Heterotic String Compactifications Research Articles

Toroidal compactification of heterotic 6D non-critical strings down to four dimensions

The low-energy limit of the 6D non-critical string theory with N = 1 SUSY and E 8 chiral current algebra compactified on T 2 is generically an N = 2 U(1) vector multiplet. We study the analog of the Seiberg-Witten solution for the low-energy effective action as a function of E 8 Wilson lines on the compactified torus and the complex modulus of that torus. The moduli space includes regions where the Seiberg-Witten curves for SU(2) QCD are recovered as well as regions where the newly discovered 4D theories with enhanced E 6, 7, 8 global symmetries appear.

Classical and quantum N = 2 supersymmetric black holes

We use heterotic/type-H prepotentials to study quantum/classical black holes with half the N = 2, D = 4 supersymmetries unbroken. We show that, in the case of heterotic string compactifications, the perturbatively corrected entropy formula is given by the tree-level entropy formula with the tree-level coupling constant replaced by the perturbative coupling constant. In the case of type-II compactifications, we display a new entropy/area formula associated with axion-free black-hole solutions, which depends on the electric and magnetic charges as well as on certain topological data of Calabi-Yau three-folds, namely the intersection numbers, the second Chem class and the Euler number of the three-fold. We show that, for both heterotic and type-II theories, there is the possibility to relax the usual requirement of the non-vanishing of some of the charges and still have a finite entropy.

Higher-order gravitational couplings and modular forms in N = 2, D = 4 heterotic string compactifications

Higher-order gravitational couplings and modular forms in N = 2, D = 4 heterotic string compactifications

Higher-order gravitational couplings and modular forms in N = 2, D = 4 heterotic string compactifications

The restrictions of target-space duality are imposed at the perturbative level on the holomorphic Wilsonian couplings that encode certain higher-order gravitational interactions in N = 2, D = 4 heterotic string compactifications. A crucial role is played by non-holomorphic corrections. The requirement of symplectic covariance and an associated symplectic anomaly equation play an important role in determining their form. For models which also admit a type-11 description, this equation coincides with the holomorphic anomaly equation for type-II compactifications in the limit that a specific Kähler-class modulus grows large. We explicitly evaluate some of the higher-order couplings for a toroidal compactification with two moduli T and U, and we express them in terms of modular forms.

SUSY gauge dynamics and singularities of 4d N = 1 string vacua

Many N = 1 heterotic string compactifications exhibit physically mysterious singularities at codimension one in the moduli space of vacua. At these singularities, Yukawa couplings of charged fields develop poles as a function of the moduli. We explain these conformal field theory singularities, in a class of examples, as arising from non-perturbative gauge dynamics of non-perturbative gauge bosons (whose gauge coupling is the sigma model coupling) in the string theory.

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 G 2 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 T 3 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.

Non-perturbative superpotentials in string theory

The non-perturbative superpotential can be effectively calculated in M-theory compactification to three dimensions on a Calabi-Yau four-fold X. For certain X, the superpotential is identically zero, while for other X, a non-perturbative superpotential is generated. Using F-theory, these results carry over to certain Type IIB and heterotic string compactifications to four dimensions with N = 1 supersymmetry. In the heterotic string case, the non-perturbative superpotential can be interpreted as coming from space-time and world-sheet instantons; in many simple cases contributions come only from finitely many values of the instanton numbers.

BPS spectra and non-perturbative gravitational couplings in N = 2, 4 supersymmetric string theories

We study the BPS spectrum in D = 4, N = 4 heterotic string compactifications, with some emphasis on intermediate N = 4 BPS states. These intermediate states, which can become short in N = 2 compactifications, are crucial for establishing an S ↔ T exchange symmetry in N = 2 compactifications. We discuss the implications of a possible S ↔ T exchange symmetry for the N = 2 BPS spectrum. Then we present the exact result for the one-loop corrections to gravitational couplings in one of the heterotic N = 2 models recently discussed by Harvey and Moore. We conjecture this model to have an S ↔ T exchange symmetry. This exchange symmetry. This exchange symmetry can then be used to evaluate non-perturbative corrections to gravitational couplings in some of the non-perturbative regions (chambers) in this particular model and also in other heterotic models.

N = 2 heterotic string threshold correction, K3 surface and generalized Kac-Moody superalgebra

We study a standard-embedding N = 2 heterotic string compactification on K3 × T 2 with a Wilson line turned on and perform a world-sheet calculation of string threshold correction. The result can be expressed in terms of the quantities appearing in the two-loop calculation of bosonic string. We also comment and speculate on the relevance of our result to generalized Kac-Moody superalgebra and N = 2 heterotic-type IIA duality.

Exact results for N=2 compactifications of heterotic strings

We search for N = 2, d = 4 theories which can be realized both as heterotic string compactifications on K 3 × T 2 and as type II string compactifications on Calabi-Yau threefolds. In such cases, the exact non-perturbative superpotential of one string theory is given in terms of tree level computations in the other string theory. In particular we find concrete examples which provide the stringy realization of the results of Seiberg and Witten on N=2 Yang-Mills theory, corrected by gravitational/stringy effects. We also discuss some examples which shed light on how the moduli spaces of different N=2 heterotic vacua are connected (This contribution to the conference proceeding has already been published in Nucl. Phys. B 450 (1995) 69).

Algebras, BPS states, and strings

We clarify the role played by BPS states in the calculation of threshold corrections of D = 4, N = 2 heterotic string compactifications. We evaluate these corrections for some classes of compactifications and show that they are sums of logarithmic functions over the positive roots of generalized Kac-Moody algebras. Moreover, a certain limit of the formulae suggests a reformulation of heterotic string in terms of a gauge theory based on hyperbolic algebras such as E 10. We define a generalized Kac-Moody Lie superalgebra associated to the BPS states. Finally we discuss the relation of our results with string duality.

Non-perturbative results on the point particle limit of N = 2 heterotic string compactifications

Using heterotic/type II string duality, we obtain exact non-perturbative results for the point particle limit ( α′ → 0) of some particular four dimensional, N = 2 supersymmetric compactifications of heterotic strings. This allows us to recover recent exact non-perturbative results on N = 2 gauge theory directly from tree-level type II string theory, which provides a highly non-trivial, quantitative check on the proposed string duality. We also investigate to what extent the relevant singular limits of Calabi-Yau manifolds are related to the Riemann surfaces that underlie rigid N = 2 gauge theory.

Exact results for N = 2 compactifications of heterotic strings

We search for N = 2, d = 4 theories which can be realized both as heterotic string compactifications on K3 × T 2 and as type II string compactifications on Calabi-Yau threefolds. In such cases, the exact non-perturbative superpotential of one string theory is given in terms of tree level computations in the other string theory. In particular we find concrete examples which provide the stringy realization of the results of Seiberg and Witten on N = 2 Yang-Mills theory, corrected by gravitational/ stringy effects. We also discuss some examples which shed light on how the moduli spaces of different N = 2 heterotic vacua are connected.

Compactification of D = 11 supergravity on spaces of exceptional holonomy

We investigate the compactification of D = 11 supergravity to D = 5,4,3, on compact manifolds of holonomy SU(3) (Calabi-Yau), G 2, and Spin(7), respectively, making use of examples of the latter two cases found recently by Joyce. In each case the lower dimensional theory is a Maxwell/Einstein supergravity theory. We find evidence for an equivalence, in certain cases, with heterotic string compactifications from D = 10 to D = 5,4,3, on compact manifolds of holonomy SU(2) ( K 3 × S 1), SU(3), and G 2, respectively. Calabi-Yau manifolds with Hodge numbers h 1,1 = h 1,2 = 19 play a significant role in the proposed equivalences.

Type IIA dual of the six-dimensional CHL compactification

We propose a candidate for the dual (in the weak/strong coupling sense) of the six-dimensional heterotic string compactification constructed recently by Chaudhuri, Hockney and Lykken. It is a type IIA string theory compactified on an orbifold K3 Z 2 , where the Z 2 action involuution of K3 with fixed points, and also has an embedding in the U(1) gauge group associated with the Ramond-Ramond sector of the type IIA string theory. This introduces flux of the U(1) gauge field concentrated at the orbifold points. This construction provides and explicit example where the dual of a super-conformal field theory background of the heterotic string theory is not a standard super-conformal field theory background of the type IIA string theory.

Asymmetric Orbifold Models of Non-Supersymmetric Heterotic Strings

We investigate asymmetric orbifold models constructed from non-supersymmetric heterotic strings. We systematically classify the asymmetric orbifold models with standard embeddings and present a list of asymmetric orbifolds which are geometrically interpreted as toroidal compactifications of non-supersymmetric heterotic strings. By studying non-standard embedding models, we also construct examples of the {\em supersymmetric} asymmetric orbifold models based on non-supersymmetric heterotic strings.

Moduli dependence of one-loop gauge couplings in (0,2) compactifications

We derive the moduli dependence of the one-loop gauge couplings for non-vanishing gauge background fields in a four-dimensional heterotic (0,2) string compactification. Remarkably, these functions turn out to have a representation as modular functions on an auxiliary Riemann surface on appropriate truncations of the full moduli space. In particular, a certain kind of one-loop functions is given by the free energy of two-dimensional solitons on this surface.

Kähler potentials for orbifolds with continuous Wilson lines and the symmetries of the string action

By employing the symmetries of the underlying conformal field theory, the tree-level Kähler potentials for untwisted moduli of the heterotic string compactifications on orbifolds with continuous Wilson lines are derived. These symmetries act linearly on bosonic (toroidal and E 8 × E 8 gauge) string coordinates as well as on the untwisted (toroidal and continuous Wilson lines) moduli; they correspond to the scaling of toroidal moduli, the axionic shift of toroidal moduli and the shift of the continuous Wilson line moduli. In turn such symmetries provide sufficient constraints to determine the form of the low-energy effective action associated with the untwisted moduli up to a multiplicative factor.

Generalized string functions of N = 1 space-time supersymmetric string vacua

We present a dual formulation of the construction of N = 2 nonlinear σ-model type conformal field theories with c = 9 which are mainly used as internal sectors of Calabi-Yau heterotic string compactifications. The supercurrents G ±( z) and the higher components of the spectral flow superfields X ±( z) + θ ± Y ±( z) turn out in each case to be tensor products of two simple currents of a c = 1 and a non-supersymmetric parafermionic c = 8 CFT. The characters of the latter model can be regarded as string functions of the coset σ U(1) . In particular, for the (1) 9 Gepner model we discuss these string functions in detail, realizing this model contains a broken E 8 gauge symmetry of which only the abelian subalgebra remains a symmetry of the spectrum. As an example, we construct a simple model leading to a string theory with a massless spectrum of 36 E 6 generations and an extended gauge symmetry E 6 × SU(3) 4.

HETEROTIC COSET MODELS

A description is given on how to construct (0, 2) supersymmetric conformal field theories as coset models. These models may be used as non-trivial backgrounds for heterotic string theory. They are realized as a combination of an anomalously gauged Wess–Zumino–Witten model, right-moving supersymmetric fermions, and left-moving current algebra fermions. Requiring the sum of the gauge anomalies from the bosonic and fermionic sectors to cancel yields the final model. Applications discussed include exact models of extremal four-dimensional charged black holes and Taub–NUT solutions of string theory. These coset models may also be used to construct important families of (0, 2) supersymmetric heterotic string compactifications. The Kazama–Suzuki models are the left-right symmetric special case of these models.