Breaking E6 via trinification in F‐theory

We consider E₆ GUT model in F‐theory approach where E₆ is broken via trinification to the Standard Model (SM) gauge group using non‐abelian fluxes. Including the gauge singlet wave function we found hierarchically small values for both the μ term as well as Dirac neutrino masses.     

On the boundary-value problems and the validity of the Post constraint in modern electromagnetism

We recall that the theory of electromagnetism consists of three building blocks: (a) the inhomogeneous Maxwell equations for the electric and magnetic excitations (D,H) (which reflects charge conservation), (b) the homogeneous Maxwell equations for the electric and magnetic field strengths (E,B) (which reflects flux conservation), and (c) the constitutive relation between (D,H) and (E,B). In the recent paper [A. Lakhtakia, Boundary-value problems and the validity of the Post constraint in modern electromagnetism, Optik 117 (2006) 188-192], Lakhtakia proposed to change the standard boundary conditions in electrodynamics in order to exclude certain constitutive parameters. We show that this is inadmissible both from the macroscopic and the microscopic points of view.     

E 6,7,8 magnetized extra-dimensional models

We study 10D super Yang–Mills theory with the gauge groups E ₆, E ₇ and E ₈. We consider the torus/orbifold compactification with magnetic fluxes and Wilson lines. They lead to 4D interesting models with three families of quarks and leptons, whose profiles in extra dimensions are quasi-localized because of magnetic fluxes.     

The ratio of the magnetic to the electric proton form factors in Quantum Chromodynamics

We propose a two parameter expression for the high momentum transfer behaviour of the ratio of proton form factors G_M(Q²)/Q_E(Q²) based on perturbation theory calculations in Quantum Chromodynamics. A fit to the present experimental data and its consistency with a previous fit to the high Q² behaviour of the Dirac form factor [1] is also discussed.     

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.     

Type IIB Green-Schwarz superstrings in AdS 5 × S 5 from the supercoset approach

We consider superstrings moving in the AdS ₅ × S ⁵ space-time and find their Green-Schwarz action using the supercoset approach based on the supergroup PSU(2, 2|4). We describe several parametrizations of the relevant supercoset and present the action in different κ-symmetry gauges. In particular, we discuss a gauge where all the fermionic coordinates corresponding to the conformal (S) supercharges are gauged away and also a light-cone type gauge where half of the Q and S supercoordinates are gauged away. The resulting action contains terms that are quadratic and quartic in fermions. In the flat-space limit, it reduces to the standard light-cone Green-Schwarz action. We comment on the possibility of fixing the bosonic light-cone gauge and of reformulating the action in terms of two-dimensional Dirac spinors.     

Chiral anomalies and constraints on the gauge group in higher-dimensional supersymmetric Yang-Mills theories

Chiral anomalies for gauge theories in any even dimension are computed and the results applied to supersymmetric theories in D = 6, 8 and 10. For D = 8 there is an anomalous chiral U(1) invariance, just as in D = 4, except for certain special groups. For D = 6 and D = 10 there is no anomalous chiral U(1) symmetry, but the gauge current is anomalous except for certain “anomaly-free” groups. For D = 6 the group is thereby constrained to be one of {SU(2), SU(3), exceptional}, while for D = 10 it is constrained to be one of {SU(n) n ≤ 5, USp(4), E₈}.     

E6 breaking in (0,2) string compactifications

The existence of a duality in (0,2) compactifications which is present at the Landau-Ginzburg point allows us to connect in a smooth manner theories with different gauge groups with the same base manifold and same number of effective generations. As we move along the Kahler moduli space of the theories with E₆ gauge group, the VEV's of SO(10) singlets are turned on and break the gauge group to SO(10). We generalize this result and break E₆ down to SU(5).     

D and D meson production near 4 GeV in e+e− annihilation

We have studied momentum spectra for D⁰ ($\text{D}$⁰) and D^± mesons produced near 4 GeV in e⁺e^? annihilation and find that production is dominated by two-body reactions involving D and D¹ states where the D¹ (charged and neutral) have masses near 2.01 GeV/c². A detailed study of D momentum spectra near E_cm = 4.028 GeV allows determination of masses and branching ratios of D and D¹ states. Lastly we find that events containing a D⁰ meson conserve strangeness, thus establishing upper limits on D⁰-$\text{D}$⁰ mixing and on the effects of charm changing neutral currents.     

Quantum and Classical Thermal Correlations in the XXZ Spin-1/2 Chain

We compute the quantum dissonance Q (non-entangled quantum correlation), entanglement E, quantum discord D (total quantum correlation) and classical correlation C in the eight-qubit XXZ spin-1/2 chain at finite temperatures. We find that not only D but also Q and C can clearly detect the critical points associated to quantum phase transitions for this model at finite temperatures. Moreover, Q can detect the special points of the system where the entanglement just appears or completely vanishes. Finally, we obtain two simple dominance relations: C≥E and D≥E+Q. Except these there are no other simple ordering relations in this model.     

D3+D6 solution and D4+D6 solution

We make the supergravity solutions describing the branes (D3 branes and D4 branes) localized within the D6 branes in the near core region of D6 brane. From the D=11 solutions (M3 branes and M4 branes with the Z_N identifications in the transverse space) we obtain the D=10 supergravity solutions of D3 branes localized within D6 branes and D4 branes localized within D6 branes by reducing the dimension down to D=10 along a circular direction of S³ part of the transverse space. M3 brane solution leads to D=10 background representing D3 branes localized on D6 branes in the region close to the D6 branes core. M4 branes lead to the D4 branes localized on D6 branes in the region close to the D6 brane core.     

Strings and D=4

It is argued that the unique infrared behaviour of non-abelian gauge couplings in four dimensions could be responsible, in closed super- (or heterotic) string theory, for dynamical supersymmetry breaking and for compactification to D=4 with string-scale compactified radii.     

Invariants for E0-Semigroups on II1 Factors

We introduce four new cocycle conjugacy invariants for E ₀-semigroups on II ₁ factors: a coupling index, a dimension for the gauge group, a super product system and a C*-semiflow. Using noncommutative Itô integrals we show that the dimension of the gauge group can be computed from the structure of the additive cocycles. We do this for the Clifford flows and even Clifford flows on the hyperfinite II ₁ factor, and for the free flows on the free group factor ${L(F_\infty)}$ L ( F ∞ ) . In all cases the index is 0, which implies they have trivial gauge groups. We compute the super product systems for these families and, using this, we show they have trivial coupling index. Finally, using the C*-semiflow and the boundary representation of Powers and Alevras, we show that the families of Clifford flows and even Clifford flows contain infinitely many mutually non-cocycle-conjugate E ₀-semigroups.     

Index of a family of Dirac operators on loop space

We use methods of constructive field theory to generalize index theory to an infinite-dimensional setting. We study a family of Dirac operatorsQ on loop space. These operators arise in the context of supersymmetric nonlinear quantum field models with HamiltoniansH=Q ². In these modelsQ is self-adjoint and Fredholm. A natural grading operator Γ exists such that ΓQ+QΓ=0. We studyQ ₊=P _? QP ₊, whereP _±=1/2 (1±Γ) are the orthogonal projections onto the eigenspaces of Γ. We calculate the indexi(Q ₊) for Wess-Zumino models defined by a superpotentialV(ω). HereV is a polynomial of degreen≧2. We establish thati(Q ₊)=n?1=degδV. In particular, the field theory models have unbroken supersymmetry, and (forn≧3) they have degenerate vacua. We believe that this is the first index theorem for a Dirac operator that couples infinitely many degrees of freedom.     

Measurement of the fine structure separation in the 42 D term of lithium by the method of electric field induced level anti-crossing

An electric field is employed to convert lithium 4² D Zeeman level crossings into anti-crossings. The lithium atoms are excited by electron impact. The anti-crossings are detected by the change in polarization of the light emitted in the 4² D-2² P transition. From the corresponding values of the magnetic field, we obtain 400 (10) MHz for the zero field fine structure energy separationE(4² D _5/2)-E(4² D _3/2).     

On the Dirac eigenvalues as observables of the on-shell <Emphasis Type="Italic">N</Emphasis> = 2<Emphasis Type="Italic">D</Emphasis> = 4 Euclidean supergravity

We generalize previous works on the Dirac eigenvalues as dynamical variables of Euclidean gravity and N =1 D = 4 supergravity to on-shell N = 2 D = 4 Euclidean supergravity. The covariant phase space of the theory is defined as the space of the solutions of the equations of motion modulo the on-shell gauge transformations. In this space we define the Poisson brackets and compute their value for the Dirac eigenvalues.      

On supersymmetry breaking in superstring theories

We show that non-zero gaugino condensates of several non-abelian gauge groups G₁⊗…⊗G_k∃E₈ in low-energy d=4 superstring E₈⊗E₆ gauge theory can lead to the exponentially small (compared to the Planck scale) supersymmetry breaking scale. The Hosotani mechanism can provide the E₈→G₁⊗…⊗G_k breaking.     

Spontaneous compactification and CPN: SU(3) × SU(2) × U(1), sin2θW, g3/g2 and SU(3)-triplet chiral fermions in four dimensions

We examine the compactification of D=4+2N, Einstein-Maxwell-Dirac theory. It is shown that the manifold CP_N × M₄ is a solution of the equations of motion. The structure of the fermions, gauge bosons and their couplings in the four-dimensional effective theory is investigated. The scale of CP_N is quantized by a generalized Dirac condition. When the results are applied to the solution with internal space CP₁×CP₂, the weak mixing angle and the ratio of the couplings of SU(3) (g₃) and SU(2) (g₂) are defined by two integers and a hypercharge. An SU(3)-triplet chiral fermion can appear in four-dimensional effective theory.     

A model for FL and R = FL/FT at low x and low Q2

A model for the longitudinal structure function F_L at low x and low Q² is presented, which includes the kinematical constraint F_L ～ Q⁴ as Q² → 0. It is based on the photon-gluon fusion mechanism suitably extrapolated to the region of low Q². The contribution of quarks having limited transverse momentum is treated phenomenologically assuming that it is described by the soft pomeron exchange mechanism. The ratio R = F_L/(F₂ ? F_L), with the F₂ appropriately extrapolated to the region of low Q², is also discussed.     

Dimensional regularization of gauge theories in spherical spacetime: Free field trace anomalies

The O(n + 1) covariant formulation of massless quantum electrodynamics in spherical spacetime is further developed to allow a calculation of the energy-momentum tensor trace anomalies for the free Dirac, electromagnetic, and SU(2) gauge fields. The principal technical development is the construction of the Faddeev-Popov ghosts for electrodynamics and SU(2) Yang-Mills theory. This construction is unconventional first in that the gauge fixing term in the Lagrangian is not a perfect square, and second because it is necessary to remove radial as well as gauge degrees of freedom from the measure of the functional integral. The ghost fields are shown to satisfy a minimal scalar field equation. The free field effective action is found to be divergent in four dimensions, and is renormalized by the inclusion in the Lagrangian of a counterterm local in the gravitational fields. The energy-momentum tensor calculated from this renormalized effective action is shown to have a trace anomaly.