Unification of gravity and elementary particle interactions in 26 dimensions?

The presence of an 11-cocycle in ten-dimensional theories containing an E₈×E₈ Yang-Mills theory coupled to supergravity suggests that the fundamental theory is a 26-dimensional string theory based on the Leech lattice. A theory with equal numbers of bosons and fermions is constructed by truncating a certain natural infinite-dimensional representation of the Monster sporadic group. This theory appears to be a certain combination of pieces of heterotic and N = 2 superstring.     

Harmless axions in superstring theories

We explore the possibility of obtaining an axion in superstring theories whose decay constant lies in a phenomenologically acceptable range. We find in agreement with Choi and Kim that this is not possible in SO(32) theories. However, we find that it appears to be possible in the E₈ × E′₈ heterotic string theory.     

On the equivalence of the two most favoured Calabi-Yau compactifications

We discuss the two known multiply connected Calabi-Yau manifolds which give rise to three generations of elementary particles when chosen as the classical vacuum configuration of theE ₈×E ₈ heterotic superstring. It is shown that these two manifolds are diffeomorphic.Part of this work carried out at and supported by the IBM T.J. Watson Research Center, Yorktown Heights, NYOn leave from Lyman Laboratory of Physics, Harvard University     

Supersymmetric string theories,superconformal algebras and exceptional groups

We study the relation between extended space-time supersymmetry and extended worldsheet symmetries within the context of four-dimensional heterotic string theories. It is shown how these symmetries follow from an underlying E₇ and E₈ symmetry which also explains the appearance of extra U(1) gauge bosons. Supersymmetry transformation aalways act within a given multiplet of E₇ and E₈.     

Supersymmetry restoration in the compactified O(16) ⊗ O (16)' heterotic string theory

We consider twisted compactifications of the O(16) ⊗ O(16)' heterotic string from ten to nine dimensions. We construct a model that interpolates between the O(16) ⊗ O(16)' model at large radii of the compact dimension, and the spontaneously broken E₈⊗E'₈ heterotic superstring at small radii. Further compactification leads to a four-dimensional model with an exponentially suppressed one-loop cosmological constant at small radii. The notion of duality between strings at small and large radii of the compact dimensions is clarified.     

Compactification and inflation in the superstring theory from the condensation of gravitino pairs

We discuss the possibility that inflation can occur in the E₈×E₈′ heterotic superstring theory, if there is a pair condensation of the gravitino field ψ_A and also of the Majorana-Weyl spinor λ, as suggested by the Helayël-Neto and Smith. In the absence of a condensation of the anti-symmetric tensor field H_MNP, then the associated potential V(θ,φ) is bounded from below and independent of the dilaton field φ. It can be made to vanish at the minimum, where the compactification scale θ is fixed. Alternatively, a small cosmological constant may remain (ultimately to be cancelled by radiative corrections at the lower energy scale of the gaugino condensation), which could in principle lead to inflation.     

Heterotic modular invariants and level-rank duality

New heterotic modular invariants are found using the level-rank duality of affine Kac-Moody algebras. They provide strong evidence for the consistency of an infinite list of heterotic Wess-Zumino-Witten (WZW) conformal field theories. We call the basic construction the dual-flip, since it flips chirality (exchanges left and right movers) and takes the level-rank dual. We compare the dual-flip to the method of conformal subalgebras, another way of constructing heterotic invariants. To do so, new level-one heterotic invariants are first bound; the complete list of a specified subclass of these is obtained. We also prove (under a mild hypothesis) an old conjecture concerning exceptional A_r,k invariants and level-rank duality.     

(MS)SM‐like models on smooth Calabi‐Yau manifolds from all three heterotic string theories

We perform model searches on smooth Calabi‐Yau compactifications for both the supersymmetric E₈ × E₈ and SO(32) as well as for the non‐supersymmetric SO(16) × SO(16) heterotic strings simultaneously. We consider line bundle backgrounds on both favorable CICYs with relatively small h₁₁ and the Schoen manifold. Using Gram matrices we systematically analyze the combined consequences of the Bianchi identities and the tree‐level Donaldson‐Uhlenbeck‐Yau equations inside the Kähler cone. In order to evaluate the model building potential of the three heterotic theories on the various geometries, we perform computer‐aided scans. We have generated a large number of GUT‐like models (up to over a few hundred thousand on the various geometries for the three heterotic theories) which become (MS)SM‐like upon using a freely acting Wilson line. For all three heterotic theories we present tables and figures summarizing the potentially phenomenologically interesting models which were obtained during our model scans.     

Fermion mass relations from a superstring inspired model

It is assumed that theE ₈ gauge group of theE ₈×E ₈ heterotic superstring can be broken intoSO(10). A model to give the mass relationm _u /m _d =m _c /m _s =m _t /m _b is presented and Kobayashi-Maskawa mixing is discussed.     

Superstring effects on D=4, N=1 supergravity

We give a lagrangian and supersymmetry transformation rules for the four-dimensional N=1 supergravity sector of superstring theories with their O(α′) corrections, obtained by the dimensional reduction á la Witten of the effective action of the ten-dimensional heterotic superstring. We also give general forms of O(α′ ″) corrections to supersymmetry transformation rules which arise through an axial vector superfield. Since our system is based on the ten-dimensional superstring without any auxiliary fields, our four-dimensional N=1 supergravity is free of auxiliary fields. Our point-field theory lagrangian is supposed to describe the mass-less fields in the untwisted sector of the ten-dimensional heterotic superstring propagating on orbifolds.     

New D = 10, N = 1 superspace supergravity and local symmetries of superstrings

The superspace formulation of new D = 10, N = 1 supergravity is developed. It is shown that the background superspace of the new theory can be coupled to a test superstring in such a way that the local symmetries of the superstring are intact. This formulation necessarily makes use of the Vainberg construction so the action is analogous to the effective action for QCD with the WZW term. The results suggest that the ambiguity between the massless two-form and six-form in the SO(32) or E₈ × E₈ superstring theories can only be resolved by a gauge invariant, Lorentz-covariant formulation of superstring field theory.     

The KN algebras and the geometrical quantization of heterotic strings

By means of the KN algebra, the Virasoro and Kac-Moody superalgebras are extended on a genus-g Riemann surface. These are realized in the framework of heterotic superstring with the WZ term coupling the fiber bundle. Then we construct the corresponding BRST operators, which provide the critical dimension.     

There is No “Theory of Everything” Inside E8

We analyze certain subgroups of real and complex forms of the Lie group E₈, and deduce that any “Theory of Everything” obtained by embedding the gauge groups of gravity and the Standard Model into a real or complex form of E₈ lacks certain representation-theoretic properties required by physical reality. The arguments themselves amount to representation theory of Lie algebras in the spirit of Dynkin’s classic papers and are written for mathematicians.     

Phenomenology of superstring theories with SO(10) unification

The phenomenology of superstring theories in which the gauge symmetry after compactification is SO(10) × E′₈, instead of E₆ × E′₈, is discussed. In particular, the generation of an intermediate scale, the radiative breaking of electroweak symmetry, and the supersymmetric particle spectrum are investigated.     

Higgs boson production at CLIC in SUSY models with hierarchy of the vacuum expectation values

Many theoretical schemes predict the existence of unconventional quarks and leptons not fitting the standard pattern of fermion families. We consider two possible kinds of non-standard fermions, mirror fermions and exceptional fermions. Mirror fermions arise in a variety of models ranging from family unification to extended supersymmetry and Kaluza-Klein theories; exceptional fermions come along with the groupE ₆ which is believed to be the low energy gauge symmetry of the superstring theory. We discuss some physical properties of these non-standard particles relevant for the LEP     

Heterotic string theory: (II). The interacting heterotic string

The theory of interacting heterotic strings is presented. Vertex operators are derived in both the bosonic and fermionic formulations of the theory and are shown to be consistent with gauge invariance, Lorentz invariance, and supersymmetry. Three- and four-point amplitudes for the scattering of massless string states are calculated and used to derive the low-energy field theory limit of the heterotic string. Divergences in string theories are discussed and it is shown that one-loop heterotic string amplitudes are finite and modular invariant only for gauge group E₈×E₈ or spin (32)/Z₂.     

A Geometric Construction of the Exceptional Lie Algebras <Emphasis Type="Italic">F</Emphasis><Subscript>4</Subscript> and <Emphasis Type="Italic">E</Emphasis><Subscript>8</Subscript>

We present a geometric construction of the exceptional Lie algebras F ₄ and E ₈ starting from the round spheres S ⁸ and S ¹⁵, respectively, inspired by the construction of the Killing superalgebra of a supersymmetric supergravity background.     

Three graded exceptional algebras and symmetric spaces

The exceptional algebras of typeE ₇ are studied from the point of view of their three graded structure. The connection between three-grading and the Jordan Pair structure of such Lie algebras is analyzed. The Jordan Pair content is in turn related to the symmetric spaces and . Coset spaces of this type have been recently suggested as possible scalar manifolds in supergravity. We develop a way of representingE ₇ in a matrix form, which makes the Jordan Pair content of theE ₇ real and complex forms quite transparent and shows whether such forms admit a three graded structure.     

N=1 supersymmetric truncations and the superstring low-energy effective theory

The question of discarding heavy fields in N=1 supersymmetric theories is analyzed. The analysis is applied to the compactification of the E₈ × E₈ superstring.