Four-dimensional Heterotic String Research Articles

Cosmic censorship conjecture in Kerr-Sen black hole

The validity of the cosmic censorship conjecture for the Kerr-Sen black hole, which is a solution to the low-energy effective field theory for four-dimensional heterotic string theory, is investigated using charged particle absorption. When the black hole absorbs the particle, the charge on it changes owing to the conserved quantities of the particle. Changes in the black hole are constrained to the equation for the motion of the particle and are consistent with the laws of thermodynamics. Particle absorption increases the mass of the Kerr-Sen black hole to more than that of the absorbed charges such as angular momentum and electric charge; hence, the black hole cannot be overcharged. In the near-extremal black hole, we observe a violation of the cosmic censorship conjecture for the angular momentum in the first order of expansion and the electric charge in the second order. However, considering an adiabatic process carrying the conserved quantities as those of the black hole, we prove the stability of the black hole horizon. Thus, we resolve the violation. This is consistent with the third law of thermodynamics.

Gravitational threshold corrections in non-supersymmetric heterotic strings

We compute one-loop quantum corrections to gravitational couplings in the effective action of four-dimensional heterotic strings where supersymmetry is spontaneously broken by Scherk–Schwarz fluxes. We show that in both heterotic and type II theories of this class, no moduli dependent corrections to the Planck mass are generated. We explicitly compute the one-loop corrections to the R2 coupling and find that, despite the absence of supersymmetry, its contributions may still be organised into representations of subgroups of the modular group, and admit a universal form, determined uniquely by the multiplicities of the ground states of the theory. Moreover, similarly to the case of gauge couplings, also the gravitational sector may become strongly coupled in models which dynamically induce large volume for the extra dimensions.

Chiral four-dimensional heterotic covariant lattices

In the covariant lattice formalism, chiral four-dimensional heterotic string vacua are obtained from certain even self-dual lattices which completely decompose into a left-mover and a right-mover lattice. The main purpose of this work is to classify all right-mover lattices that can appear in such a chiral model, and to study the corresponding left-mover lattices using the theory of lattice genera. In particular, the Smith-Minkowski-Siegel mass formula is employed to calculate a lower bound on the number of left-mover lattices. Also, the known relationship between asymmetric orbifolds and covariant lattices is considered in the context of our classification.

Permutation orbifolds of heterotic Gepner models

We study orbifolds by permutations of two identical N = 2 minimal models within the Gepner construction of four-dimensional heterotic strings. This is done using the new N = 2 supersymmetric permutation orbifold building blocks we have recently developed. We compare our results with the old method of modding out the full string partition function. The overlap between these two approaches is surprisingly small, but whenever a comparison can be made we find complete agreement. The use of permutation building blocks allows us to use the complete arsenal of simple current techniques that is available for standard Gepner models, vastly extending what could previously be done for permutation orbifolds. In particular, we consider ( 0 , 2 ) models, breaking of SO ( 10 ) to subgroups, weight-lifting for the minimal models and B-L lifting. Some previously observed phenomena, for example concerning family number quantization, extend to this new class as well, and in the lifted models three-family models occur with abundance comparable to two or four.

OBSERVABLE/HIDDEN SECTOR BROKEN SYMMETRY FOR SYMMETRIC BOUNDARY CONDITIONS

A four-dimensional heterotic string model of free fermionic construction is presented wherein mirror symmetry breaking between observable and hidden sector gauge groups occurs in spite of mirror symmetry between observable and hidden sector worldsheet fermion boundary conditions. The differentiation is invoked by an asymmetry in GSO projections necessarily resulting from the symmetry of the free fermionic boundary conditions. In the specific examples shown, an expected nonchiral Pati–Salam mirror universe model is transformed into a chiral model with enhanced hidden sector gauge symmetry and reduced observable sector gauge symmetry: [ SU (4)C ⊗ SU (2)L ⊗ SU (2)R]O ⊗ [ SU (4)C ⊗ SU (2)L ⊗ SU (2)R]H, is necessarily transformed into a chiral [ SU (4)C ⊗ SU (2)L]O ⊗ [ SO (10) ⊗ SU (2)R]H model because of an unavoidable asymmetry in GSO projections.

Statistics on the heterotic landscape: Gauge groups and cosmological constants of four-dimensional heterotic strings

Recent developments in string theory have reinforced the notion that the space of stable supersymmetric and nonsupersymmetric string vacua fills out a landscape whose features are largely unknown. It is then hoped that progress in extracting phenomenological predictions from string theory--such as correlations between gauge groups, matter representations, potential values of the cosmological constant, and so forth--can be achieved through statistical studies of these vacua. To date, most of the efforts in these directions have focused on type I vacua. In this note, we present the first results of a statistical study of the heterotic landscape, focusing on more than 10{sup 5} explicit nonsupersymmetric tachyon-free heterotic string vacua and their associated gauge groups and one-loop cosmological constants. Although this study has several important limitations, we find a number of intriguing features which may be relevant for the heterotic landscape as a whole. These features include different probabilities and correlations for different possible gauge groups as functions of the number of orbifold twists. We also find a vast degeneracy amongst nonsupersymmetric string models, leading to a severe reduction in the number of realizable values of the cosmological constant as compared with naieve expectations. Finally, we find strong correlations between cosmological constantsmore » and gauge groups which suggest that heterotic string models with extremely small cosmological constants are overwhelmingly more likely to exhibit the standard model gauge group at the string scale than any of its grand-unified extensions. In all cases, heterotic world sheet symmetries such as modular invariance provide important constraints that do not appear in corresponding studies of type I vacua.« less

Dimensional reduction of 4D heterotic string black holes

We perform a spherical symmetric dimensional reduction $4\stackrel{\ensuremath{\rightarrow}}{d}2d$ of heterotic string theory. We find a class of two-dimensional (2D) dilaton gravity models that gives a general description of the near-horizon, near-extremal behavior of four-dimensional (4D) heterotic string black holes. We show that the duality group of the 4D theory is realized in two dimensions in terms of Weyl transformations of the metric. We use the 2D dilaton gravity theory to compute the statistical entropy of a near-extremal 4D, $a=1/\sqrt{3},$ black hole.

Wrapped branes and supersymmetry

Configurations of two or more branes wrapping different homology cycles of space-time are considered and the amount of supersymmetry preserved is analysed, generalising the analysis of multiple branes in flat space. For K3 compactifications, these give the Type II or M-theory origin of certain supersymmetric four-dimensional heterotic string solutions that fit into spin- 3 2 multiplets and which become massless at certain points in moduli space. The interpretation of these BPS states and the possibility of supersymmetry enhancement are discussed.

Duality in superstring compactifications with magnetic field backgrounds

Motivated by the work of Polchinski and Strominger on type IIA theory, where the effect of non-trivial field strenghts for p-form potentials on a Calabi-Yau space was discussed, we study four-dimensional heterotic string theory in the presence of a magnetic field on a 2-cycle in the internal manifold, for both N = 4 and N = 2 cases. We show that at special points in the moduli space certain perturbative charged states become tachyonic and stabilize the vacuum by acquiring vacuum expectation values, thereby restoring supersymmetry. We discuss both the cases where the tachyons appear with a tower of Landau levels, which become light in the limit of large volume of the 2-cycle, and the case where such Landau levels are not present. In the latter case it is sufficient to restrict the analysis to the quartic potential for the tachyon. On the other hand, in the former case it is necessary to include the Landau levels in the analysis of the potential; for toroidal and orbifold examples, we give an explicit CFT description of the new supersymmetric vacuum. The resulting new vacuum turns out to be in the same class as the original supersymmetric one. Finally, using duality, we discuss the role of the Landau levels on the type IIA side.

“Anomalous” U( l) symmetry in orbifold string models

“Anomalous” U(1) gauge symmetry with a Green-Schwarz anomaly cancellation mechanism is discussed in the orbifold construction of four-dimensional heterotic string models. Some conditions are given as criteria to have “anomalous” U(1) in orbifold string models. In particular, “anomalous” U(1) is absent if the massless twisted matter has no mixing between visible and hidden sectors or if a certain type of discrete symmetries are found. We then give a general procedure for classifying orbifold models with “anomalous” U(1) and for identifying the “anomalous” U(1) basis. We illustrate our procedure in Z 3 and Z 4 orbifold models. According to our procedure, the classification of “anomalous” U(1) can be reduced to classification in the absence of a Wilson line. We also discuss discrete symmetries left unbroken after the “anomalous” U(1) breaking. This includes a possible relation between “anomalous” U(1) and discrete R symmetries.

Large radii and string unification

We study strong coupling effects in four-dimensional heterotic string models where supersymmetry is spontaneously broken with large internal dimensions, consistently with perturbative unification of gauge couplings. These effects give rise to thresholds associated to the dual theories: type I superstring or M-theory. In the case of one large dimension, we find that these thresholds appear close to the field-theoretical unification scale ∼ 10 16 GeV, offering an appealing scenario for unification of gravitational and gauge interactions. We also identify the inverse size of the eleventh dimension of M-theory with the energy at which four-fermion effective operators become important.

S-DUALITY AND THE ENTROPY OF BLACK HOLES IN HETEROTIC STRING THEORY

Four-dimensional heterotic string effective action is known to admit non-rotating electrically and magnetically charged black hole solutions. The partition function and entropy is computed for electrically charged black holes and is vanishing in some extremal limit. For the magnetically charged black holes the entropy is also argued to be vanishing in the same extremal limit when these black hole solutions are related by S-duality transformations.

Three-Family SO(10) Grand Unification in String Theory.

The construction of a supersymmetric $SO(10)$ grand unification with 5 left-handed and 2 right-handed families in the four-dimensional heterotic string theory is presented. The model has one $SO(10)$ adjoint Higgs field. The $SO(10)$ current algebra is realized at level 3.

Perturbative and non-perturbative monodromies in N = 2 heterotic string vacua

In this talk we summarise our recent results on perturbative and non-perturbative monodromies in four-dimensional heterotic strings with $N=2$ space-time supersymmetry, and we compare our results with the rigid $SU(2)$ $N=2$ Yang-Mills monodromies.

Perturbative and non-perturbative results for N = 2 heterotic strings

In this paper we summarize our recent work about perturbative and non-perturbative effects in four-dimensional heterotic strings with $N=2$ space-time supersymmetry.

Dynamics of extreme black holes and massive string states.

In a recent paper, Duff and Rahmfeld argued that certain massive $N_R=1/2$ states of the four-dimensional heterotic string correspond to extreme black hole solutions. We provide further, dynamical, evidence for this identification by comparing the scattering of these elementary string states with that of the corresponding extreme black holes, in the limit of low velocities.

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.

On the computation of one-loop amplitudes with external fermions in 4D heterotic superstrings

We present the technical tools needed to compute any one-loop amplitude involving external spacetime fermions in a four-dimensional heterotic string model à la Kawai-Lewellen-Tye. As an example, we compute the one-loop three-point amplitude with one “photon” and two external massive fermions (“electrons”). As a check of our computation, we verify that the one-loop contribution to the Anomalous Magnetic Moment vanishes if the model has spacetime supersymmetry, as required by the supersymmetric sum rules.

Massive string states as extreme black holes

We consider the Schwarz-Sen spectrum of elementary electrically charged massive N R = 1 2 states of the four-dimensional heterotic string and show the maximum spin 1 supermultiplets to correspond to extreme black hole solutions. The N L = 1 states and N L > 1 states (with vanishing left-moving internal momentum) admit a single scalar-Maxwell description with parameters a = √3 or a = 1, respectively. The corresponding solitonic magnetically charged spectrum conjectured by Schwarz and Sen on the basis of S-duality is also described by extreme black holes.

ON THE ANOMALOUS MAGNETIC MOMENT IN HETEROTIC SUPERSTRINGS

We address the problem of computing amplitudes with external space-time fermions in four-dimensional heterotic string theories. As a non-trivial example we consider the anomalous magnetic moment at one-loop level for an "electron" with mass of the order of the Planck mass. We check that the anomalous magnetic moment vanishes if the model is space-time supersymmetric, as required by the supersymmetric sum rules.