Fermion spectra from superstrings

Some compactifications of the ten-dimensional anomaly-free E₈ × E₈ and SO(32) theories that correspond to superstrings are studied. Compactification is achieved by setting the classical gauge field equal to the spin connection. The resulting chiral fermion spectra are obtained for any six-dimensional manifold, under the condition Tr F² = 30 Tr R², plus a quantization condition for U(1) charges. For E₈ × E₈ these conditions lead to potentially realistic models for any irreducible six-dimensional manifold and any embedding of the holonomy group. Apart from a few more exotic examples, the four-dimensional models we obtain are more or less standard SU(5), SO(10), SU(4) × SU(2) × SU(2) or E₆ models.     

On the mass and mixings of the ZE

The experimental data on the neutral current couplings are used to derive lower bounds on the mass of Z_E, the extra neutral gauge boson appearing in the minimal ‘beyond the standard model’ scenario favoured in superstring compactifications. This is based on the gauge group SU(3)_c×SU(2)_L×U(1)_Y×U(1)_E. Taking sin²θ_w=0.229, m_W=80.76 GeV and m_Z=91.59 GeV it is found that the mixing angle θ between Z and Z_E must satisfy −0.136<sin θ<−0.007 corresponding to m_ZE>152 GeV or, assuming E₆ unification m_ZE>155 GeV.     

Cosmological constant in a model with superstring-inspired E 6 unification and shadow θ-particles

We have developed the concept of parallel existence of the ordinary (O-) and mirror (M-), or shadow (Sh-) worlds. In the first part of the paper we consider a mirror world with broken mirror parity and the breaking E ₆→SU(3)³ in both worlds. We show that in this case the evolutions of coupling constants in the O- and M-worlds are not identical, having different parameters for similar evolutions. E ₆ unification, inspired by superstring theory, restores the broken mirror parity at the scale ～10¹⁸ GeV. With the aim to explain the tiny cosmological constant, in the second part we consider the breakings: E ₆→SO(10)×U(1) _Z in the O-world, and E′₆→SU(6)′×SU(2)′ _θ in the Sh-world. We assume the existence of shadow θ-particles and the low-energy symmetry group SU(3)′ _C ×SU(2)′ _L ×SU(2)′ _θ ×U(1)′ _Y in the shadow world, instead of the Standard Model. The additional non-Abelian SU(2)′ _θ group with massless gauge fields, “thetons”, has a macroscopic confinement radius 1/Λ′ _θ . The assumption that Λ′ _θ ≈2.3?10^?3 eV explains the tiny cosmological constant given by recent astrophysical measurements. In this way the present work opens the possibility to specify a grand unification group, such as E ₆, from cosmology.     

On the sign of the n-p mass difference in gauge models

We examine the sign of the n-p mass difference in some gauge models based on the SU(2) × U(1) × U(1) or SU(2)_L × SU(2)_R × U(1) group, and show that a few specific elements of the neutral-vector-meson mass matrix can determine the sign of Δm|_n?p. We also present an SU(2) × U(1) × U(1) model which can give the correct Δm|_n?p.     

Flipped SO(10)

We constract an N = 1 supersymmetric SO(10) GUT broken down to SU(3)_c×SU(2)_L×U(1)_Y with an intermediate flipped SU(5)×U(1)_X gauge symmetry. A solution to the triplet-doublet mass-splitting problem is proposed in terms of a non-minimal missing-partner mechanism.     

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.     

Symmetry breaking in a supersymmetric model of strong and electroweak interactions

We describe a supersymmetric model of strong and electroweak interactions based on the gauge groupSU(3)×SU(2)×U(1)×?(1). We concentrate on the pattern of the spontaneous symmetry breaking by the tree level scalar potential. It is possible to break the?(1) factor at superlarge energies relative to the simultaneous breaking scale ofSU(2)×U(1) and supersymmetry. The model has?(1) anomalies. Attempts to make an anomaly-free model based on the groupE ₆ are described. We also comment on possible modifications of the?(1) anomaly problem due to gravitational effects.     

Pattern of E6 symmetry breaking in the superstring theory

A mechanism of symmetry breaking by the Wilson loop is discussed. In particular, we take the Wilson loop to break the E₆ symmetry of superstring theory down to SU(6)×U(1)_T3R and then to SU(3)_L×U(1)_Y in succession. By the fine tuning parameters we obtain sin²θ_W=0.215, the proton life time τ_p≈10³⁴yr and the two intermediate mass scales M_I≈10¹⁶⁻¹⁷ GeV and M_II≈10⁵⁻¹⁰ GeV.     

Bosonic construction of the Lie algebras of some non-compact groups appearing in supergravity theories and their oscillator-like unitary representations

We give a construction of the Lie algebras of the non-compact groups appearing in four dimensional supergravity theories in terms of boson operators. Our construction parallels very closely their emergence in supergravity and is an extension of the well-known construction of the Lie algebras of the non-compact groups $\text{SP}\text{(2n,}\text{R}$ and $\text{SO}\text{(2n)}{}^1$ from boson operators transforming like a fundamental representation of their maximal compact subgroup U(n). However this extension is non-trivial only for n?4 and stops at n = 8 leading to the Lei algebras of SU(4) × SU(1, 1), SU(1, 1), SU(5, 1), SO(12)¹ and E₇(7). We then give a general construction of an infinite class of unitary irreducible representations of the respective non-compact groups (except for E₇₍₇₎ and SO(12)¹ obtained from the extended construction). We illustrate our construction with the examples of SU(5, 1) and SO(12)¹.     

N = 3 and N = 1 supersymmetry in a new class of solutions for d = 11 supergravity

We present a new class of compactifying solutions for d = 11 supergravity. The internal 7-spaces are described by coset manifolds N^pqr of the form SU(3) × U(1)/U(1) × U(1). The three integers p, q, r characterize the embedding of the stability subgroup U(1) × U(1) in SU(3) × U(1).Their supersymmetry content is quite remarkable. For a particular choice of p, q, r the isometry of N^pqr is SU(3) × SU(2): in this case we find that N = 3 supersymmetry survives. For all the other values of p, q, r, supersymmetry is broken to N = 1, and the isometry group is SU(3) × U(1).We also find a class of solutions with internal photon curl F_αβγδ ≠ 0, breaking all supersymmetries.     

Nonabelian electric and magnetic flux in unified SU(5) gauge theory

We study the long-distance behaviour of pure unified SU(5) gauge theory in the limit when the electroweak subgroup is unbroken. We show that the symmetry breaking pattern SU(5)→SU(3)_c×SU(2)×U(1)_Y, with SU(3)_c and SU(2) ×U(1)_Y realized, respectively, in confining and coulombic phases, is a possible dynamical phase of the SU(5) theory. The proof relies on showing that the duality equation of 't Hooft, relating the electric and magnetic flux, is exactly satisfied for the above symmetry breaking pattern. The infrared structure of SU(5), broken down to SU(3)_c×SU(2)×U(1)_Y, is not self-dual.     

SU(3)×SU(2)×U(1) next-to-leading corrections for proton decay in the SU(5) model

We compute in the standard model of SU(3)^c×(SU(2)×U(1)) with massless quarks and leptons the two-loop anomalous dimensions of the four-fermion operators relevant to proton decay in process involving (u, d, e, ν_e). The calculation is carried out by the use of dimensional reduction, a variant of dimensional regularization. Our aim is to give a complete calculation within the SU(5) GUT model of the next-to-leading enhancement-suppression factor for nucleon decay due to renormalization effects arising from hard gluons, W's and B's in process which involve (u, d, e, ν_e). It turns out that the result is sensitive to the ratios x_(i) = M_{H (i)}/M_X where M_H(i) are the masses of the twelve superheavy Higgs scalars in the $\text{24}$ multiplet which breaks SU(5) → SU(3)×SU(2)×U(1).     

Neutral-current constraints on gauge models of weak and electromagnetic interactions

Sehgal and Hung and Sakurai have recently argued that neutrino-hadron neutral-current couplings must lie in one of two allowed regions in coupling-parameter space. We study this conjecture using realistic BNL ν_μ and ν&#x0304;_μ spectra in the elastic ν_μp (ν&#x0304;_μp) calculations and also study constraints imposed by theq²-distributions. On comparing to gauge models, we find that the Weinberg-Salam and SU(2)_L×SU(2)_R×U(1) models fall within one allowed region, while a vectorlike SU(3)×U(1) model and a hybrid SU(2)×U(1) model with a (u, b)_R doublet fall in the other region.     

Prospects for superstring models with two vacuum expectation values for standard model singlets

The spontaneous breaking of rank-six intermediate groups to the standard model in superstring phenomenology is examined. It requires the existence of two vacuum expectation values, one for each standard model singlet in the 27 chiral representation of E₆. We use a simplified model based on the group SU(3)_c×SU(2)_L×SU(2)_R×U(1)_L×U(1)_R. It is found that the well-known phenomenological constraints such as proton decay, vanishing neutrino masses and flavour-changing neutral currents allow for the possibility of sizeable Yukawa couplings for the two standard model singlets which can originate low energy negative masses. The proof of this radiative breaking relies, however, on several parameters whose magnitude is unpredicted, but is facilitated if the mass of the exotic quark is large (∼300 GeV).     

Radiative corrections to quark-lepton mass matrices in superstring-inspired models

We examine if quark-lepton mass matrices are modified by generation changing currents in superstring-inspired models. It is shown that sufficiently large corrections to the quark mass matrices can be derived in an SU(3)_C × SU(2)_L × SU(2)_R × U(1)_L × U(1)_R model with δ ⩾ 2 and an SU(3)_C × SU(2)_L × U(1)_L × U(1)_R model. Consistency with other experiments are investigated by means of renormalization group equations.     

Z′ in the 3-3-1 model

Phenomenological implications of the Z′ in SU(3) × SU(3) × U(1) extension of the standard model are studied. We find that the current experimental value of R_b puts severe constraints on the Z′ mass in this model. The model improves slightly the fit for large E_T jet cross section observed by CDF.     

Composite symmetries and sub-constituent models

Assuming the internal A-spin, B-spin and C-spin of particles from basic symmetry SO(4), the color SU(3), horizontal SU(3)', electroweak SU(2)'_w×U(1) and other higher composite symmetries are derived.     

Quark-lepton symmetry and B − L as the U(1) generator of the electroweak symmetry group

We seek an interpretation of the U(1) part of the electroweak symmetry group in terms of the quantum number B ? L. We show that the electroweak symmetry group, for which U(1) can be interpreted as a local B ? L symmetry, is the left-right symmetry group SU(2)_L × SU(2)_R × U(1)_L+R. The equating of U_L+R(1) to U_B?L(1) should lead to physical consequences which are not shared by standard gauge theory. B ? L may also help to explain the inversion of quark and lepton mass spectra.     

Operator analysis of proton decay in an SU(7) gut

An SU(7) model, with a surviving low-energy SU(4) × SU(3) × U(1) gauge symmetry, may reduce the number of low-energy effective four-fermion baryon number violating interactions from six to two. A simple argument, applicable to general SU(N), shows that the terms allowed by SU(4) × SU(3) × U(1) are the same as those allowed by SU(7).     

The link between the emergence of the GIM mechanism and the nature of the neutral-current parity violation

We show that minimization of the Higgs potential within the unifying symmetry [SU(4)]⁴ together with the requirement that the GIM mechanism should emerge as a consequence of spontaneous breakdown of the symmetry on the flavor side leaves us with onechoice regarding the nature of parity violation: charged current as well as neutral current parity violations must have one and the same origin; if the former is à la SU(2)_L×U(1), so must be the latter. Furthermore, there appear to be only two possible alternative forms for the low-energy electroweak symmetry: (i) the familiar SU(2)_L×U(1), and (ii) and extended symmetry SU(2)_L×U(1)_L×?(1)_R differing from the former only in the parity-conserving neutral current sector.