How effective is the weak mixing angle?

The usefulness of an effective weak mixing angle to parameterise the electroweak couplings of quarks and leptons measured at LEP is discussed. After a review of the theoretical formalism used to handle the electroweak radiative corrections to LEP processes, some suggestions for procedures to be used to extract the mixing angle are given and the various definitions of the effective weak mixing angle used by the experiments are examined. This is followed by an attempt to extract a coherent set of mixing angle values from the four experiments with the published 1989/90 (and some 1991) measurements of the Z⁰ line-shapes, asymmetries and polarisation. These results are updated with preliminary results from the 1991 data presented at the XXVI International Conference on High Energy Physics, in Dallas, USA, in August 1992, including the preliminary measurement ofA _LR at the SLC. The average value found for the effective weak mixing angle, defined for leptons, is sin² _eff ^lept =02322±0.0010. The error on sin² _eff ^lept can be further reduced by imposing the constraints between the parameters implicit in the MSM. With the additional constraint _s=0.123±0.006 imposed in the fit, the result is sin² _eff ^lept , where the central value is form _H =300 GeV, and the second error is the variation ifm _H is changed to 50 GeV (lower error) and 1000 GeV (upper error). Within the MSM, sin² _lept ^eff is directly related to the top-quark mass, and the corresponding value ism _t =153 _–25–23 ⁺²²⁺¹⁹ GeV, where the errors have the same meaning as those for sin² _eff ^lept . Finally, the prospects for improved precision are discussed.     

Warped string compactification via singular Calabi–Yau conformal field theory

We construct spacetime supersymmetric, modular invariant partition functions of strings on the conifold-type singularities which include contributions from the discrete-series representations of SL(2,R)$\mathit{SL}(2,\mathbf{R})$. The discrete spectrum is automatically consistent with the GSO projection in the continuous sector, and contains massless matter fields localized on a four-dimensional submanifold at the tip of a cigar. In particular, they are in the 27⊕1$27\oplus 1$ of E₆$E_6$ for the E₈×E₈$E_8\times E_8$ heterotic string. We speculate about a possible realization of local E₆$E_6$ GUT by using this framework.     

Does string theory predict an open universe?

It has been claimed that the string landscape predicts an open universe, with negative curvature. The prediction is a consequence of a large number of metastable string vacua, and the properties of the Coleman–De Luccia instanton which describes vacuum tunneling. We examine the robustness of this claim, which is of particular importance since it seems to be one of string theory's few claims to falsifiability. We find that, due to subleading tunneling processes, the prediction is sensitive to unknown properties of the landscape. Under plausible assumptions, universes like ours are as likely to be closed as open.     

Derivation of the polyakov string theory from planar φ3 field theory

A rigorous derivation is given of the Polyakov surface theory by summing over all planar Feynman graphs of a φ³ scalar field theory. It uses a discretization of surfaces through the triangulation induced by the dual graphs of the Feynman graphs. No approximation is made for the propagators and the metric is shown to be locally defined. The Green's functions of both theories are shown to coincide for any finite external momenta.     

On the “covariantized light-cone” string field theory II

We present a full non-linear BRS transformation which corresponds to one of the generators of the OSp(1, 1|2) or OSp(26, 2|2) algebra using the covariantly extended joining-splitting type interaction vertex functions in open string field theory.     

Precision measurement of the weak mixing angle in Møller scattering

We report on a precision measurement of the parity-violating asymmetry in fixed target electron-electron (M?ller) scattering: A(PV) = [-131 +/- 14(stat) +/- 10(syst)] x 10(-9), leading to the determination of the weak mixing angle sin2(thetaW(eff) = 0.2397 +/- 0.0010(stat) +/- 0.0008(syst), evaluated at Q2 = 0.026 GeV2. Combining this result with the measurements of sin2(thetaW(eff) at the Z0 pole, the running of the weak mixing angle is observed with over 6sigma significance. The measurement sets constraints on new physics effects at the TeV scale.     

Flat coordinates of topological conformal field theory and solutions of the Gauss–Manin system

A luminescent trace has been observed in a ruby crystal (Al₂O₃: Cr³⁺) that rotates at a frequency of 2 to 200 Hz and is irradiated by 532-nm coherent electromagnetic radiation. A method has been proposed to determine the lifetime of the excited electronic state of chromium ions from the measurement of the length of an arc of the trajectory of a light spot on the surface of a rotating ruby single crystal. A “comet trace” formed at the passage of radiation through the rotating crystal near the absorption band of the material has been detected inside the ruby crystal. It has been shown that the theory based on the analysis of the motion of polaritons in the rotating reference frame is in satisfactory agreement with experimental results.     

The group of local biholomorphisms of ℂ1 and conformal field theory in the operator formalism

Motivated by the operator formulation of conformal field theory on Riemann surfaces, we study the properties of the infinite dimensional group of local biholomorphic transformations (conformal reparametrizations) of ¹ and develop elements of its representation theory.     

Geometric field theory and weak Euler–Lagrange equation for classical relativistic particle-field systems

A manifestly covariant, or geometric, field theory of relativistic classical particle-field systems is developed. The connection between the space-time symmetry and energy-momentum conservation laws of the system is established geometrically without splitting the space and time coordinates; i.e., space-time is treated as one entity without choosing a coordinate system. To achieve this goal, we need to overcome two difficulties. The first difficulty arises from the fact that the particles and the field reside on different manifolds. As a result, the geometric Lagrangian density of the system is a function of the 4-potential of the electromagnetic fields and also a functional of the particles’ world lines. The other difficulty associated with the geometric setting results from the mass-shell constraint. The standard Euler–Lagrange (EL) equation for a particle is generalized into the geometric EL equation when the mass-shell constraint is imposed. For the particle-field system, the geometric EL equation is further generalized into a weak geometric EL equation for particles. With the EL equation for the field and the geometric weak EL equation for particles, the symmetries and conservation laws can be established geometrically. A geometric expression for the particle energy-momentum tensor is derived for the first time, which recovers the non-geometric form in the literature for a chosen coordinate system.     

How can the neutrino interact with the electromagnetic field?

Maxwell electrodynamics in the fixed Minkowski space-time background can be described in an equivalent way in a curved Riemannian geometry that depends on the electromagnetic field and that we call the electromagnetic metric(e-metric for short). After showing such geometric equivalence we investigate the possibility that new processes dependent on the e-metric are allowed. In particular, for very high values of the field, a direct coupling of uncharged particles to the electromagnetic field may appear.     

Killing spinors for the bosonic string and Kaluza–Klein theory with scalar potentials

The paper consists mainly of two parts. In the first part, we obtain well-defined Killing spinor equations for the low-energy effective action of the bosonic string with the conformal anomaly term. We show that the conformal anomaly term is the only scalar potential that one can add into the action that is consistent with the Killing spinor equations. In the second part, we demonstrate that Kaluza–Klein theory can be gauged so that the Killing spinors are charged under the Kaluza–Klein vector. This gauging process generates a scalar potential with a maximum that gives rise to an AdS spacetime. We also construct solutions of these theories.     

Kaluza-Klein states versus winding states: can both be above the string scale?

Closed strings in extra compactified dimensions give rise to both Kaluza-Klein states and winding states. Since the masses of these states play a reciprocal role, it is often believed that either the lightest Kaluza-Klein states or the lightest winding states must be at or below the string scale. In this Letter, we demonstrate the contrary, showing that there exist toroidal compactifications for which all Kaluza-Klein states as well as all winding states are heavier than the string scale. Within the context of low-scale string theories, this implies that it may be possible to cross the string scale without detecting any states associated with spacetime compactification.     

Effective field theory of a topological insulator and the Foldy–Wouthuysen transformation

Employing the Foldy–Wouthuysen transformation, it is demonstrated straightforwardly that the first and second Chern numbers are equal to the coefficients of the 2+1 and 4+1 dimensional Chern–Simons actions which are generated by the massive Dirac fermions coupled to the Abelian gauge fields. A topological insulator model in 2+1 dimensions is discussed and by means of a dimensional reduction approach the 1+1 dimensional descendant of the 2+1 dimensional Chern–Simons theory is presented. Field strength of the Berry gauge field corresponding to the 4+1 dimensional Dirac theory is explicitly derived through the Foldy–Wouthuysen transformation. Acquainted with it, the second Chern numbers are calculated for specific choices of the integration domain. A method is proposed to obtain 3+1 and 2+1 dimensional descendants of the effective field theory of the 4+1 dimensional time reversal invariant topological insulator theory. Inspired by the spin Hall effect in graphene, a hypothetical model of the time reversal invariant spin Hall insulator in 3+1 dimensions is proposed.     

Renormalization of Möbius infinities and partition function representation for the string theory effective action

We show that subtraction of the Möbius group volume in the open string massless amplitudes can be realized as a renormalization of linear 2D ultraviolet divergences in the generating functional (“partition function”). This implies that the vector field effective action can be represented as a renormalized partition function (i.e. as a path integral of the “Wilson factor”). We check this by computing several leading terms in the non-abelian effective action.