Investigation of Quasi--Realistic Heterotic String Models with Reduced Higgs Spectrum

Quasi--realistic heterotic-string models in the free fermionic formulation typically contain an anomalous U(1), which gives rise to a Fayet-Iliopolous term that breaks supersymmetry at the one--loop level in string perturbation theory. Supersymmetry is restored by imposing F- and D-flatness on the vacuum. In Phys. Rev. D 78 (2008) 046009, we presented a three generation free fermionic standard-like model which did not admit stringent F- and D-flat directions, and argued that the all the moduli in the model are fixed. The particular property of the model was the reduction of the untwisted Higgs spectrum by a combination of symmetric and asymmetric boundary conditions with respect to the internal fermions associated with the compactified dimensions. In this paper we extend the analysis of free fermionic models with reduced Higgs spectrum to the cases in which the SO(10) symmetry is left unbroken, or is reduced to the flipped SU(5) subgroup. We show that all the models that we study in this paper do admit stringent flat directions. The only examples of models that do not admit stringent flat directions remain the strandard-like models of reference Phys. Rev. D 78 (2008) 046009.Comment: 38 pages, 1 figur

A Minimal Superstring Standard Model I: Flat Directions

Three family SU(3)_C x SU(2)_L x U(1)_Y string models in several constructions generically possess two features: (i) an extra local anomalous U(1)_A and (ii) numerous (often fractionally charged) exotic particles beyond those in the minimal supersymmetric model (MSSM). Recently, we demonstrated that the observable sector effective field theory of such a free fermionic string model can reduce to that of the MSSM, with the standard observable gauge group being just SU(3)_C x SU(2)_L x U(1)_Y and the SU(3)_C x SU(2)_L x U(1)_Y-charged spectrum of the observable sector consisting solely of the MSSM spectrum. An example of a model with this property was shown. We continue our investigation of this model by presenting a large set of different flat directions of the same model that all produce the MSSM spectrum. Our results suggest that even after imposing the conditions for the decoupling of exotic states, there may remain sufficient freedom to satisfy the remaining phenomenological constraints imposed by the observed data.Comment: 64 pages. Latex. Revisions to match version in Int. J. Mod. Physics

Left-Right Symmetric Heterotic-String Derived Models

Recently it was demonstrated that free fermionic heterotic-strings can produce models with solely the Minimal Supersymmetric Standard Model states in the low energy spectrum. This unprecedented result provides further strong evidence for the possibility that the true string vacuum shares some of the properties of the free fermionic models. Past free fermionic models have focused on several possible unbroken observable SO(10) subgroups at the string scale, which include the flipped SU(5) (FSU5), the Pati-Salam (PS) string models, and the string Standard-like Models (SLM). We extend this study to include the case in which the SO(10) symmetry is broken to the Left-Right Symmetric (LRS) gauge group, SO(10) -> SU(3)_C X U(1)_{B-L} X SU(2)_L X SU(2)_R. We present several models of this type and discuss their phenomenological features. The most striking new outcome of the LRS string models, in contrast to the case of the FSU5, the PS, and the SLM string models, is that they can produce effective field theories that are free of Abelian anomalies. We discuss the distinction between the two types of free fermionic models which result in the presence, or absence, of an anomalous U(1). As a counter example we also present a LRS model that does contain an anomalous U(1). Additionally, we discuss how in string models the Standard Model spectrum may arise from the three \mbf 16 representations of SO(10), while the weak-hypercharge does not have the canonical SO(10) embedding.Comment: 39 pages. Standard Latex. Version to appear in PR

Dynamical supersymmetry breaking in a superstring inspired model

We present a dilaton dominated scenario for supersymmetry breaking in a recently constructed realistic superstring inspired model with an anomalous U(1) symmetry. Supersymmetry is broken via gaugino condensation due to a confining SU(Nc) gauge group in the hidden sector. In particular, we find that by imposing on the model the phenomenological constraint of the absence of observed flavor changing neutral currents, there is a range of parameters related to the hidden sector and the Kahler potential for which we obtain a low energy spectrum consistent with present experimental bounds. As an illustrative example, we derive the low energy spectrum of a specific model. We find that the LSP is the lightest neutralino with a mass of 53 GeV and the lightest Higgs has a mass of 104 GeV.Comment: 13 page

The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory

We present an exact description of the metric on the moduli space of vacua and the spectrum of massive states for four dimensional N=2 supersymmetric SU(n) gauge theories. The moduli space of quantum vacua is identified with the moduli space of a special set of genus n-1 hyperelliptic Riemann surfaces.Comment: 11 pages, Revtex, 2 figures. Reference adde

Units and Numerical Values of the Effective Couplings in Perturbative Heterotic String Vacua

We determine the units and numerical values for a class of couplings in the effective theory of perturbative heterotic string vacua, with the emphasis on the correct translation between the canonical gauge coupling g and Planck scale M_Planck ~ 1.2 x 10^19 GeV as used in the effective theory description and the string coupling g_string and string tension alpha' as used in the S-matrix amplitude calculation. In particular, we determine the effective couplings in the superpotential and revisit the Fayet-Iliopoulos (FI) term in a class of models with an anomalous U(1). We derive the values of the effective Yukawa couplings (at the third and fourth order) after the restabilization of vacuum along a particular F- and D-flat direction and show that they are comparable in magnitude. The result corrects results quoted in the literature, and may have implications for the string derived phenomenology, e.g., that of fermion textures.Comment: RevTeX, 8p

A Statistical Interpretation of Space and Classical-Quantum duality

By defining a prepotential function for the stationary Schr\"odinger equation we derive an inversion formula for the space variable $x$ as a function of the wave-function $\psi$. The resulting equation is a Legendre transform that relates $x$, the prepotential ${\cal F}$, and the probability density. We invert the Schr\"odinger equation to a third-order differential equation for ${\cal F}$ and observe that the inversion procedure implies a $x$-$\psi$ duality. This phenomenon is related to a modular symmetry due to the superposition of the solutions of the Schr\"odinger equation. We propose that in quantum mechanics the space coordinate can be interpreted as a macroscopic variable of a statistical system with $\hbar$ playing the role of a scaling parameter. We show that the scaling property of the space coordinate with respect to $\tau=\partial_{\psi}^2{\cal F}$ is determined by the ``beta-function''. We propose that the quantization of the inversion formula is a natural way to quantize geometry. The formalism is extended to higher dimensions and to the Klein-Gordon equation.Comment: 11 pages. Standard Latex. Final version to appear in Physical Review Letters. Revised and extended version. The formalism is extended to higher dimensions and to the Klein-Gordon equation. A possible connection with string theory is considered. The $x-\psi$ duality is emphasized by a minor change in the title. The new title is: Duality of $x$ and $\psi$ and a statistical interpretation of space in quantum mechanic

Dirac brackets from magnetic backgrounds

In symplectic mechanics, the magnetic term describing the interaction between a charged particle and an external magnetic field has to be introduced by hand. On the contrary, in generalised complex geometry, such magnetic terms in the symplectic form arise naturally by means of B-transformations. Here we prove that, regarding classical phase space as a generalised complex manifold, the transformation law for the symplectic form under the action of a weak magnetic field gives rise to Dirac's prescription for Poisson brackets in the presence of constraints.Comment: 9 page

Physics Implications of Flat Directions in Free Fermionic Superstring Models I: Mass Spectrum and Couplings

From the "top-down" approach we investigate physics implications of the class of D- and F- flat directions formed from non-Abelian singlets which are proven flat to all orders in the nonrenormalizable superpotential, for a prototype quasi-realistic free fermionic string model with the standard model gauge group and three families (CHL5). These flat directions have at least an additional U(1)' unbroken at the string scale. For each flat direction, the complete set of effective mass terms and effective trilinear superpotential terms in the observable sector are computed to all orders in the VEV's of the fields in the flat direction. The "string selection-rules" disallow a large number of couplings allowed by gauge invariance, resulting in a massless spectrum with a large number of exotics, in most cases excluded by experiment, thus signifying a generic flaw of these models. Nevertheless, the resulting trilinear couplings of the massless spectrum possess a number of interesting features which we analyse for two representative flat directions: for the fermion texture; baryon- and lepton-number violating couplings; R-parity breaking; non-canonical mu terms; and the possibility of electroweak and intermediate scale symmetry breaking scenarios for U(1)'. The gauge coupling predictions are obtained in the electroweak scale case. Fermion masses possess t-b and tau-mu universality, with the string scale Yukawa couplings g and $g/\sqrt{2}$, respectively. Fermion textures are present for certain flat directions, but only in the down-quark sector. Baryon- and lepton- number violating couplings can trigger proton-decay, $N-{\bar N}$ oscillations, leptoquark interactions and R-parity violation, leading to the absence of a stable LSP.Comment: 36 pages, 5 tables, 4 figures, RevTeX, minor change