Grand Unified Theories From Superstrings

Physics Letters Section B, 1986

An analysis is presented of an E a ® E a superstring-inspired ten-dimensional supergravity model following from eompactification on a particular Calabi-Yau manifold which gives rise to three generations. The multiplet structure and discrete symmetries after compactification are determined. It is shown that the model has flat directions which allow for breaking of the gauge group to the standard SU(3) ® SU(2) ® U(I) model at a high scale. The resulting low-energy theory has a realistic spectrum and, remarkably, the discrete symmetries predict a reasonable structure for the Kobayashi-Maskawa mixing matrix. Without unnatural adjustments, proton decay is inhibited and neutrino masses consistent with experimental limits are obtained.

1994

We explore the possibility of embedding supersymmetric GUT texture ideas into superstring models. We discuss the construction of GUT models using free fermionic strings. We find SO(10) models with adjoint scalars, three generations of chiral fermions, and a fundamental Higgs with a Yukawa coupling to only the third generation.

Arxiv preprint hep-ph/0703027, 2007

This paper summarizes several developments in string-derived (Minimal Supersymmetric) Standard Models. Part one reviews the first string model containing solely the three generations of the Minimal Supersymmetric Standard Model and a single pair of Higgs as the matter in the observable sector of the low energy effective field theory. This model was constructed by Cleaver, Faraggi, and Nanopoulos in the Z_2 x Z_2 free fermionic formulation of weak coupled heterotic strings. Part two examines a representative collection of string/brane-derived MSSMs that followed. These additional models were obtained from various construction methods, including weak coupled Z_6 heterotic orbifolds, strong coupled heterotic on elliptically fibered Calabi-Yau's, Type IIB orientifolds with magnetic charged branes, and Type IIA orientifolds with intersecting branes (duals of the Type IIB). Phenomenology of the models is compared. In String Theory Research Progress, Ferenc N. Balogh, editor., (ISBN 978-1-60456-075-6), Nova Science Publishers, Inc.}

Physics Letters B, 1986

A complete classification is given of all supersymmetric theories of free massless two-dimensional fermions. This, in particular, implies a classification of all free-fermion representations of super Kac-Moody algebras. It is shown that these cannot be used to construct new string theories with unbroken supersymmetry in Minkowski space-time, other than the torus-compactifications of the known ten-dimensional superstrings. Assuming anti-de-Sitter space-time could -restore conformal invariance, it is shown how one could construct a string theory whose low-lying excitations form a multiplet of gauged N = 8 supergravity.

Particles, Strings and Cosmology (PASCOS 99), 2000

It is shown that in the Standard Model, the property of charge quantization holds for a Higgs with arbitrary isospin and hypercharge. These defining quantum numbers of the Higgs remain unconstrained while the whole basic and fundamental structure of the Standard Model remains intact. Hence it is shown that the Higgs cannot be a physical particle. Higgs is the underlying 'vacuum' over which the whole edifice of the Standard Model stands. Also on most general grounds it is established here that as per the Standard Model there is no electric charge above the electro-weak phase transition temperature. Hence there was no electric charge present in the Early Universe. The Superstring Theories are flawed in as much as they are incompatible with this requirement.

This are some notes of introduction on string theories. This notes include -Classical Strings ( Why string theory?, The point particle theory, The Nambu-Goto Action and the Polyakov action, Equations of motion, constrains and mode expansion) -Quantization of strings( Covariant quantization, Lightcone quantization, Casimir energy, String Spectrum, Lorentz invariance, Comments on superstrings) - Open strings and D − Branes (Open strings spectra, The Dirac action, Multiple branes: where are strings?) -CFT (Stress energy tensor and Nöether charges, Operator product expansion, Virasoro Algebra, Example: The free scalar field, central charges, Something about CFTs with boundary) -Path integral formulation of strings (The ghost CFT, An aside: Liouville quantum gravity, States and vertex operators, Examples: closed and open string in flat space). -String interactions (closed string amplitude, open string amplitude, one loop amplitude, partition function: a node to string field theory). -Effective action and low energy (Einstein equations, string effective action, solution of e.o.m., compactification and moduli) -Sugra (from global to local Susy, the gravitino, Gravity as (a sort of) gauge theory, pure N=1 Sugra in D= 4, pure N=1 Sugra in D= 4 with Cosmological constant , matter couplings, physical feature of Sugra, Super-Higgs mechanism, Duality , extended SuGra, Black holes in N=2 Sugra)

Nuclear Physics B, 2001

Recently, we demonstrated the existence of heterotic-string solutions in which the observable sector effective field theory just below the string scale reduces to that of the MSSM, with the standard observable gauge group being just SU (3) C × SU (2) L × U (1) Y and the SU (3) C × SU (2) L × U (1) Y-charged spectrum of the observable sector consisting solely of the MSSM spectrum. Associated with this model is a set of distinct flat directions of vacuum expectation values (VEVs) of non-Abelian singlet fields that all produce solely the MSSM spectrum. In this paper, we study the effective superpotential induced by these choices of flat directions. We investigate whether sufficient degrees of freedom exist in these singlet flat directions to satisfy various phenomenological constraints imposed by the observed Standard Model data. For each flat direction, the effective superpotential is given to sixth order. The variations in the singlet and hidden sector low energy spectrums are analyzed. We then determine the mass matrices (to all finite orders) for the three generations of MSSM quarks and leptons. Possible Higgs µ-terms are investigated. We conclude by considering generalizations of our flat directions involving VEVs of non-Abelian fields.

2015

Over the past three decades, considerable effort has been devoted to studying the rich and diverse phenomenologies of heterotic strings exhibiting spacetime supersymmetry. Unfortunately, during this same period, there has been relatively little work studying the phenomenologies associated with their non-supersymmetric counterparts. The primary reason for this relative lack of attention is the fact that strings without spacetime supersymmetry are generally unstable, exhibiting large one-loop dilaton tadpoles. In this paper, we demonstrate that this hurdle can be overcome in a class of tachyon-free four-dimensional string models realized through coordinate-dependent compactifications. Moreover, as we shall see, it is possible to construct models in this class whose low-lying states resemble the Standard Model (or even potential unified extensions thereof)-all without any light superpartners, and indeed without supersymmetry at any energy scale. The existence of such models thus opens the door to general studies of non-supersymmetric string phenomenology, and in this paper we proceed to discuss a variety of theoretical and phenomenological issues associated with such non-supersymmetric strings. On the theoretical side, we discuss the finiteness properties of such strings, the general characteristics of their mass spectra, the magnitude and behavior of their one-loop cosmological constants, and their interpolation properties. By contrast, on the phenomenological side, the properties we discuss are more model-specific and include their construction techniques, their natural energy scales, their particle and charge assignments, and the magnitudes of their associated Yukawa couplings and scalar masses.

1999

In the context of the free-fermionic formulation of the heterotic superstring, we construct a three generation N=1 supersymmetric SU(4)xSU(2)LxSU(2)R model supplemented by an SU(8) hidden gauge symmetry and five Abelian factors. The symmetry breaking to the standard model is achieved using vacuum expectation values of a Higgs pair in (4bar,2R)+(4,2R) at a high scale. One linear combination of the Abelian symmetries is anomalous and is broken by vacuum expectation values of singlet fields along the flat directions of the superpotential. All consistent string vacua of the model are completely classified by solving the corresponding system of F- and D-flatness equations including non-renormalizable terms up to sixth order. The requirement of existence of electroweak massless doublets further restricts the phenomenologically viable vacua. The third generation fermions receive masses from the tree-level superpotential. Further, a complete calculation of all non-renormalizable fermion mas...

Physics Reports, 1990

The superparticle in background supergravitational 1. Introduction 223 fields 258 2. Classical superparticles and the twistor transform 225 3. The superstring in curved superspace 269 2.1. Constrained dynamics of massless particles 225 3.1. The superstring action 270 2.2. A first look at the superparticle 228 3.2. The constraints in "flat" superspace 276 2.3. Superspace 229 3.3. The first-class constraints in curved space 277 2.4. Constrained dynamics of the superparticle 234 4. Recent developments 280 2.5. The superparticle in background Yang-Mills fields 239 Appendix A. Gamma matrices 282 2.6. Constraint equations and the super-Yang-Mills equa-Al. The Dirac algebra 282 tions of motion 247 A.2. Fierz identities 284 2.7. The ten-dimensional twistor transform 252 References 286