We construct a supersymmetric standard model in the context of the $Z_{12-I}$ orbifold compactification of the heterotic string theory. The gauge group is $SU(3)_c\times SU(2)_L\times U(1)_Y\times U(1)^4\times[SO(10)\times U(1)^3]'$. We obtain three chiral families, $3\times\{Q,d^c,u^c,L,e^c,\nu^c\}$, and Higgs doublets. There are numerous neutral singlets many of which can have VEVs so that low energy phenomenology on Yukawa couplings can be satisfied. In one assignment (Model E) of the electroweak hypercharge, we obtain the string scale value of $sin^2\theta_W^0={3/8}$ and another exactly massless {\it exphoton} (in addition to the photon) coupling to exotic particles only. There are color triplet and anti-triplet exotics, $\alpha$ and $\bar{\alpha}$, $SU(2)_L$ doublet exotics, $\delta$ and $\bar{\delta}$, and $SU(3)_c\times SU(2)_L$ singlet but $Y={2/3},-{1/3},-{2/3},{1/3}$ exotics, $\xi,\eta,\bar{\xi}, \bar{\eta}$. We show that all these vector-like exotics achieve heavy masses by appropriate VEVs of neutral singlets. One can find an effective R-parity between light (electroweak scale) particles so that proton and the LSP can live sufficiently long. In another assignment (Model S) of the electroweak hypercharge, there does not appear any exotic particle but $sin^2\theta_W^0={3/14}$.

Superstring standard model from Z_{12-I} orbifold compactification with and without exotics, and effective R-parity

We provide the methods to compute the complete massless spectra of a class of recently introduced supersymmetric E8 ? E8 heterotic string models which invoke vector bundles with U(N) structure group on simply connected Calabi-Yau manifolds and which yield flipped SU(5) and MSSM string vacua of potential phenomenological interest. We apply Leray spectral sequences in order to derive the localisation of the cohomology groups Hi(X,?Va???Vb), Hi(X,?2V) and Hi(X,?S2V) for vector bundles defined via Fourier-Mukai transforms on elliptically fibered Calabi-Yau manifolds. By the method of bundle extensions we define a stable U(4) vector bundle leading to the first flipped SU(5) model with just three generations, i.e. without any vector-like matter. Along the way, we propose the notion of ?-stability for heterotic bundles.

Massless Spectra of Three Generation U(N) Heterotic String Vacua

We construct a supersymmetric standard model in the context of the 12−I orbifold compactification of the heterotic string theory. The gauge group is SU(3)c × SU(2)L × U(1)Y × U(1)4 × [SO(10) × U(1)3]'. We obtain three chiral families, 3 × {Q, dc, uc, L, ec, νc}, and Higgs doublets. There are numerous neutral singlets many of which can have VEVs so that low energy phenomenology on Yukawa couplings can be satisfied. In one assignment (Model E) of the electroweak hypercharge, we obtain the string scale value of sin 2 θW0 = (3/8) and another exactly massless exphoton (in addition to the photon) coupling to exotic particles only. There are color triplet and anti-triplet exotics, α and , SU(2)L doublet exotics, δ and , and SU(3)c × SU(2)L singlet but Y = 2/3, −1/3, −2/3, 1/3 exotics, ξ, η, , . We show that all these vector-like exotics achieve heavy masses by appropriate VEVs of neutral singlets. One can find an effective R-parity between light (electroweak scale) particles so that proton and the LSP can live sufficiently long. In another assignment (Model S) of the electroweak hypercharge, there does not appear any exotic particle but sin2 θW0 = 3/14.

Superstring standard model from ℤ12−I orbifold compactification with and without exotics, and effective R-parity

We provide the methods to compute the complete massless spectra of a class of recently introduced supersymmetric E8 x E8 heterotic string models which invoke vector bundles with U(N) structure group on simply connected Calabi-Yau manifolds and which yield flipped SU(5) and MSSM string vacua of potential phenomenological interest. We apply Leray spectral sequences in order to derive the localisation of the cohomology groups H^i(X,V_a \times V_b), H^i(X,\bigwedge^2 V) and H^i(X,{\bf S}^2 V) for vector bundles defined via Fourier-Mukai transforms on elliptically fibered Calabi-Yau manifolds. By the method of bundle extensions we define a stable U(4) vector bundle leading to the first flipped SU(5) model with just three generations, i.e. without any vector-like matter. Along the way, we propose the notion of Lambda-stability for heterotic bundles.

Spinor–vector duality in heterotic SUSY vacua

Three generation heterotic string vacua in the free fermionic formulation gave rise to models with solely the MSSM states in the observable standard model charged sector. The relation of these models to Z2×Z2 orbifold compactifications dictates that they produce three pairs of untwisted Higgs multiplets. The reduction to one pair relies on the analysis of supersymmetric flat directions, which give a superheavy mass to the dispensable Higgs states. We explore the removal of the extra Higgs representations by using the free fermion boundary conditions, and hence we work directly at the string level, rather than in the effective low energy field theory. We present a general mechanism that achieves this reduction by using asymmetric boundary conditions between the left- and right-moving internal fermions. We incorporate this mechanism in explicit string models containing three twisted generations and a single untwisted Higgs doublet pair. We further demonstrate that an additional effect of the asymmetric boundary conditions is to substantially reduce the supersymmetric moduli space.

Minimal standard heterotic string models

Quasirealistic string models in the free fermionic formulation typically contain an anomalous U(1), which gives rise to a Fayet-Iliopoulos D-term that breaks supersymmetry at the one-loop level in string perturbation theory. Supersymmetry is traditionally restored by imposing F and D flatness on the vacuum. By employing the standard analysis of flat directions, we present a quasirealistic three-generation string model in which stringent F- and D-flat solutions do not appear to exist to all orders in the superpotential. We speculate that this result is indicative of the nonexistence of supersymmetric flat F and D solutions in this model. We provide some arguments in support of this scenario and discuss its potential implications. Bose-Fermi degeneracy of the string spectrum implies that the one-loop partition function, and hence the one-loop cosmological constant, vanishes in the model. If our assertion is correct, this model may represent the first known example with vanishing cosmological constant and perturbatively broken supersymmetry. We discuss the distinctive properties of the internal free fermion boundary conditions that may correspond to a large set of models that share these properties. The geometrical moduli in this class of models are fixed due to asymmetric boundary conditions, whereas absence of supersymmetric flat directionsmore » would imply that the supersymmetric moduli are fixed as well and the dilaton may be fixed by hidden sector nonperturbative effects.« less

Quasirealistic heterotic-string models with vanishing one-loop cosmological constant and perturbatively broken supersymmetry?

Three generation heterotic-string vacua in the free fermionic formulation gave rise to models with solely the MSSM states in the observable Standard Model charged sector. The relation of these models to Z_2 x Z_2 orbifold compactifications dictates that they produce three pairs of untwisted Higgs multiplets. The reduction to one pair relies on the analysis of supersymmetric flat directions, that give superheavy mass to the dispensable Higgs states. We explore the removal of the extra Higgs representations by using the free fermion boundary conditions and hence directly at the string level, rather than in the effective low energy field theory. We present a general mechanism that achieves this reduction by using asymmetric boundary conditions between the left- and right-moving internal fermions. We incorporate this mechanism in explicit string models containing three twisted generations and a single untwisted Higgs doublet pair. We further demonstrate that an additional effect of the asymmetric boundary conditions is to substantially reduce the supersymmetric moduli space.

Minimal Standard Heterotic String Models

We discuss toroidal orbifolds of the E
 8×E
 8 heterotic string, in which the free-fermionic Higgs–matter splitting is implemented by a shift in the internal lattice coupled with the fermion numbers of the gauge degrees of freedom. We consider models in which some choices of the orbifold result in the projection of the graviton. In the models that we consider the projection also results in flipping the spin–statistics assignments in the massive string spectrum, whereas the massless spectrum retains the conventional spin–statistics assignments. We argue that the partition functions are mathematically consistent for one- and multi-loop amplitudes, owning to the existence of supersymmetry in the spectrum. A duality between different models at non-zero temperature is briefly discussed.

Little heterotic strings

/pdf/heterotic-string-models-with-perturbatively-broken-1c0gboxjvi.pdf

Elisa Manno

Papers

Minimal standard heterotic string models

Quasirealistic heterotic-string models with vanishing one-loop cosmological constant and perturbatively broken supersymmetry?

Minimal Standard Heterotic String Models

Little heterotic strings

Heterotic String Models with Perturbatively Broken Supersymmetry