Formulation of 11-dimensional supergravity in superspace

We formulate on-shell 11-dimensional supergravity in superspace and express its equations of motion in terms of purely geometrical quantities. All torsion and curvature components are solved in terms of a single superfield W_rstu, totally antisymmetric in its (flat vector) indices. The dimensional reduction of this formulation is expected to be related to the superspace formulation of N=8 extended supergravity and might explain the origin of the hidden (local) SU(8) and (global) E₇ symmetries present in this theory.     

Orbifold models and modular transformation

The orbifold models of the heterotic string are constructed on the quotient spaces of generalized tori by translational and rotational discrete symmetries. In order to obtain the consistent orbifold models, the conditions of the modular invariance are derived from a one-loop vacuum amplitude. Z₃ orbifold models satisfying such conditions are searched systematically. It is shown that there are infinite possible models with N = 2 supersymmetry. Among these models, two examples having E₆ and E₇ gauge groups are discussed. The orbifold models with N = 1 supersymmetry are also discussed in detail. It is shown that there are only five consistent models in the class of these models based on E₈ ⊗ E′₈ heterotic string in which the extra six-dimensional torus and the E₈ ⊗ E′₈ maximal torus are modded out by the rotational and the translational Z₃ symmetries respectively.     

Gauge group breaking by Wilson loops

We examine the breaking of gauge symmetries by Wilson loops in the Hosotani-Toms model by determining the background gauge field which minimises the one-loop effective potential for massless Dirac fermions. For anti-periodic fermions, all gauge groups remain unbroken. For periodic fermions, the groups G₂, F₄ and E₈ are broken by quantum corrections due to fermions in any irreducible representation, whereas E₆, E₇ and the classical groups only break if the fermion representation is in the same congruency class as the adjoint.     

Superconformal deformation,zero-norm states and space-time symmetries of the superstring theories

We present a formalism to study type II and Heterotic superstrings with massless and massive background fields in the bosonic sector. This formalism is appropriate to study high energy symmetries of the superstring. As an example, we explicitly relate all massless symmetries to the massless zero-norm states in the spectrum. This includes theE ₈ ?E ₈ andSO (32) gauge symmetries in the ten-dimensional Heterotic string. The first (evenG-parity) massive level is briefly described. We then argue the existence of new symmetries for the massive Yang-Mills-like gauge bosons and tensor fields at each fixed mass level. These enlarged stringy symmetries correspond to the decoupling of massive zero-norm states in the spectrum.     

Negative dimensions and E7 symmetry

The invariant length and volume which characterize the Lorentz group are extended to a quadratic and a quartic supersymmetric invariant. The symmetry group of the Grassmann sector can be SO(2), SU(2), SU(2) × SU(2) × SU(2), Sp(6), SU(6), SO(12) or E₇, which are also possible global symmetries of extended supergravities. Diophantine conditions which yield this classification follow from the corresponding conditions in d bosonic dimensions by the replacement d → ?d.     

Black holes and groups of type E 7

We report some results on the relation between extremal black holes in locally supersymmetric theories of gravity and groups of type E ₇, appearing as generalized electric-magnetic duality symmetries in such theories. Some basics on the covariant approach to the stratification of the relevant symplectic representation are reviewed, along with a connection between special K?hler geometry and a ??generalization?? of groups of type E ₇.     

On Hexagonal Structures in Higher Dimensional Theories

We analyze the geometrical background under which many Lie groups relevant to particle physics are endowed with a (possibly multiple) hexagonal structure. There are several groups appearing, either as special holonomy groups on the compactification process from higher dimensions, or as dynamical string gauge groups; this includes groups like SU(2), SU(3), G ₂, Spin(7), O(8) as well as E ₈ and O(32). We emphasize also the relation of these hexagonal structures with the octonion division algebra, as we expect as well eventually some role for octonions in the interpretation of symmetries in High Energy Physics.     

High-spin states in109Sn and their decay to the ground state

An extended level scheme of¹⁰⁹Sn is presented showing high-spin states up to E_x≈ 8 MeV and spins up toJπ=(41/2+). Their decay to the 5/2+ ground state has been observed identifying a 12.8 keV 7/2⁺ → 5/2⁺ transition. A half-life of T_1/2=7(1) ns has been measured for the 17/2⁺ state atE _x =2114 keV. The experimental data are compared with the predictions of shell-model calculations.     

Oscillator-like unitary representations of non-compact groups with a jordan structure and the non-compact groups of supergravity

We give a general bosonic construction of oscillator-like unitary irreducible representations (UIR) of non-compact groups whose coset spaces with respect to their maximal compact subgroups are Hermitian symmetric. With the exception of E₇₍₇₎, they include all the non-compact invariance groups of extended supergravity theories in four dimensions. These representations have the remarkable property that each UIR is uniquely determined by an irreducible representation of the maximal compact subgroup. We study the connection between our construction, the Hermitian symmetric spaces and the Tits-Koecher construction of the Lie algebras of corresponding groups. We then give the bosonic construction of the Lie algebra ofE ₇₍₇₎ in SU(8), SO(8) and U(7) bases and study its properties. Application of our method toE ₇₍₇₎ leads to reducible unitary representations.Dedicated to Feza Gürsey on the occasion of his 60th birthdayAlexander von Humboldt Fellow, on leave from Physics Dept., Bogaziçi University, Istanbul/Turkey: work supported in part by TBTAK, The National Science and Technology Council of Turkey     

The N = 4 supersymmetric E8 gauge theory and coset space dimensional reduction

Reasons are given to suggest that the N = 4 supersymmetric E₈ gauge theory be considered as a serious candidate for a physical theory. The symmetries of this theory are broken by a scheme based on coset space dimensional reduction. The resulting theory possesses four conventional generations of low-mass fermions together with their mirror particles.     

Hartree-Fock-calculation of parity-violation in cesium

We present a relativistic Hartree-Fock calculation of the parity violatingE1-matrixelement of the 6s?7s transition in cesium. Our resultE1= ?8.4·10^?12 iea ₀ for sin² θ _w = 0.22 is in good agreement with the experimental value. We also give a general discussion of the consequences of a violation of discrete symmetries for the solutions of the Dirac equation.     

Lagrangian constraints and gauge symmetries

Within the study of degenerate Lagrangian systems, a new intrinsic expression is proposed for the conditions under which the solutions of the dynamical equation i=dE do exist and are second-order vector fields. Such conditions are expressed in terms of generalized symmetries for the Lagrangian and constitute further progress in understanding the connection between constraints and gauge invariance within the Lagrange framework.     

On generalized Yang-Mills theories and extensions of the standard model in Clifford (tensorial) spaces

We construct the Clifford-space tensorial-gauge fields generalizations of Yang-Mills theories and the Standard Model that allows to predict the existence of new particles (bosons, fermions) and tensor-gauge fields of higher-spins in the 10 Tev regime. We proceed with a detailed discussion of the unique D₄ − D₅ − E₆ − E₇ − E₈ model of Smith based on the underlying Clifford algebraic structures in D = 8, and which furnishes all the properties of the Standard Model and Gravity in four-dimensions, at low energies. A generalization and extension of Smith’s model to the full Clifford-space is presented when we write explicitly all the terms of the extended Clifford-space Lagrangian. We conclude by explaining the relevance of multiple-foldings of D = 8 dimensions related to the modulo 8 periodicity of the real Cliford algebras and display the interplay among Clifford, Division, Jordan, and Exceptional algebras, within the context of D = 26, 27, 28 dimensions, corresponding to bosonic string, M and F theory, respectively, advanced earlier by Smith. To finalize we describe explicitly how the E₈ × E₈ Yang-Mills theory can be obtained from a Gauge Theory based on the Clifford (16) group.     

Representations of the Exceptional Lie Superalgebra E(3,6) II: Four Series of Degenerate Modules

Four ℤ₊-bigraded complexes with the action of the exceptional infinite-dimensional Lie superalgebra E(3,6) are constructed. We show that all the images and cokernels and all but three kernels of the differentials are irreducible E(3,6)-modules. This is based on the list of singular vectors and the calculation of homology of these complexes. As a result, we obtain an explicit construction of all degenerate irreducible E(3,6)-modules and compute their characters and sizes. Since the group of symmetries of the Standard Model SU(3) ×SU(2) ×U(1) (divided by a central subgroup of order six) is a maximal compact subgroup of the group of automorphisms of E(3,6), our results may have applications to particle physics. Received: 22 January 2001 / Accepted: 8 June 2001     

Properties of Generalized Univariate Hypergeometric Functions

Based on Spiridonov’s analysis of elliptic generalizations of the Gauss hypergeometric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions. In each case we derive the symmetries of the generalized hypergeometric function under the Weyl group of type E ₇ (elliptic, hyperbolic) and of type E ₆ (trigonometric) using the appropriate versions of the Nassrallah-Rahman beta integral, and we derive contiguous relations using fundamental addition formulas for theta and sine functions. The top level degenerations of the hyperbolic and trigonometric hypergeometric functions are identified with Ruijsenaars’ relativistic hypergeometric function and the Askey-Wilson function, respectively. We show that the degeneration process yields various new and known identities for hyperbolic and trigonometric special functions. We also describe an intimate connection between the hyperbolic and trigonometric theory, which yields an expression of the hyperbolic hypergeometric function as an explicit bilinear sum in trigonometric hypergeometric functions.     

E2 component in subcoulomb breakup of 8B

We calculate the angular distribution and total cross section of the ⁷Be fragment emitted in the break up reaction of ⁸B on ⁵⁸Ni and ²⁰⁸Pb targets at the subcoulomb beam energy of 25.8 MeV, within the non-relativistic theory of Coulomb excitation with proper three-body kinematics. The relative contributions of the E1, E2 and M1 multipolarities to the cross sections are determined. The E2 component makes up about 65% and 40% of the ⁷Be total cross section for the ⁵⁸Ni and ²⁰⁸Pb targets respectively. We find that the extraction of the astrophysical S-factor, S₁₇(0), for the ⁷Be(p,γ)⁸B reaction at solar energies from the measurements of the cross sections of the ⁷Be fragment in the Coulomb dissociation of ⁸B at sub-Coulomb energies is still not free from the uncertainties of the E2 component.     

Unification of families based on a coset space E7/SU(5) × SU(3) × U(1)

We show that the usual three families of quarks and leptons are identifiable with quasi Nambu-Goldstone fermions in a supersymmetric non-linear realization of E₇ corresponding to the Kähler manifold E₇/SU(5) × SU(3) × U(1). So the triplication of families suggests the underlying preon theory realizing the global E₇ linearly. Possible connections with N = 8 supergravity are also discussed.     

Interactions between carriers and LO phonons in bulk p-GaSb and p-InSb: Raman interference lineshapes

Coherent interaction between single-particle excitations of carriers located near Γ and large wavevector LO phonons results in a Fanotype Raman lineshape when the incident photon energy is resonant with the E₁ or E₁ + Δ₁ energy gaps of heavily doped p-GaSb and p-InSb. The present results are simpler to interpret than our previous data on lightly doped samples which involve interactions between carriers confined within the surface accumulation layer and extended bulk phonons.     

The Intermediate Vertex Subalgebras of the Lattice Vertex Operator Algebras

A notion of intermediate vertex subalgebras of lattice vertex operator algebras is introduced, as a generalization of the notion of principal subspaces. Bases and the graded dimensions of such subalgebras are given. As an application, it is shown that the characters of some modules of an intermediate vertex subalgebra between E ₇ and E ₈ lattice vertex operator algebras satisfy some modular differential equations. This result is an analogue of the result concerning the “hole” of the Deligne dimension formulas and the intermediate Lie algebra between the simple Lie algebras E ₇ and E ₈.     

N = 8 supergravity

The complete structure of N = 8 supergravity is presented with an optional local SO(8) invariance. The SO(8) gauge interactions break E₇ invariance, but leave the local SU(8) unaffected. Exploiting E₇ × SU(8) invariance and using explicit lowest order results, we first derive the complete action and transformation laws. Subsequently, we introduce local SO(8) invariance and prove the consistency of the theory. Possible implications of our results are discussed.