Can the superstring inspire the standard model?

We discuss general features of models in which the E₈ × E′₈ heterotic superstring is compactified on a specific Calabi-Yau manifold. The gauge group of rank-6 in four dimensions is supposed to be broken down at an intermediate scale m_I to the standard model group SU(3)_C × SU(2)_L × U(1)_Y, as a result of two neutral scalar fields acquiring large vacuum expectations (vev's) in one of many flat directions of the effective potential. We find that it is difficult to generate such an intermediate scale by radiative symmetry breaking, whilst such models have prima facie problems with baryon decay mediated by massive particles and with non-perturbative behaviour of the gauge couplings, unless m_I ≳ 10¹⁶ GeV. Rapid baryon decay mediated by light particles, large neutrino masses, other Δ L ≠ 0 processes and flavour-changing neutral currents are generic features of these models. We illustrate these observations with explicit calculations in a number of different models given by vev's in different flat directions.     

Left-right symmetry breaking scale and supersymmetry in unified theories

We propose a class of supersymmetric grand unified models where parity and SU(2)_R breaking scales are widely separated and compatible with a low-lying mass for the right-handed gauge boson W_R. The intermediate symmetry SU(4)_c×SU(2)_L×SU(2)_R and Higgs content are uniquely fixed if m_WR < 10⁹ GeV. The unification scale lies within an order of magnitude below the Planck mass.     

Low-energy parity restoration and unification mass scale within maximal symmetries

We investigate the hierarchy of gauge boson masses in the maximal grand unified theory by studying the renormalization group equations for the running coupling constants associated with the symmetry breaking of SU(16)viaSU(12) _q×SU(4) _l×U(1) _|B|?|L| chain. Particular attention is given to the contribution of Higgs scalars to these equations. It is found that the intermediate mass scale M_L, associated with right-handed gauge bosons could be as low as 10 ³ GeV only for sin ²θ _w(M _L) as high as 0.265 with α _s(M _L)=0.13. In this chain of symmetry breaking, we have also examined the lowest unification mass that is allowed by the low-energy data for sin ²θ _w(M _L) and the assumed gauge hierarchy. This has been done in two cases; first for the case where SU(3) ^c is vectorial, second, for the case where SU(3) ^c is axial. In both cases the lowest unification mass scales were found to be 10 ¹³, 10 ¹¹, 10 ⁸ and 10 ⁷ GeV for sin ²θ _w(M _L) = 0.22, 0.24, 0.26,and0.265 respectively with α _s(M _L) = 0.13. The implication of these low unification masses on baryon non-conserving processes is also discussed.     

Very large intermediate scales in three-generation models

The issue of large intermediate scales is addressed in a class of three-generation models based on the best-known Calabi-Yau compactification of the heterotic string. The renormalisation group equations for this class are studied to determine the scale, μ≡M_I, at which the first “intermediate-scale” symmetry breaking occurs. Throughout most of the parameter space specifying the models, M_I is found to be extremely close to the compactification scale, M_c, as is required by phenomenology. This is due to the large number of fields which are massless below M_c. Depending on unknown normalisation factors, different directions of symmetry breaking are possible, including the one thus far preferred on phenomenological grounds.     

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.     

Chiral and deconfinement phase transitions in QED<Subscript>3</Subscript> with finite gauge boson mass

Based on the experimental observation that there is a coexisting region between the antiferromagnetic (AF) and d-wave superconducting (dSC) phases, the influences of gauge boson mass m _a on chiral symmetry restoration and deconfinement phase transitions in QED₃ are investigated simultaneously within a unified framework, i.e., Dyson–Schwinger equations. The results show that the chiral symmetry restoration phase transition in the presence of the gauge boson mass m _a is a typical second-order phase transition; the chiral symmetry restoration and deconfinement phase transitions are coincident; the critical number of fermion flavors N ^c _f decreases as the gauge boson mass m _a increases, which implies that there exists a boundary that separates the N ^c _f –m _a plane into chiral symmetry breaking/confinement region for (N ^c _f , m _a ) below the boundary and chiral symmetry restoration/deconfinement region for (N ^c _f , m _a ) above it.     

Gauge hierarchies and mass bounds

We consider the effects of weak symmetry breaking by radiative corrections in a scheme of gauge hierarchies. We obtain new mass bounds on heavy fermions and show how discovery of a Higgs boson may distinguish between two different approaches to hierarchial spontaneous gauge symmetry breakdown. If there are no intrinsic mass scales below ～10¹⁵ GeV then discovery of a Higgs boson at ～9 GeV implies the existence of heavy fermions.     

Radiatively induced spontaneous symmetry breaking and phase transitions in curved spacetime

Local gauge symmetries which are spontaneously broken in flat spacetime are shown to be restored for large spacetime curvatures. The case of symmetry breaking due to radiative quantum corrections in gauge theories with elementary scalar fields is considered explicitly. In spacetimes with a positive Ricci curvature scalar R and a cosmological event horizon, the critical curvature R_C is of O(m_H²) or O(m_W²), depending on whether the theory is formulated with conformal or minimal scalar fields. In Ricci flat spacetimes with a conventional event horizon the symmetry is expected to be restored when the temperature of the Hawking thermal radiation is of O(m_W). This phenomenon is described in detail, using functional integral methods and dimensional renormalization, for massless scalar electro-dynamics in de-Sitter spacetime. For conformal scalars, the symmetry restoring phase transition is first order, the critical curvature being R_C = 0.910 m_H². For minimal scalars, an anomalous, curvature dependent mass counterterm is required. The phase transition in this case is second order, and occurs at R_C = 83.57 m_W². Symmetry restoration at finite temperature in flat spacetime is considered in an appendix. The critical temperature at which a first-order phase transition occurs in the Weinberg-Salam model is found to be T_C = 0.329 m_W.     

Low-scale axion from large extra dimensions

The mass of the axion and its decay rate are known to depend only on the scale of Peccei–Quinn symmetry breaking, which is constrained by astrophysics and cosmology to be between 10⁹ and 10¹² GeV. We propose a new mechanism such that this effective scale is preserved and yet the fundamental breaking scale of U(1)_PQ is very small (a kind of inverse seesaw) in the context of large extra dimensions with an anomalous U(1) gauge symmetry in our brane. The production and decay of the associated Z_A gauge boson, which ends up as two gluons and two axions, is a distinct collider signature of this scenario.     

The structure of the gauge theory vacuum

The finite action Euclidean solutions of gauge theories are shown to indicate the existence of tunneling between topologically distinct vacuum configurations. Diagonalization of the Hamiltonian then leads to a continuum of vacua. The construction and properties of these vacua are analyzed. In non-abelian theories of the strong interactions one finds spontaneous symmetry breaking of axial baryon number without the generation of a Goldstone boson, a mechanism for chiral SU(N) symmetry breaking and a possible source of T violation.     

ΔB = −ΔL, neutron →e−π+, e−K+, μ−π+ and μ−K+ decay modes in SU(2)L × SU(2)R × SU(4)col or SO(10)

It is stressed that within the simplest model SU(4) of color, unifying quarks with leptons, where B  L is a gauge symmetry, a spontaneous breaking of this symmetry leads naturally to baryonlepton decays like n→e^?k⁺, e^?K⁺, μ^?π⁺, μ^?K⁺ [in constant to SU(5) where B  L is not gauged]. Our mechanism is crucially tied to the presence of the Higgs multiplet (2, 2, 15) of SU(2) × SU(2) × SU(4), which is needed to account for the observed quarklepton mass ratios.     

Chiral quarks,chiral limit,nonanalytic terms and baryon spectroscopy

It is shown that the principal pattern in baryon spectroscopy, which is associated with the flavor-spin hyperfine interactions, is due to the spontaneous breaking of chiral symmetry in QCD and persists in the chiral limit. All corrections, which are associated with a finite quark (Goldstone boson) mass are suppressed by the factor (μ/Λ_χ)² and higher.     

Pion properties at finite isospin chemical potential with isospin symmetry breaking

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 0 and μI 0 in the phase diagram, and different values for the charged pion mass(or decay constant) and neutral pion mass(or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses.     

Phenomenology ofSO(10) unified superstring models with intermediate scaleSU R(2) breaking

Electroweak breaking and the supersymmetric particle spectrum are discussed in superstring theories where the gauge group after compactification isSO(10)×E _s ^′ , and where the gauge symmetry after flux breaking isSU(3)×SU(2)×SU(2)×U(1).     

Black holes and large N species solution to the hierarchy problem

We provide the perturbative and non‐perturbative arguments showing that theories with large number of species of the quantum fields, imply an inevitable hierarchy between the masses of the species and the Planck scale, shedding a different light on the hierarchy problem. In particular, using the black hole physics, we prove that any consistent theory that includes N Z₂‐conserved species of the quantum fields of mass Λ, must have a value of the Planck mass, which in large N limit is given by M_P² \gsim N Λ². An useful byproduct of this proof is that any exactly conserved quantum charge, not associated with a long‐range classical field, must be defined maximum modulo N, with N \gsim (M_P/m)², where m is the mass of the unit charge. For example, a continuous global U(1) ‘baryon number’ symmetry, must be explicitly broken by gravity, at least down to a Z_N subgroup, with N \lsim (M_P/m_b)², where m_b is the baryon mass. The same constraint applies to any discrete gauge symmetry, as well as to other quantum‐mechanically‐detectable black hole charges that are associated with the massive quantum hair of the black hole. We show that the gravitationally‐coupled N‐species sector that solves the gauge hirearchy problem, should be probed by LHC.     

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.     

Spontaneous Symmetry Breaking in Presence of Electric and Magnetic Charges

Starting with the definition of quaternion gauge theory, we have undertaken the study of SU(2) _e ×SU(2) _m ×U(1) _e ×U(1) _m in terms of the simultaneous existence of electric and magnetic charges along with their Yang-Mills counterparts. As such, we have developed the gauge theory in terms of four coupling constants associated with four-gauge symmetry SU(2) _e ×SU(2) _m ×U(1) _e ×U(1) _m . Accordingly, we have made an attempt to obtain the abelian and non-Abelian gauge structures for the particles carrying simultaneously the electric and magnetic charges (namely dyons). Starting from the Lagrangian density of two SU(2)×U(1) gauge theories responsible for the existence of electric and magnetic charges, we have discussed the consistent theory of spontaneous symmetry breaking and Higgs mechanism in order to generate the masses. From the symmetry breaking, we have generated the two electromagnetic fields, the two massive vector W ^± and Z ⁰ bosons fields and the Higgs scalar fields.     

Baryon asymmetry,stable proton and n-n̄ oscillations in superstring models

The violation of baryon number is discussed in the context of a gauge model inspired by the E₈ × E₈ superstring theory. Lepton number is an accidental unbroken symmetry of the model. The proton, as a consequence, is essentially stable. The model yields an acceptable value (∼10⁻¹⁰) for the baryon asymmetry in the universe. It also predicts n-n̄ oscillations at a rate which may be amenable to ongoing experimental searches.     

Color Superconductivity in Supersymmetric Gauge Theories

The studies of superconductivity, dual superconductivity and color superconductivity have been undertaken through the breaking of supersymmetric gauge theories which automatically incorporate the condensation of monopoles and dyons leading to confining and superconducting phases. Constructing the total effective Lagrangian of N=2 SU(2) gauge theory with N _f =2 quark multiplets and quark chemical potential at classical and quantum levels, it has been demonstrated that baryon number symmetry is spontaneously broken as a consequence of the SU(2) strong gauge dynamics and the color superconductivity dynamically takes space at the non-SUSY vacuum.