arXiv subjects

Alon E. Faraggi

Publications and source records attributed to Alon E. Faraggi.

At least 127 records · Page 7Linked to original sources

arXiv1999

Elevating the Free-Fermion $Z_2\times Z_2$ Orbifold Model to a Compactification of F-Theory

We study the elliptic fibrations of some Calabi-Yau three-folds, including the $Z_2\times Z_2$ orbifold with $(h_{1,1},h_{2,1})=(27,3)$, which is equivalent to the common framework of realistic free-fermion models, as well as related orbifold models with $(h_{1,1},h_{2,1})=(51,3)$ and (31,7). However, two related puzzles arise when one considers the $(h_{1,1},h_{2,1})=(27,3)$ model as an F-theory compactification to six dimensions. The condition for the vanishing of the gravitational anomaly is not satisfied, suggesting that the F-theory compactification does not make sense, and the elliptic fibration is well defined everywhere except at four singular points in the base. We speculate on the possible existence of N=1 tensor and hypermultiplets at these points which would cancel the gravitational anomaly in this case.

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arXiv1999

The Equivalence Principle of Quantum Mechanics: Uniqueness Theorem

Recently we showed that the postulated diffeomorphic equivalence of states implies quantum mechanics. This approach takes the canonical variables to be dependent by the relation p=\partial_q S_0 and exploits a basic GL(2,C)-symmetry which underlies the canonical formalism. In particular, we looked for the special transformations leading to the free system with vanishing energy. Furthermore, we saw that while on the one hand the equivalence principle cannot be consistently implemented in classical mechanics, on the other it naturally led to the quantum analogue of the Hamilton-Jacobi equation, thus implying the Schroedinger equation. In this letter we show that actually the principle uniquely leads to this solution. Furthermore, we find the map reducing any system to the free one with vanishing energy and derive the transformations on S_0 leaving the wave function invariant. We also express the canonical and Schroedinger equations by means of the brackets recently introduced in the framework of N=2 SYM. These brackets are the analogue of the Poisson brackets with the canonical variables taken as dependent.

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arXiv1999

The Equivalence Postulate of Quantum Mechanics

The Equivalence Principle (EP), stating that all physical systems are connected by a coordinate transformation to the free one with vanishing energy, univocally leads to the Quantum Stationary HJ Equation (QSHJE). Trajectories depend on the Planck length through hidden variables which arise as initial conditions. The formulation has manifest p-q duality, a consequence of the involutive nature of the Legendre transform and of its recently observed relation with second-order linear differential equations. This reflects in an intrinsic psi^D-psi duality between linearly independent solutions of the Schroedinger equation. Unlike Bohm's theory, there is a non-trivial action even for bound states. No use of any axiomatic interpretation of the wave-function is made. Tunnelling is a direct consequence of the quantum potential which differs from the usual one and plays the role of particle's self-energy. The QSHJE is defined only if the ratio psi^D/psi is a local self-homeomorphism of the extended real line. This is an important feature as the L^2 condition, which in the usual formulation is a consequence of the axiomatic interpretation of the wave-function, directly follows as a basic theorem which only uses the geometrical gluing conditions of psi^D/psi at q=\pm\infty as implied by the EP. As a result, the EP itself implies a dynamical equation that does not require any further assumption and reproduces both tunnelling and energy quantization. Several features of the formulation show how the Copenhagen interpretation hides the underlying nature of QM. Finally, the non-stationary higher dimensional quantum HJ equation and the relativistic extension are derived.

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arXiv1999

Phenomenological Issues in TeV scale Gravity with Light Neutrino Masses

The possible existence of bulk singlet neutrinos in the scenario with large compactified dimensions and low string scale $M_*$ has important consequences for low-energy observables. We demonstrate that intergenerational mass splitting and mixing lead to the effective violation of the lepton universality and flavor changing processes in charged lepton sector. Current experimental constraints push $M_*$ to the scale of 10 TeV over most of the interesting range for neutrino mass splitting.

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arXiv1999

Quantum Mechanics from an Equivalence Principle

We postulate that physical states are equivalent under coordinate transformations. We then implement this equivalence principle first in the case of one-dimensional stationary systems showing that it leads to the quantum analogue of the Hamilton-Jacobi equation which in turn implies the Schroedinger equation. In this context the Planck constant plays the role of covariantizing parameter. The construction is deeply related to the GL(2,C)-symmetry of the second-order differential equation associated to the Legendre transformation which selects, in the case of the quantum analogue of the Hamiltonian characteristic function, self-dual states which guarantee its existence for any physical system. The universal nature of the self-dual states implies the Schroedinger equation in any dimension.

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arXiv1998

Equivalence Principle, Planck Length and Quantum Hamilton-Jacobi Equation

The Quantum Stationary HJ Equation (QSHJE) that we derived from the equivalence principle, gives rise to initial conditions which cannot be seen in the Schroedinger equation. Existence of the classical limit leads to a dependence of the integration constant $\ell=\ell_1+i\ell_2$ on the Planck length. Solutions of the QSHJE provide a trajectory representation of quantum mechanics which, unlike Bohm's theory, has a non-trivial action even for bound states and no wave guide is present. The quantum potential turns out to be an intrinsic potential energy of the particle which, similarly to the relativistic rest energy, is never vanishing.

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arXiv1998

Equivalence Principle: Tunnelling, Quantized Spectra and Trajectories from the Quantum HJ Equation

A basic aspect of the recently proposed approach to quantum mechanics is that no use of any axiomatic interpretation of the wave function is made. In particular, the quantum potential turns out to be an intrinsic potential energy of the particle, which, similarly to the relativistic rest energy, is never vanishing. This is related to the tunnel effect, a consequence of the fact that the conjugate momentum field is real even in the classically forbidden regions. The quantum stationary Hamilton-Jacobi equation is defined only if the ratio psi^D/psi of two real linearly independent solutions of the Schroedinger equation, and therefore of the trivializing map, is a local homeomorphism of the extended real line into itself, a consequence of the Moebius symmetry of the Schwarzian derivative. In this respect we prove a basic theorem relating the request of continuity at spatial infinity of psi^D/psi, a consequence of the q - 1/q duality of the Schwarzian derivative, to the existence of L^2(R) solutions of the corresponding Schroedinger equation. As a result, while in the conventional approach one needs the Schroedinger equation with the L^2(R) condition, consequence of the axiomatic interpretation of the wave function, the equivalence principle by itself implies a dynamical equation that does not need any assumption and reproduces both the tunnel effect and energy quantization.

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arXiv1998

Quantum Transformations

We show that the stationary quantum Hamilton-Jacobi equation of non-relativistic 1D systems, underlying Bohmian mechanics, takes the classical form with $\partial_q$ replaced by $\partial_{\hat q}$ where $d\hat q={dq\over \sqrt{1-β^2}}$. The $β^2$ term essentially coincides with the quantum potential that, like $V-E$, turns out to be proportional to a curvature arising in projective geometry. In agreement with the recently formulated equivalence principle, these ``quantum transformations'' indicate that the classical and quantum potentials deform space geometry.

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arXiv1998

The $Z_2\times Z_2$ Orbifold and the SUSY Flavor Problem

The characteristic property of the $Z_2\times Z_2$ orbifold is its cyclic permutation symmetry. It is argued that this property may be instrumental in explaining simultaneously the fermion mass hierarchy and the squark mass degeneracy. Detailed studies in free fermionic models that preserve the cyclic permutation symmetry of anomalous U(1) charges of the three generations are discussed.

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arXiv1998

A Family--Universal Anomalous U(1) in String Models as the Origin of Supersymmetry Breaking and Squark Degeneracy

Recently a promising mechanism for supersymmetry breaking that utilizes both an anomalous U(1) gauge symmetry and an effective mass term m ~ 1TeV of certain relevant fields has been proposed. In this paper we examine whether such a mechanism can emerge in superstring derived free fermionic models. We observe that certain three generation string solutions, though not all, lead to an anomalous U(1) which couples universally to all three families. The advantages of this three-family universality of $U(1)_A$, compared to the two-family case, proposed in earlier works, in yielding squark degeneracy, while avoiding radiative breaking of color and charge, are noted. The root cause of the flavor universality of $U(1)_A$ is the cyclic permutation symmetry that characterizes the $Z_2\times Z_2$ orbifold compactification with standard embedding, realized in the free fermionic models by the NAHE set. It is shown that non--renormalizable terms which contain hidden--sector condensates, generate the required suppression of the relevant mass term $m$, compared to the Planck scale. While the D-term of the family universal $U(1)_A$ leads to squark degeneracy, those of the family dependent U(1)'s, remarkably enough, are found to vanish for the solutions considered, owing to minimization of the potential.

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arXiv1998

Toward the M(F)--Theory Embedding of Realistic Free-Fermion Models

We construct a Landau-Ginzburg model with the same data and symmetries as a $Z_2\times Z_2$ orbifold that corresponds to a class of realistic free-fermion models. Within the class of interest, we show that this orbifolding connects between different $Z_2\times Z_2$ orbifold models and commutes with the mirror symmetry. Our work suggests that duality symmetries previously discussed in the context of specific $M$ and $F$ theory compactifications may be extended to the special $Z_2\times Z_2$ orbifold that characterizes realistic free-fermion models.

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arXiv1998

Family Universal Anomalous U(1) in Realistic Superstring Derived Models

An important issue in supersymmetry phenomenology is the suppression of squarks contributions to Flavor Changing Neutral Currents (FCNC). Recently it was noted that in some free fermionic three generation models the anomalous U(1) is family universal. It was further shown that if the $D$--term of the $U(1)_A$ is the dominant source of supersymmetry breaking, the squark masses are indeed approximately degenerate. In this paper I discuss the properties of the superstring models that give rise to the flavor universal anomalous U(1). The root cause for the universal $U(1)_A$ is the cyclic permutation symmetry, the characteristic property of the $Z_2\times Z_2$ orbifold compactification, realized in the free fermionic models by the NAHE set of boundary condition basis vectors. The properties of the three generation models that preserve this cyclic permutation symmetry in the flavor charges are discussed. The cyclic permutation symmetry of the $Z_2\times Z_2$ orbifold compactification is proposed to be the characteristic property, of phenomenological interest, that distinguishes it from other classes of superstring compactifications.

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arXiv1997

On the anomalous U(1) in free fermionic superstring models

The realistic free fermionic models have had an intriguing success in explaining different properties of the observed particle spectrum. In this paper we discuss in some detail the anomalous U(1) symmetry which exists in these models. We study the properties of the anomalous U(1) in both the more realistic NAHE--based free fermionic models and those in a general NAHE class. Appearance of an anomalous U(1) in the more realistic NAHE models is shown to be an effect of reduction of world-sheet supersymmetry from (2,2) to (2,0). We show, however, that in more general (2,1) and (2,0) models, all U(1) can remain anomaly-free under certain conditions. Several phenomenological issues related to the anomalous U(1) are discussed. In particular, we note that in some examples the anomalous U(1) arises from the breaking $E_6 -> SO(10) X U(1)_A$, resulting in $U(1)_A$ being family universal.

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arXiv1997

Exotic leptoquarks from superstring derived models

The H1 and ZEUS collaborations have recently reported a significant excess of events at high $Q^2$ in positron-proton collisions. While there exists insufficient data to conclusively determine the origin of this excess, one possibility is that it is due to a new leptoquark at mass scale around 200 GeV. We examine the type of leptoquark states that exist in superstring derived standard-like models, and show that, while these models may contain the standard leptoquark states which exist in Grand Unified Theories, they also generically contain new and exotic leptoquark states with fractional lepton number, $\pm1/2$. In contrast to the traditional GUT-type leptoquark states, the couplings of the exotic leptoquarks to the Standard Model states are generated after the breaking of $U(1)_{B-L}$. This important feature of the exotic leptoquark states may result in local discrete symmetries which forbid some of the undesired leptoquark couplings. We examine these couplings in several models and study the phenomenological implications. The flavor symmetries of the superstring models are found to naturally suppress leptoquark flavor changing processes.

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arXiv1997

M-Theory Model-Building and Proton Stability

We study the problem of baryon stability in M theory, starting from realistic four-dimensional string models constructed using the free-fermion formulation of the weakly-coupled heterotic string. Suitable variants of these models manifest an enhanced custodial gauge symmetry that forbids to all orders the appearance of dangerous dimension-five baryon-decay operators. We exhibit the underlying geometric (bosonic) interpretation of these models, which have a $Z_2 \times Z_2$ orbifold structure similar, but not identical, to the class of Calabi-Yau threefold compactifications of M and F theory investigated by Voisin and Borcea. A related generalization of their work may provide a solution to the problem of proton stability in M theory.

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arXiv1997

Toward the classification of the realistic free fermionic models

The realistic free fermionic models have had remarkable success in providing plausible explanations for various properties of the Standard Model which include the natural appearance of three generations, the explanation of the heavy top quark mass and the qualitative structure of the fermion mass spectrum in general, the stability of the proton and more. These intriguing achievements makes evident the need to understand the general space of these models. While the number of possibilities is large, general patterns can be extracted. In this paper I present a detailed discussion on the construction of the realistic free fermionic models with the aim of providing some insight into the basic structures and building blocks that enter the construction. The role of free phases in the determination of the phenomenology of the models is discussed in detail. I discuss the connection between the free phases and mirror symmetry in (2,2) models and the corresponding symmetries in the case of the (2,0) models. The importance of the free phases in determining the effective low energy phenomenology is illustrated in several examples. The classification of the models in terms of boundary condition selection rules, real world-sheet fermion pairings, exotic matter states and the hidden sector is discussed.

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arXiv1997

Superstring phenomenology -- present and future perspective

The objective of superstring phenomenology is to develop the models and methodology needed to connect quantitatively between Planck scale physics and electroweak scale experimental data. I review the present status of this endeavor with a focus on the three generation free fermionic models.

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arXiv1997

Meeting the Constraint of Neutrino-Higgsino Mixing in Gravity Unified Theories

In Gravity Unified Theories all operators that are consistent with the local gauge and discrete symmetries are expected to arise in the effective low-energy theory. Given the absence of multiplets like 126 of SO(10) in string models, and assuming that B-L is violated spontaneously to generate light neutrino masses via a seesaw mechanism, it is observed that string theory solutions generically face the problem of producing an excessive $ν_L-{\tilde H}$ mixing mass at the GUT scale, which is some nineteen orders of magnitude larger than the experimental bound of 1 MeV. The suppression of $ν_L-{\tilde H}$ mixing, like proton longevity, thus provides one of the most severe constraints on the validity of any string theory solution. We examine this problem in a class of superstring derived models. We find a family of solutions within this class for which the symmetries of the models and an allowed pattern of VEVs, surprisingly, succeed in adequately suppressing the neutrino-Higgsino mixing terms. At the same time they produce the terms required to generate small neutrino masses via a seesaw mechanism.

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