Spinor-vector duality and light Z' in heterotic string vacua

We discuss the construction of heterotic--string models that allow for the existence of an extra $Z^\prime$ at low scales. One of the main difficulties encountered is that the desired symmetries tend to be anomalous in the prevailing three generation constructions. The reason is that these models utilise the symmetry breaking pattern $E_6\rightarrow SO(10)\times U(1)_\zeta$ by GGSO projections. Consequently, $U(1)_\zeta$ becomes anomalous. The spinor--vector duality that was observed in the fermionic $Z_2\times Z_2$ orbifold compactifications is used to construct a phenomenological three generation Pati--Salam heterotic--string model in which $U(1)_\zeta$ is anomaly free and therefore can be a component of a low scale $Z^\prime$. The model implies existence of matter states at the $Z^\prime$ breaking scale, which are required for anomaly cancelation. Moreover, the string model gives rise to exotic states, which are $SO(10)$ singlets but carry exotic $U(1)_\zeta$ charges. These states arise due to the breaking of $E_6$ by discrete Wilson lines and provide natural dark matter candidates. Initial indications suggest that the existence of additional gauge symmetries at the TeV scale may be confirmed in run II of the LHC experiment.Comment: To appear in the proceedings of PLANCK 2015 international conference, 25-29 May 2015, Ioannnina, Greece. 17 pages. Standard LaTex. 2 figure

A Light Z' Heterotic-String Derived Model

The existence of an extra Z' inspired from heterotic-string theory at accessible energy scales attracted considerable interest in the particle physics literature. Surprisingly, however, the construction of heterotic--string derived models that allow for an extra Z' to remain unbroken down to low scales has proven to be very difficult. The main reason being that the U(1) symmetries that are typically discussed in the literature are either anomalous or have to be broken at a high scale to generate light neutrino masses. In this paper we use for that purpose the self duality property under the spinor vector duality, which was discovered in free fermionic heterotic-string models. The chiral massless states in the self--dual models fill complete 27 representations of E6. The anomaly free gauge symmetry in the effective low energy field theory of our string model is $SU(4)_C\times SU(2)_L\times SU(2)_R\times U(1)_\zeta$, where $U(1)_\zeta$ is the family universal $U(1)$ symmetry that descends from E6, and is typically anomalous in other free fermionic heterotic-string models. Our model therefore allows for the existence of a low scale Z', which is a combination of $B-L$, $T_{3_L}$ and $T_{3_R}$. The string model is free of exotic fractionally charged states in the massless spectrum. It contains exotic SO(10) singlet states that carry fractional, non--E6 charge, with respect to $U(1)_\zeta$. These non-E6 states arise in the string model due to the breaking of the E6 symmetry by discrete Wilson lines. They represent a distinct signature of the string vacua and cannot arise in E6 Grand Unified Theories. They may provide viable dark matter candidates.Comment: 18 pages. Standard LaTeX. 3 table

Classification of Flipped SU(5) Heterotic-String Vacua

We extend the classification of the free fermionic heterotic-string vacua to models in which the SO(10) GUT symmetry at the string scale is broken to the flipped SU(5) subgroup. In our classification method, the set of basis vectors defined by the boundary conditions which are assigned to the free fermions is fixed and the enumeration of the string vacua is obtained in terms of the Generalised GSO (GGSO) projection coefficients entering the one-loop partition function. We derive algebraic expressions for the GGSO projections for all the physical states appearing in the sectors generated by the set of basis vectors. This enables the analysis of the entire string spectrum to be programmed in to a computer code therefore, we performed a statistical sampling in the space of 2^{44} (approximately 10^{13}) flipped $SU(5)$ vacua and scanned up to 10^{12} GGSO configurations. For that purpose, two independent codes were developed based on JAVA and FORTRAN95. All the results presented here are confirmed by the two independent routines. Contrary to the corresponding Pati-Salam classification, we do not find exophobic flipped SU(5) vacua with an odd number of generations. We study the structure of exotic states appearing in the three generation models that additionally contain a viable Higgs spectrum. Moreover, we demonstrate the existence of models in which all the exotic states are confined by a hidden sector non-Abelian gauge symmetry as well as models that may admit the racetrack mechanism.Comment: Minor changes (Version 2) - 51 pages - 3 figures - Added acknowledgement

Top Quark Mass in Exophobic Pati--Salam Heterotic String Model

We analyse the phenomenology of an exemplary exophobic Pati-Salam heterotic string vacuum, in which no exotic fractionally charged states exist in the massless string spectrum. Our model also contains the Higgs representations that are needed to break the gauge symmetry to that of the Standard Model and to generate fermion masses at the electroweak scale. We show that the requirement of a leading mass term for the heavy generation, which is not degenerate with the mass terms of the lighter generations, places an additional strong constraint on the viability of the models. In many models a top quark Yukawa may not exist at all, whereas in others two or more generations may obtain a mass term at leading order. In our exemplary model a mass term at leading order exist only for one family. Additionally, we demonstrate the existence of supersymmetric F- and D-flat directions that give heavy mass to all the colour triplets beyond those of the Standard Model and leave one pair of electroweak Higgs doublets light. Hence, below the Pati-Salam breaking scale, the matter states in our model that are charged under the observable gauge symmetries, consist solely of those of the Minimal Supersymmetric Standard Model.Comment: 16 pages. 2 figures. Minor typos correcte

On the Heterotic Effective Action at One-Loop, Gauge Couplings and the Gravitational Sector

We present in detail the procedure for calculating the heterotic one-loop effective action. We focus on gravitational and gauge couplings. We show that the two-derivative couplings of the gravitational sector are not renormalized at one loop when the ground state is supersymmetric. Arguments are presented that this non-renormalization theorem persists to all orders in perturbation theory. We also derive the full one-loop correction to the gauge coupling. For a class of $N=2$ ground states, namely those that are obtained by toroidal compactification to four dimensions of generic six-dimensional $N=1$ models, we give an explicit formula for the gauge-group independent thresholds, and show that these are equal within the whole family.Comment: LateX, 17pp. A minor correction mad

The 750 GeV di-photon LHC excess and extra Z's in heterotic-string derived models

The ATLAS and CMS collaborations recently recorded possible di-photon excess at 750 GeV and a less significant di-boson excess around 1.9 TeV. Such excesses may be produced in heterotic-string derived Z' models, where the di-photon excess may be connected with the Standard Model singlet scalar responsible for the Z' symmetry breaking, whereas the di-boson excess arises from production of the extra vector boson. Additional vector-like states in the string Z' model are instrumental to explain the relatively large width of the di-photon events and mandated by anomaly cancellation to be in the vicinity of the Z' breaking scale. Wilson line breaking of the non-Abelian gauge symmetries in the string models naturally gives rise to dark matter candidates. Future collider experiments will discriminate between the high-scale heterotic-string models, which preserve the perturbative unification paradigm indicated by the Standard Model data, versus the low scale string models. We also discuss the possibility for the production of the di-photon events with high scale $U(1)_{Z^\prime}$ breaking.Comment: 17 pages. 1 figure. Minor revisions. References added. Published versio

Anomalous U(1)s in Type I superstring vacua

We perform a systematic string computation of the masses of anomalous U(1) gauge bosons in four-dimensional orientifold vacua, and we study their localization properties in the internal (compactified) space. We find that N=1 supersymmetric sectors yield four-dimensional contributions, localized in the whole six-dimensional internal space, while N=2 sectors give contributions localized in four internal dimensions. As a result, the U(1) gauge fields can be much lighter than the string scale, so that when the latter is at the TeV, they can mediate new non-universal repulsive forces at submillimeter distances much stronger than gravity. We also point out that even U(1)s which are free of four-dimensional anomalies may acquire non-zero masses as a consequence of six-dimensional anomalies.Comment: LateX, 30pages, (v2) minor corrections, versio to appear in Nucl. Phys.