauged linear sigma model is canceled by the classical anomaly of a gauged WZW model. Semi-classically, this corresponds to fibering the WZW model over the naive target space of the sigma model. When the gauge group is abelian, we recover known non-Kahler compactifications; non-abelian models describe novel quasi-geometric flux vacua of the heterotic string.
We study F-theory duals of six dimensional heterotic vacua in extreme regions of moduli space where the heterotic string is very strongly coupled. We demonstrate how to use orientifold limits of these F-theory duals to regain a perturbative string description. As an example, we reproduce the spectrum of a $T^4/\ZZ_{4}$ orientifold as an F-theory vacuum with a singular $K3$ fibration. We relate this vacuum to previously studied heterotic $E_8\times E_8$ compactifications on $K3$.
We find attractor equations describing moduli stabilization for heterotic compactifications with generic SU(3)-structure. Complex structure and Kähler moduli are treated on equal footing by using SU(3)xSU(3)-structure at intermediate steps. All independent vacuum data, including VEVs of the stabilized moduli, is encoded in a pair of generating functions that depend on fluxes alone. We work out an explicit example that illustrates our methods.
We compute the one-loop threshold corrections to the gauge and gravitational couplings for a large class of N=2 non-Kähler heterotic compactifications with three-form flux, consisting in principal two-torus bundles over K3 surfaces. We obtain the results as sums of BPS-states contributions, depending on the topological data of the bundle. We analyse also the worldsheet non-perturbative corrections coming from instantons wrapping the torus fiber, that are mapped under S-duality to D-instanton corrections in type I flux compactifications.
We discuss compactifications of heterotic string theory to four dimensions in the presence of H-fluxes, which deform the geometry of the internal manifold, and a gaugino condensate which breaks supersymmetry. We focus on the compensation of the two effects in order to obtain vacua with zero cosmological constant and we comment on the effective superpotential describing these vacua.
We study supersymmetric compactification to four dimensions with non-zero H-flux in heterotic string theory. The background metric is generically conformally balanced and can be conformally Kahler if the primitive part of the H-flux vanishes. Analyzing the linearized variational equations, we write down necessary conditions for the existence of moduli associated with the metric. In a heterotic model that is dual to a IIB compactification on an orientifold, we find the metric moduli in a fixed H-flux background via duality and check that they satisfy the required conditions. We also discuss exp…
Chiral gauge theories in two dimensions with (0,2) supersymmetry admit a much broader, and more interesting, class of vacuum solutions than their better studied (2,2) counterparts. In this thesis, we will explore some of the possibilities that are offered by this additional freedom by including field-dependent theta-angles and FI parameters. The moduli spaces that will result from this procedure correspond to heterotic string backgrounds with non-trivial H-flux and NS-brane sources. Along the way, a remarkable relationship between (0,2) gauge anomalies and H-flux will emerge.
We study Heterotic supergravity on Hyper-Kahler manifolds in the presence of non-trivial warping and three form flux with Abelian bundles in the large charge limit. We find exact, regular solutions for multi-centered Gibbons-Hawking spaces and Atiyah-Hitchin manifolds. In the case of Atiyah-Hitchin, regularity requires that the circle at infinity is of the same order as the instanton number, which is taken to be large. Alternatively there may be a non-trivial density of smeared five branes at the bolt.
By studying phase transitions in supersymmetric gauge theories with Green-Schwarz anomaly cancellation, a natural relation is found between sigma models on certain non-Kahler manifolds with intrinsic torsion and asymmetric Landau-Ginzburg orbifolds. In these orbifold limits, a quantum anomaly of the orbifold action is cancelled by discrete phases in the partition function. These intrinsic torsion phases are derived by blowing down cycles supporting non-trivial H-flux in the linear model. This correspondence extends the CY-LG correspondence to special non-Kahler manifolds and provides computati…
In this paper we consider compactifications of heterotic strings in the presence of background flux. The background metric is a T^2 fibration over a K3 base times four-dimensional Minkowski space. Depending on the choice of three-form flux different amounts of supersymmetry are preserved (N=2,1,0). For supersymmetric solutions unbroken space-time supersymmetry determines all background fields except one scalar function which is related to the dilaton. The heterotic Bianchi identity gives rise to a differential equation for the dilaton which we discuss in detail for solutions preserving an N=2 …
We explore the possibility of obtaining de Sitter vacua in strongly coupled heterotic models by adding various corrections to the supergravity potential energy. We show that, in a generic compactification scenario, Fayet-Iliopoulos terms can generate a de Sitter vacuum. The cosmological constant in this vacuum can be fine tuned to be consistent with observation. We also study moduli potentials in non-supersymmetric compactifications of $E_8 \times E_8$ theory with anti five-branes and $E_8 \times \bar E_8$ theory. We argue that they can be used to create a de Sitter vacuum only if some of the …
We investigate the construction of non-supersymmetric vacua in compactifications of heterotic string theory with intrinsic torsion and background fluxes. We do this by using the technique of domain-wall supersymmetry breaking (DWSB) that was developed in the context of type II compactifications. By means of a scalar potential we derive conditions on the compactification manifold that must hold in order to satisfy the equations of motion up to order alpha'.
We report on some recent progress in understanding heterotic flux compactifications, from a worldsheet perspective mainly. We consider local models consisting in torus fibration over warped Eguchi-Hanson space and non-Kähler resolved conifold geometries. We analyze the supergravity solutions and define a double-scaling limit of the resolved singularities, defined such that the geometry is smooth and weakly coupled. We show that, remarkably, the heterotic solutions admit solvable worldsheet CFT descriptions in this limit. This allows in particular to understand the important role of worldsheet …
Generic heterotic M-theory compactifications contain five-branes wrapping non-isolated genus zero or higher genus curves in a Calabi-Yau threefold. Non-perturbative superpotentials do not depend on moduli of such five-branes.We show that fluxes and non-perturbative effects can stabilize them in a non-supersymmetric AdS vacuum. We also show that these five-branes can be stabilized in a dS vacuum, if we modify the supergravity potential energy by Fayet-Iliopoulos terms. This allows us to stabilize all heterotic M-theory moduli in a dS vacuum in the most general compactification scenarios. In add…
We study to what extent Wilson lines in heterotic Calabi-Yau compactifications lead to non-trivial H-flux via Chern-Simons terms. Wilson lines are basic ingredients for Standard Model constructions but their induced H-flux may affect the consistency of the leading order background geometry and of the two-dimensional worldsheet theory. Moreover H-flux in heterotic compactifications would play an important role for moduli stabilization and could strongly constrain the supersymmetry breaking scale. We show how to compute H-flux and the corresponding superpotential, given an explicit complete inte…
We consider flux compactifications of heterotic string theory in the presence of fermionic condensates on M_{1,2} times X_7 with both factors carrying a Killing spinor. In other words, M_{1,2} is either de Sitter, anti-de Sitter or Minkowski, and X_7 possesses a nearly parallel G_2-structure or has G_2-holonomy. We solve the complete set of field equations and the Bianchi identity to order alpha'. The latter is satisfied via a non-standard embedding by choosing the gauge field to be a G_2-instanton. It is shown that none of the solutions to the field equations is supersymmetric.
We present the potential energy due to flux and gaugino condensation in heterotic M-theory compactifications with anti-branes in the vacuum. For reasons which we explain in detail, the contributions to the potential due to flux are not modified from those in supersymmetric contexts. The discussion of gaugino condensation is, however, changed by the presence of anti-branes. We show how a careful microscopic analysis of the system allows us to use standard results in supersymmetric gauge theory in describing such effects - despite the explicit supersymmetry breaking which is present. Not surpris…
We argue that $(0,1)$ heterotic string models with 4 non-heterotic spacetime dimensions may provide an instability of the vacuum to gravitational polarization in globally strong gravitational fields. This instability would be triggered during gravitational collapse by a non-local quantum switching process, and lead to the formation of regions of a high temperature broken symmetry phase which would be the equivalent in these string models of conventional black holes.
We compute the corrections to heterotic-string backgrounds with (2,0) world-sheet supersymmetry, up to two loops in sigma-model perturbation theory. We investigate the conditions for these backgrounds to preserve spacetime supersymmetry and we find that a sufficient requirement for consistency is the applicability of the $\partial\bar\partial$-lemma. In particular, we investigate the $α'$ corrections to (2,0) heterotic-string compactifications and we find that the Calabi-Yau geometry of the internal space is deformed to a Hermitian one. We show that at first order in $α'$, the heterotic anomal…
We derive the most general flux-induced superpotential for N=1 M-theory compactifications on seven-dimensional manifolds with SU(3) structure. Imposing the appropriate boundary conditions, this result applies for heterotic M-theory. It is crucial for the latter to consider SU(3) and not G_2 group structure on the seven-dimensional internal space. For a particular background that differs from CY(3) x S^1/Z_2 only by warp factors, we investigate the flux-generated scalar potential as a function of the orbifold length. We find a positive cosmological constant minimum, however at an undesirably la…
We study heterotic Calabi-Yau models with hypercharge flux breaking, where the visible E8 gauge group is directly broken to the standard model group by a non-flat gauge bundle, rather than by a two-step process involving an intermediate grand unified theory and a Wilson line. It is shown that the required alternative E8 embeddings of hypercharge, normalized as required for gauge unification, can be found and we classify these possibilities. However, for all but one of these embeddings we prove a general no-go theorem which asserts that no suitable geometry and vector bundle leading to a standa…
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 hetero…
We address the construction of non-supersymmetric vacua in heterotic compactifications with intrinsic torsion and background fluxes. In particular, we implement the approach of domain-wall supersymmetry breaking (DWSB) previously developed in the context of type II flux compactifications. This approach is based on considering backgrounds where probe NS5-branes wrapping internal three-cycles and showing up as four-dimensional domain-walls do not develop a BPS bound, while all the other BPS bounds characterizing the N=1 supersymmetric compactifications are preserved at tree-level. Via a scalar p…
We examine heterotic M-theory compactified on a Calabi-Yau manifold with an additional parallel M5 brane. The dominant non-perturbative effect stems from open membrane instantons connecting the M5 with the boundaries. We derive the four-dimensional low-energy supergravity potential for this situation including subleading contributions as it turns out that the leading term vanishes after minimisation. At the minimum of the potential the M5 gets stabilised at the middle of the orbifold interval while the vacuum energy is shown to be manifestly positive. Moreover, induced by the non-trivial runni…
Curvature squared terms are added to a consistent formulation of supergravity on manifolds with boundary which is meant to represent the low energy limit of the strongly coupled heterotic string. These terms are necessary for the cancellation of gravitational anomalies and for reduction to lower dimensions with broken chiral symmetry. The consequences of anomaly cancellation when flux and extrinsic curvature terms are taken into account have yet to be fully exploited, but some implications for flux terms are discussed.
In these lectures, we present cosmological vacuum solutions of Horava-Witten theory and discuss their physical properties. We begin by deriving the five-dimensional effective action of strongly coupled heterotic string theory by performing a reduction, on a Calabi-Yau three-fold, of M-theory on S1/Z2. The effective theory is shown to be a gauged version of five-dimensional N=1 supergravity coupled, for simplicity, to the universal hypermultiplet and four-dimensional boundary theories with gauge and universal gauge matter fields. The static vacuum of the theory is a pair of BPS three-brane doma…
We study heterotic supergravity on the conifold and its Z2 orbifold with Abelian gauge fields and three-form flux. At large distances, these solutions are locally Ricci-flat, have a magnetic flux through the two-sphere at infinity as well as non-zero five-brane charge. For a given flux, our family of solutions has three real parameters, the size of the pair of two spheres in the IR and the dilaton zero mode. We present an explicit analytic solution for the decoupled near horizon region where for a given flux, the size of the cycles is frozen and the only parameter is the dilaton zero mode. We …
We compute the six-dimensional effective action of the heterotic string compactified on K3 for the standard embedding and for a class of backgrounds with line bundles and appropriate Yang-Mills fluxes. We compute the couplings of the charged scalars and the bundle moduli as functions of the geometrical K3 moduli from a Kaluza-Klein analysis. We derive the D-term potential and show that in the flux backgrounds U(1) vector multiplets become massive by a Stuckelberg mechanism.
We consider, in flux compactification of heterotic string theory, spacetime-filling five-branes. Stabilizing the fivebrane involves minimizing the combined energy density of the tension and a Coulomb potential associated with an internal 2-dimensional wrapping. After reviewing the generalized calibration under such circumstances, we consider a particular internal manifold based on a $T^2$ bundle over a conformally rescaled $K3$. Here, we find two distinct types of wrapping. In one class, the fivebrane wraps the fibre $T^2$ which belongs to a cyclic homotopy group. The winding number is not ext…
We discuss supersymmetric compactifications of heterotic strings in the presence of H-flux and general condensates using the formalism of G-structures and intrinsic torsion. We revisit the examples based on nearly-Kaehler coset spaces and show that supersymmetric solutions, where the Bianchi identity is satisfied, can be obtained when both gaugino and dilatino condensates are present.
Recently it was proposed that the ten dimensional tachyonic superstring vacua may serve as good starting points for the construction of viable phenomenological models. Such phenomenologically viable models enlarge the space of possible string solutions, and may offer novel insight into some of the outstanding problems in string phenomenology. In this paper we present a three generation standard--like model that may be regarded as a compactification of a ten dimensional tachyonic vacuum. We discuss the features of the model as compared to a similar model that may be regarded as compactification…
In heterotic flux compactification with supersymmetry, three different connections with torsion appear naturally, all in the form $ω+a H$. Supersymmetry condition carries $a=-1$, the Dirac operator has $a=-1/3$, and higher order term in the effective action involves $a=1$. With a view toward the gauge sector, we explore the geometry with such torsions. After reviewing the supersymmetry constraints and finding a relation between the scalar curvature and the flux, we derive the squared form of the zero mode equations for gauge fermions. With $\d H=0$, the operator has a positive potential term, …
A Novel Construction of de Sitter Vacua in Heterotic String Theory
Irving K. Barber School of Arts and Sciences, University of British Columbia Okanagan（不列颠哥伦比亚大学奥卡纳根分校阿瑟·K·巴伯艺术与科学学院）；Canadian Quantum Research Center（加拿大量子研究中心）；Department of Mathematical Sciences, Durham University（杜伦大学数学科学系）；Computational Mathematics Group, Faculty of Sciences, Hasselt University（哈瑟尔特大学理学院计算数学组）
We study the low-energy effective Lagrangian of $N=2$ heterotic string vacua at the classical and quantum level. The couplings of the vector multiplets are uniquely determined at the tree level, while the loop corrections are severely constrained by the exact discrete symmetries of the string vacuum. We evaluate the general transformation law of the perturbative prepotential and determine its form for the toroidal compactifications of six-dimensional $N=1$ supersymmetric vacua.
We propose a scenario to stabilize all geometric moduli - that is, the complex structure, Kahler moduli and the dilaton - in smooth heterotic Calabi-Yau compactifications without Neveu-Schwarz three-form flux. This is accomplished using the gauge bundle required in any heterotic compactification, whose perturbative effects on the moduli are combined with non-perturbative corrections. We argue that, for appropriate gauge bundles, all complex structure and a large number of other moduli can be perturbatively stabilized - in the most restrictive case, leaving only one combination of Kahler moduli…
We study heterotic backgrounds with non-trivial $H$-flux and non-vanishing expectation values of fermionic bilinears, often referred to as gaugino condensates. The gaugini appear in the low energy action via the gauge-invariant three-form bilinear $Σ_{MNP}={\rm tr}\:\barχΓ_{MNP}χ$. For Calabi-Yau compactifications to four dimensions, the gaugino condensate corresponds to an internal three-form $Σ_{mnp}$ that must be a singlet of the holonomy group. This condition does not hold anymore when an internal $H$-flux is turned on and ${\cal O}(α')$ effects are included. In this paper we study flux co…
It is shown how metastable de Sitter vacua might arise from heterotic M-theory. The balancing of its two non-perturbative effects, open membrane instantons against gaugino condensation on the hidden boundary, which act with opposing forces on the interval length, is used to stabilize the orbifold modulus (dilaton) and other moduli. The non-perturbative effects break supersymmetry spontaneously through F-terms which leads to a positive vacuum energy density. In contrast to the situation for the weakly coupled heterotic string, the charged scalar matter fields receive non-vanishing vacuum expect…
We consider Narain T-duality on a nontrivially fibered n-torus bundle in the presence of a topologically nontrivial NS H flux. The action of the duality group on the topology and H flux of the corresponding type II and heterotic string backgrounds is determined. The topology change is specialized to the case of supersymmetric T^2-fibered torsional string backgrounds with nontrivial H flux. We prove that it preserves the global tadpole condition in the total space as well as on the base of the torus fibration. We find that some of these T-dualities exchange half of the field strength of an unbr…
We study the effective action of the heterotic string compactified on particular half-flat manifolds which arise in the context of mirror symmetry with NS-NS flux. We explicitly derive the superpotential and Kahler potential at lowest order in alpha' by a reduction of the bosonic action. The superpotential contains new terms depending on the Kahler moduli which originate from the intrinsic geometrical flux of the half-flat manifolds. A generalized Gukov formula, valid for all manifolds with SU(3) structure, is derived from the gravitino mass term. For the half-flat manifolds it leads to a supe…
We present a new mechanism, the S-Track, to stabilize the volume modulus S in heterotic M-theory flux compactifications along with the orbifold-size T besides complex structure and vector bundle moduli stabilization. The key dynamical ingredient which makes the volume modulus stabilization possible, is M5-instantons arising from M5-branes wrapping the whole Calabi-Yau slice. These are natural in heterotic M-theory where the warping shrinks the Calabi-Yau volume along S^1/Z_2. Combined with H-flux, open M2-instantons and hidden sector gaugino condensation it leads to a superpotential W which st…
We consider N=2 supersymmetric QCD with the U(N) gauge group (with no Fayet-Iliopoulos term) and N_f flavors of massive quarks deformed by the mass term μfor the adjoint matter, W=μA^2, assuming that N\leq N_f<2N. This deformation breaks N=2 supersymmetry down to N=1. This theory supports non-Abelian flux tubes (strings) which are stabilized by W. They are referred to as F-term stabilized strings. We focus on the studies of such strings in the vacuum in which N squarks condense, at small μ, so that the Z_N strings preserve, in a sense, their BPS nature. We calculate string tensions both in the…
Heterotic M-Theory is a promising candidate for that corner of M-theory which makes contact with the real world. However, while the theory requires one of its expansion parameters, $ε$, to be perturbatively small, a successful phenomenology requires $ε= {\cal O}(1)$. We show that the constraint to have small $ε$ is actually unnecessary: instead of the original flux compactification background valid to linear order in $ε$ one has to use its appropriate non-linear extension, the exact background solution. The exact background is determined by supersymmetry and consequently one expects the tree-l…
We consider the possibility that the unification of the electroweak interactions and the strong force arises from string theory, at energies significantly lower than the string scale. As a tool, an effective grand unified field theory in six dimensions is derived from an anisotropic orbifold compactification of the heterotic string. It is explicitly shown that all anomalies cancel in the model, though anomalous Abelian gauge symmetries are present locally at the boundary singularities. In the supersymmetric vacuum additional interactions arise from higher-dimensional operators. We develop meth…
An attractive mechanism to break supersymmetry in vacua with zero vacuum energy arose in E_8 x E_8 heterotic models with hidden sector gaugino condensate. An H-flux balances the exponentially small condensate on shell and fixes the complex structure moduli. At quantum level this balancing is, however, obstructed by the quantization of the H-flux. We show that the warped flux compactification background in heterotic M-theory can solve this problem through a warp-factor suppression of the integer flux relative to the condensate. We discuss the suppression mechanism both in the M-theory and the 4…
We show that six-dimensional backgrounds that are T^2 bundle over a Calabi-Yau two-fold base are consistent smooth solutions of heterotic flux compactifications. We emphasize the importance of the anomaly cancellation condition which can only be satisfied if the base is K3 while a T^4 base is excluded. The conditions imposed by anomaly cancellation for the T^2 bundle structure, the dilaton field, and the holomorphic stable bundles are analyzed and the solutions determined. Applying duality, we check the consistency of the anomaly cancellation constraints with those for flux backgrounds of M-th…
Compactifications of the heterotic string with NS flux normally require non Calabi-Yau internal spaces which are complex but no longer Kähler. We point out that this conclusion rests on the assumption of a maximally symmetric four-dimensional space-time and can be avoided if this assumption is relaxed. Specifically, it is shown that an internal Calabi-Yau manifold is consistent with the presence of NS flux provided four-dimensional space-time is taken to be a domain wall. These Calabi-Yau domain wall solutions can still be associated with a covariant four-dimensional N=1 supergravity. In this …
