Anti-Su(5)

We discuss ordinary as well as supersymmetric SU(5) ×?(1) models in the hope of accomodating acceptable τ_p and sin²θ_W. The ordinary SU(5) ×?(1) model does not have the monopole. The supersymmetric SU(5) ×?(1) model can be unified in SO(10).     

A supersymmetric left-right confining model of the weak interactions

We extend the supersymmetric, confining theory of weak interactions to a left-right symmetric model. This model is based on the gauge group SU(M)_SC×SU(2)_R×SU(2)_L×SU(3)_c×U(1) and is more natural as far as supersymmetry breaking is concerned. Supersymmetry protects chiral symmetries from spontaneous breakdown and allows a solution to the strong CP problem. This model can accommodate at most three generations of quarks and leptons.     

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.     

Towards a finite N = 2 susy GUT

We consider finite, N = 2 supersymmetric GUTs based on gauge groups SU(n) and SO(n). As an example, we discuss a semirealistic model based on SO(12). We argue that in finite, N = 2 supersymmetric GUTs, gauge symmetry breaking should occur dynamically. We present a heuristic picture in which this is induced by soft, finiteness preserving SUSY breaking terms. The bound states formed cause a very rapid evolution of the SO(12) coupling constant and break SO(12) into SU(4)×SU(3)_C×U(1).     

High-colour and mass hierarchies

We present a model based on the gauge group G = G_HC × G_S × SU(2)_L × U(1), where the hypercolour gauge group G_HC is responsible for the dynamical breaking of the strong group G_S to SU(3)_C of QCD. Chiral symmetry breaking of high-colour representations produces dynamical breaking of the electroweak SU(2)_L × U(1) gauge group. Fermion masses and flavour mixing are dynamically generated from the condensations of high-colour representations. A phenomenological analysis of the model is also presented.     

Prospects for supersymmetric SO(10) models with an intermediate mass scale

We investigate possible patterns of SO(10) gauge symmetry breaking compatible with supersymmetry, limiting ourselves to the cases with one intermediate breaking scale. It is found that the one where a 54 representation breaks SO(10) into a Pati-Salam group SU(4)_C×SU(2)_L×SU(2)_R and the one where a 210 breaks it into SU(3)_C× U(1)_C×SU(2)_L×SU(2)_R are the most preferable patterns when supersymmetry is taken into account. Two models with the Pati-Salam intermediate symmetry are studied in more detail.     

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.     

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.     

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 ν̄_μ spectra in the elastic ν_μp (ν̄_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).     

Grand unified model with a stable proton and no axion problem

We present a grand unified model of the strong, electromagnetic and weak interactions based on a local SU(8)_L×SU(8)_R gauge theory which possesses a global U(8)_L × U(8)_R invariance. We break the symmetry down to the standard SU(3)_C × SU(2)_L × U(1) model, with the proton remaining stable and the left-handed neutrinos obliged to remain massless. A novel feature of our model is the simultaneous absence of both strong CP violations and of axions.     

Gravity-induced weak symmetry breaking and supergravity

We give here a review of the recent developments of grand unified theories based onN=1 supergravity. We start with a brief introduction of supersymmetry and supergravity multiplets, and then discuss the construction of an invariant Lagrangian. The phenomena of gravity-induced weak symmetry breaking via the super Higgs effect at the tree level, corresponding to the conventional SU(5) gauge group, are then considered. We then extend this idea to the larger group SO(10), showing two possible breaking chains given as (i) SO(10)×susy→SU(2) _L ×U(1) _R ×U(1) _B-L ×SU(3) _C (≡ G₂₁₁₃)×susy→U(1)_em×SU(3) _C (G _LE ) predicting a secondZ-boson having mass lower than 1 TeV, and (ii) SO(10)×susy→SU(2) _L ×SU(2) _R ×SU(4)→(≡G₂₂₄)×susy→ SU(2) _L ×U(1) _Y ×SU(3) _C (≡ G₂₁₃)×susy→U(1)_em×SU(3) _C . We also consider the radiative breaking of weak symmetry via renormalisation group effects, which predicts the top quark mass. Some experimental signatures of the supersymmetric particles are investigated and possible future outlook is discussed. Invited talk presented at the International Symposium on Theoretical Physics, Bangalore, November 1984.     

Sensitivity of low energy neutral current parameters to new mass scales withinSU(2)×SU(2)×U(1) andSO(10) unification

Sensitivity of low energy weak parameters to possible new mass scales is discussed withinSU(2) ×SU(2)×U(1) models andSO(10) unification. Accuracy better than 0.5% is needed for meaningful tests of the standard model in region up to 1 TeV and of theSU(5) prediction for sin²θ.     

On the structure of the low energy superpotential in superstring theory

We show that after the gauge symmetry breaking of the E₆ grand unified group to the H=SU(3)^c×SU(2)_L×U(1)_Y× U(1)_E subgroup by the Hosotany mechanism a number of additional Yukawa terms not present in a decomposition of 27×27×27 may appear in the low energy superpotential. Some of these terms cause a rapid proton decay.     

Spontaneous breaking of global baryon number symmetry

We study the possibility that theU(1) _B global symmetry associated with baryon number is spontaneously broken. We present realistic examples implemented in the context of a suitably extended standardSU(2) _L×U(1)×SU(3)_c model and of a composite model of quarks and leptons. The globalU(1) _B symmetry in both cases is spontaneously broken at a relatively low mass scale without any conflict with observations. The dominant baryon number nonconserving process in these models obeys the ΔB=2 selection rule.     

Chiral symmetry breaking and condensates in the rishon model

The rishon model is studied in the limit g_c → 0, α → 0 when its global flavour symmetry is SU(6) × SU(6) × U(1) analogous to six massless flavour QCD. Recently it was shown that the ad hoc breaking SU(6) × SU(6) → SU(3) × SU(3) allows the anomaly constraint to be satisfied. In this paper this is shown to be but one of several successful patterns of chiral symmetry breaking. The condensates required to perform these breakings are fully discussed. A plausibility argument based on single gauge boson exchange is presented which determines the condensate uniquely to be 〈(v_LV_L)³〉 corresponding to the original breaking above. The same argument applies to QCD, which is argued to differ in its chiral behaviour due to the large intrinsic masses of the quarks. The implications of the above condensate and pattern of chiral symmetry breaking for the rishon model include the prediction of integer charged colour octet fermions, a naive mass formula m_e = 2m_u ? m_d, new insight into the parity-violating condensate 〈(v_Lv_L)²(v_Rv_R)〉 and the prediction of 52 new pseudos whose masses are estimated.     

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.     

Grand unification with local supersymmetry

We study general conditions for obtaining spontaneous breaking of local supersymmetry in N = 1 supergravity coupled to supersymmetric matter. We consider in particular the coupling of N = 1 supergravity to grand unified theories like SU(5) and study the conditions which must be met in order to obtain a realistic model. Specific models are built in which local supersymmetry is broken at a scale √M_Wm_p ～ 10¹⁰ GeV. This breaking of supersymmetry is only detected at low energies through soft terms breaking explicitly the global supersymmetry. These soft terms (scalar masses, gaugino masses and trilinear scalar couplings) are renormalized at low energies according to the renormalization group. The (mass)² of the Higgs doublet evolve towards negative values at low energies giving rise to SU(2) × U(1) breaking as a radiative effect of local supersymmetry breaking. We finally point out the possible relevance of non-renormalizable superpotentials for the problem of fermion masses.     

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.     

Primordial two-component maximally symmetric inflation

We propose a two-component inflation model, based on maximally symmetric supergravity, where the scales of reheating and the inflation potential at the origin are decoupled. This is possible because of the second-order phase transition from SU(5) to SU(3)×SU(2)×U(1) that takes place when φ?φ_c<φ₀, when φ₀?O(M) is the value of the inflation at the global minimum, and leads to a reheating temperature T_R?(10¹⁵–10¹⁶) GeV. This makes it possible to generate baryon asymmetry in the conventional way without any conflict with experimental data on proton lifetime. The mass of the gravitinos is $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{?10}{}^{12}\text{GeV}$, thus avoiding the gravitino problem. Monopoles are diluted by residual inflation in the broken phase below the cosmological bounds if φ_c?0.3M.