Recently, a class of inflation models in supergravity with gauge non-singlet matter fields as the inflaton has been proposed. It is based on a `tribrid' structure in the superpotential and on a Heisenberg symmetry for solving the eta-problem. We suggest that a generalization of this model class may be suitable for realising inflation in heterotic orbifold compactifications, where the Heisenberg symmetry is a property of the tree-level K"ahler potential of untwisted matter fields. We discuss moduli stabilization in this setup and propose a mechanism to stabilize the modulus associated to the inflaton, which respects the symmetry in the large radius limit. Inflation ends via a waterfall phase transition, as in hybrid inflation. We give conditions which have to be satisfied for realising inflation along these lines in the matter sector of heterotic orbifolds.
We study moduli stabilization in combination with inflation in heterotic orbifold compactifications in the light of a large Hubble scale and the favored tensor-to-scalar ratio $r \approx 0.05$. To account for a trans-Planckian field range we implement aligned natural inflation. Although there is only one universal axion in heterotic constructions, further axions from the geometric moduli can be used for alignment and inflation. We argue that such an alignment is rather generic on orbifolds, since all non-perturbative terms are determined by modular weights of the involved fields and the Dedeki…
We propose the natural inflation from the heterotic string theory on "Swiss-Cheese" Calabi-Yau manifold with multiple $U(1)$ magnetic fluxes. Such multiple $U(1)$ magnetic fluxes stabilize the same number of the linear combination of the universal axion and Kähler axions and one of the Kähler axions is identified as the inflaton. This axion decay constant can be determined by the size of one-loop corrections to the gauge kinetic function of the hidden gauge groups, which leads effectively to the trans-Planckian axion decay constant consistent with the WMAP, Planck and/or BICEP2 data. During th…
University of Edinburgh（爱丁堡大学）；University of Lethbridge（莱斯布里奇大学）；Indian Statistical Institute（印度统计研究所）；University of Sussex（萨塞克斯大学）；Universidade do Estado do Rio de Janeiro（里约热内卢州立大学）；Massachusetts Institute of Technology（麻省理工学院）
A glossary overview of the phenomenological studies of quasi-realistic free fermionic heterotic string models is presented. I elaborate on the correspondence of these models with Z2XZ2 orbifolds.
We propose a model for large field inflation in heterotic string theory. The construction applies the near alignment mechanism of Kim, Nilles, and Peloso. By including gaugino condensates and world-sheet instanton non-perturbative effects, we obtain a large effective axion decay constant.
We give a complete classification of Z_N orbifold compactification of the heterotic SO(32) string theory and show its potential for realistic model building. The appearance of spinor representations of SO(2n) groups is analyzed in detail. We conclude that the heterotic SO(32) string constitutes an interesting part of the string landscape both in view of model constructions and the question of heterotic-type I duality.
In the framework of $Z_N$ orbifolds, we discuss effects of heterotic string backgrounds including discrete Wilson lines on the Yukawa matrices and their connection to CP violation.
We study soft SUSY breaking terms in heterotic M-theory. We show that both weakly and strongly coupled heterotic string models lead to the same relations of soft SUSY breaking terms, $A=-M$ and $m^2 = M^2/3$, up to $O((αT/S)^2)$.
We provide a simple example of dilaton stabilization in the framework of heterotic string theory. It requires a gaugino condensate and an up-lifting sector similar to the one postulated in type IIB string theory. Its signature is a hybrid mediation of supersymmetry breakdown with a variant of a mirage pattern for the soft breaking terms. The set-up is suited for the discussion of heterotic MSSM candidates.
We derive the universal threshold corrections in heterotic string theory including a continuous Wilson line. Unification of gauge and gravitational couplings is shown to be possible even within perturbative string theory. The relative importance of gauge group dependent and independent thresholds on unification is clarified. Equipped with these results we can then attempt an extrapolation to the strongly coupled heterotic string -- M-theory. We argue that such an extrapolation might be meaningful because of the holomorphic structure of the gauge coupling function and the close connection of th…
We investigate the possibility of lowering the string scale in four dimensional heterotic models possessing a non-perturbative extension of the gauge group. In particular, we consider a class of compactifications in which the perturbative gauge sector is massive, and all the gauge bosons are non-perturbative, with a coupling independent on the Planck and string scales.
We study the flavor structure in $SO(32)$ heterotic string theory on six-dimensional torus with magnetic fluxes. In particular, we focus on models with the flavor symmetries $SU(3)_f$ and $Δ(27)$. In both models, we can realize the realistic quark masses and mixing angles.
The three generation heterotic-string models in the free fermionic formulation are among the most realistic string vacua constructed to date, which motivated their detailed investigation. The classification of free fermion heterotic string vacua has revealed a duality under the exchange of spinor and vector representations of the SO(10) GUT symmetry over the space of models. We demonstrate the existence of the spinor-vector duality using orbifold techniques, and elaborate on the relation of these vacua to free fermionic models.
We first investigate the attractor solution associated with Assisted Inflation in Heterotic M-Theory to see if it is stable. By perturbing the solutions we find a solitary stable fixed point with the general path through phase space dependent upon the Calabi-Yau data and the number of five-branes. We then go on to examine the effect of including non-perturbative corrections to the inflaton potential arising from boundary-brane instantons as well as higher order brane interaction terms. The result is that Assisted Inflation is only possible if we allow fine tuning of the superpotential, and tha…
An overview of old and new results in studies of the quasi-realistic free fermionic models is presented, which include the recent discovery of exophobic string vacua and reproduction of the Higgs-matter splitting mechanism in a corresponding orbifold construction.
In T-duality invariant effective supergravity with gaugino condensation as the mechanism for supersymmetry breaking, there is a residual discrete symmetry that could play the role of R-parity in supersymmetric extensions of the Standard Model.
The discovery of the Higgs boson at the LHC supports the hypothesis that the Standard Model provides an effective parameterisation of all subatomic experimental data up to the Planck scale. String theory, which provides a viable perturbative approach to quantum gravity, requires for its consistency the existence of additional gauge symmetries beyond the Standard Model. The construction of heterotic--string models with a viable light $Z^\prime$ is, however, highly constrained. We outline the construction of standard--like heterotic--string models that allow for an additional Abelian gauge symme…
We explore the phenomenological viability of a light Z' in heterotic-string models, whose existence has been motivated by proton stability arguments. A class of quasi-realistic string models that produce such a viable Z' are the Left-Right Symmetric (LRS) heterotic-string models in the free fermionic formulation. A key feature of these models is that the matter charges under U(1)_Z' do not admit an E6 embedding. The light Z' in the LRS heterotic-string models forbids baryon number violating operators, while allowing lepton number violating operators, hence suppressing proton decay yet allowing…
Using Z3 asymmetric orbifolds in heterotic string theory, we construct N=1 SUSY three-generation models with the standard model gauge group SU(3)_C \times SU(2)_L \times U(1)_Y and the left-right symmetric group SU(3)_C \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}. One of the models possesses a gauge flavor symmetry for the Z3 twisted matter.
The spinor-vector duality was discovered in free fermionic constructions of the heterotic-string in four dimensions. It played a key role in the construction of heterotic-string models with an anomaly free extra $Z^\prime$ symmetry that may remain unbroken down to low energy scales. A generic signature of the low scale string derived $Z^\prime$ model is via di-photon excess that may be within reach of the LHC. A fascinating possibility is that the spinor-vector duality symmetry is rooted in the structure of the heterotic-string compactifications to two dimensions. The two dimensional heterotic…
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 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.
We find that dilaton dominated supersymmetry breaking and spontaneous CP violation can be achieved in heterotic string models with superpotentials singular at the fixed points of the modular group. A semi--realistic picture of CP violation emerges in such models: the CKM phase appears due to a complex VEV of the T-modulus, while the soft supersymmetric CP phases are absent due to an axionic--type symmetry.
The most promising MSSM candidates of the heterotic string reveal some distinctive properties. These include gauge-top unification, a specific solution to the mu-problem and mirage pattern for the gaugino masses. The location of the top- and the Higgs-multiplets in extra dimensions differs significantly from that of the other quarks and leptons leading to a characteristic signature of suppressed soft breaking terms, reminiscent of a scheme known as natural supersymmetry.
Some recent developments in the weakly-coupled heterotic string phenomenology are reviewed. We discuss several important issues such as dilaton/moduli stabilization, supersymmetry breaking (by hidden-sector gaugino condensation), gauge coupling unification (or the Newton's constant), the QCD axion, as well as cosmological problems involving the dilaton/moduli and the axion.
We investigate the impact of sterile neutrinos on the decay rate of extra $Z'$s with mass in the TeV range in heterotic string derived models. We explore the impact of sterile neutrinos on the current $Z'$ mass exclusion limits at the LHC, and how these bounds change when the parameter space of this specific class of models is modified.
We present a novel string-derived $U(1)$ combination that satisfies necessary properties to survive to low scales. We discuss previous attempts at acquiring such an abelian gauge symmetry from two different string embeddings and the pitfalls associated with them. Finally, we give an example of how a satisfactory model may be constructed within our framework.
We explicitly give the correspondence between spectra of heterotic string theory compactified on $T^2$ and string junctions in type IIB theory compactified on $S^2$.
We review some exact solitonic solutions of string theory with higher-membrane structure. These include an axionic instanton solution of bosonic string theory as well as multi-instanton and multimonopole solutions of heterotic string theory. The heterotic solutions reveal some interesting aspects of string theory as a theory of quantum gravity.
We study $SO(32)$ heterotic string theory on torus with magnetic fluxes. Non-vanishing fluxes can lead to non-universal gauge kinetic functions for $SU(3) \times SU(2) \times U(1)_Y$ which is the important features of $SO(32)$ heterotic string theory in contrast to the $E_8\times E_8$ theory. It is found that the experimental values of gauge couplings are realized with ${\cal O}(1)$ values of moduli fields based on the realistic models with the $SU(3) \times SU(2) \times U(1)_Y$ gauge symmetry and three chiral generations of quarks and leptons without chiral exotics.
The ten dimensional string theories as well as eleven dimensional supergravity are conjectured to arise as limits of a more basic theory, traditionaly dubbed M--theory. This notion is confined to the ten dimensional supersymmetric theories. String theory, however, also contains ten dimensional nonsupersymmetric theories that have not been incorporated into this picture. In this note we explore the possibility of generating the low energy spectra of various nonsupersymmetric heterotic string vacua form the Horava--Witten model. We argue that this can be achieved by imposing on the Horava--Witte…
In this talk we argue that a certain class of heterotic orbifolds can be the underlying fundamental theory for recently studied field theory GUTs. In addition we demonstrate that symmetric heterotic Z2 times Z2 orbifolds can give rise to three generation models if quantised Wilson lines are switched on.
The relic abundance of stable neutralinos is investigated in $E_8 \times E_8'$ heterotic string theory when supersymmetry is spontaneously broken by hidden-sector gaugino condensates. In the weak coupling regime, very large scalar masses (compared to gaugino masses) are shown to lead to a too large relic abundance of the neutralinos, incompatible with cosmological observations in most of parameter space. The problem does not arise in the strong coupling regime (heterotic M-theory) because there scalar and gaugino masses are generically of the same order of magnitude.
The $Z_2\times Z_2$ heterotic string orbifold gives rise to a large space of phenomenological three generation models that serves as a testing ground to explore how the Standard Model of particle physics may be incorporated in a theory of quantum gravity. Recently, we demonstrated the existence of type 0 $Z_2\times Z_2$ heterotic string orbifolds in which there are no massless fermionic states. In this paper we demonstrate the existence of non--supersymmetric tachyon--free $Z_2\times Z_2$ heterotic string orbifolds that do not contain any massless bosonic states from the twisted sectors. We du…
We classify potential cosmic strings according to the topological charge measurable outside the string core. We conjecture that in string theory it is this charge that governs the stability of long strings. This would imply that the SO(32) heterotic string can have endpoints, but not the E_8 x E_8 heterotic string. We give various arguments in support of this conclusion.
We establish a symmetry map which relates two low-energy heterotic string theories with different numbers of the Abelian gauge fields compactified from the diverse to three dimensions on a torus. We discuss two applications of the established symmetry: a generation of the heterotic string theory solutions from the stationary Einstein-Maxwell fields and one non-trivial submersion of the heterotic string theory into the bosonic one.
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.
A type IIA string compactified on a Calabi-Yau manifold which admits a K3 fibration is believed to be equivalent to a heterotic string in four dimensions. We study cases where a Calabi-Yau manifold can have more than one such fibration leading to equivalences between perturbatively inequivalent heterotic strings. This allows an analysis of an example in six dimensions due to Duff, Minasian and Witten and enables us to go some way to prove a conjecture by Kachru and Vafa. The interplay between gauge groups which arise perturbatively and nonperturbatively is seen clearly in this example. As an e…
A precise formula for the elliptic genus of three E-strings is presented. The related refined free energy coincides with the result calculated from topological string on local half K3 Calabi-Yau threefold up to genus twelve. The elliptic genus of three heterotic strings computed from M9 domain walls matches with the result from orbifold formula to high orders. This confirms the n=3 case of the recent conjecture that n pairs of E-strings can recombine into n heterotic strings.
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 direct…
Brane actions with chiral bosons present special challenges. Recent progress in the description of the two main examples -- the M theory five-brane and the heterotic string -- is described. Also, double dimensional reduction of the M theory five-brane on K3 is shown to give the heterotic string.
Physical aspects of the thermofield dynamics of the D=10 heterotic thermal string theory are exemplified through the infrared behaviour of the one-loop dual symmetric cosmological constant in association with the global phase structure of the thermal string ensemble.
The thermofield dynamics of the D = 10 heterotic thermal string theory is described in proper reference to the thermal duality symmetry as well as the thermal stability of modular invariance in association with the global phase structure of the D = 10 heterotic thermal string ensemble.
We present a class of heterotic compactifications where it is possible to lower the string unification scale down to the GUT scale, while preserving the validity of the perturbative analysis. We illustrate this approach with an explicit example of a four-dimensional chiral heterotic vacuum with N=1 supersymmetry.
Since T-duality has been proved only perturbatively and most of the heterotic states map into solitonic, non-perturbative, type II states, the 6-dimensional string-string duality between the heterotic string and the type II string is not sufficient to prove the S-duality of the former, in terms of the known T-duality of the latter. We nevertheless show in detail that perturbative T-duality, together with the heterotic-type II duality, does imply the existence of heterotic H-monopoles, with the correct multiplicity and multiplet structure. This construction is valid at a generic point in the mo…
Physical aspects of the thermofield dynamics of the D=10 heterotic string theory are exemplified through the infrared behaviour of the one-loop dual symmetric cosmological constant in association with the global phase structure of the thermal string ensemble.
We analyse the BRST cohomology of the Ramond sector of heterotic ambitwistor theory. We also write the free string field theory action and compute the supersymmetry transformations.
We show that all three conditions for the cosmological relevance of heterotic cosmic strings, the right tension, stability and a production mechanism at the end of inflation, can be met in the strongly coupled M-theory regime. Whereas cosmic strings generated from weakly coupled heterotic strings have the well known problems posed by Witten in 1985, we show that strings arising from M5-branes wrapped around 4-cycles (divisors) of a Calabi-Yau in heterotic M-theory compactifications, solve these problems in an elegant fashion.
The SO(32) heterotic string can be obtained from the type IIB string by gauging a discrete symmetry that acts as $(-1)^{F_L}$ on the perturbative string states and reverses the parity of the D-string. Consistency requires the presence of 32 NS 9-branes -- the S-duals of D9-branes -- which give SO(32) Chan-Paton factors to open D-strings. At finite string coupling, there are SO(32) charges tethered to the heterotic string world-sheet by open D-strings. At zero-coupling, the D-string tension becomes infinite and the SO(32) charges are pulled onto the world-sheet, and give the usual SO(32) world-…
In this paper we work out some basic results concerning heterotic string compactifications on stacks and, in particular, gerbes. A heterotic string compactification on a gerbe can be understood as, simultaneously, both a compactification on a space with a restriction on nonperturbative sectors, and also, a gauge theory in which a subgroup of the gauge group acts trivially on the massless matter. Gerbes admit more bundles than corresponding spaces, which suggests they are potentially a rich playground for heterotic string compactifications. After we give a general characterization of heterotic …
We study supersymmetry conditions for the heterotic pure superstring preserving and N=1 supersymmetry in four dimensions directly from the curved superspace defined by the Berkovits-Howe constraints.
In this paper we analyze discrete torsion in perturbative heterotic string theory. In previous work we have given a purely mathematical explanation of discrete torsion as the choice of orbifold group action on a B field, in the case that d H = 0; in this paper, we perform the analogous calculations in heterotic strings where d H is nonzero.
We show that there exist two 27 and one 27 bar of E6, net one D=4, N=1 chiral matter supermultiplet as zero modes localized on the intersection of two 5-branes in the E8 x E8 heterotic string theory. The smeared intersecting 5-brane solution is used via the standard embedding to construct a heterotic background, which provides, after a compactification of some of the transverse dimensions, a five-dimensional Randall-Sundrum II like brane-world set-up in heterotic string theory. As a by-product, we present a new proof of anomaly cancellation between those from the chiral matter and the anomaly …
Two classes of stringy instanton effects, stronger than standard field theory instantons, are identified in the heterotic string theory. These contributions are established using type IIA/heterotic and type I/heterotic dualities. They provide examples for the heterotic case of the effects predicted by Shenker based on the large-order behavior of perturbation theory. The corrections vanish as the radius of the compactification goes to infinity. For appropriate amplitudes, they are computable worldsheet or worldline instanton effects on the dual side. Some potential applications are discussed.
The thermofield dynamics of the $D = 10$ heterotic thermal string theory is exemplified at any finite temperature through the infrared behaviour of the one-loop cosmological constant in proper reference to the thermal duality symmetry in association with the global phase structure of the thermal string ensemble.
M-theory suggests the large N limit of the matrix description of a collection of N Type IA D-particles should provide a nonperturbative formulation of heterotic string theory. In this paper states in the matrix theory corresponding to fundamental heterotic strings are identified, and their interactions are studied. Comments are made about analogous states in Type IIA string theory, which correspond to bound states of D-particles and D-eightbranes.
