Bounds on the anomalous magnetic moment and the electric dipole moment of the $\tau$ neutrino are calculated through the reaction $e^{+}{e}^{-}\to \nu \overline{\nu }\gamma$ at the $Z_1$ pole, and in the framework of a left-right symmetric model. The results are based on the recent data reported by the L3 Collaboration at CERN $e^{+}{e}^{-}$ collider LEP. We find that the bounds are almost independent of the mixing angle $\phi$ of the model in the allowed experimental range for this parameter. In addition, the analytical and numerical results for the cross section have never been reported in the literature before.

We argue that the chiral anomaly of $\mathcal{N}=1\mathrm{}$ super Yang-Mills theory admits a dual description as spontaneous symmetry breaking in M theory on $G_2$ holonomy manifolds. We identify an angle of the $G_2$ background dual to the anomalous ${U\left(1\right)\mathrm{}}_R$ current in field theory. This angle is not an isometry of the metric and we therefore develop a theory of “massive isometry” to describe fluctuations about such angles. Another example of a massive isometry occurs in the Atiyah-Hitchin metric.

$\mathcal{N}=2\mathrm{}$ gauge theories broken down to $\mathcal{N}=1\mathrm{}$ by a tree level superpotential are necessarily at the points in the moduli space where the Seiberg-Witten curve factorizes. We find an exact solution to the factorization problem of Seiberg-Witten curves associated with the breaking of the ${U(N}_c)$ gauge group down to two factors ${U(N}_1)\times {U(N}_2).\mathrm{}$ The result is a function of three discrete parameters and two continuous ones. We find discrete identifications between various sets of parameters and comment on their relation to the global structure of $\mathcal{N}=1\mathrm{}$ vacua and their various possible dual descriptions. In an appendix we show directly that the integrality of the periods leads to factorization.

We elaborate a full superfield description of the interacting system of dynamical $D=4,$ $N=1\mathrm{}$ supergravity and a dynamical superstring. As far as a minimal formulation of simple supergravity is used, such a system should contain as well the tensor (real linear) multiplet which describes the dilaton and the two-superform gauge field whose pullback provides the Wess-Zumino term for the superstring. The superfield action is given by the sum of the Wess-Zumino action for $D=4,$ $N=1\mathrm{}$ superfield supergravity, the superfield action for the tensor multiplet in curved superspace, and the Green-Schwarz superstring action. The latter includes the coupling to the tensor multiplet both in the Nambu-Goto and in the Wess-Zumino terms. We derive superfield equations of motion including, besides the superfield supergravity equations with the source, the source-full superfield equations for the linear multiplet. The superstring equations keep the same form as for the superstring in supergravity and 2-superform background. The analysis of gauge symmetries shows that the superfield description of the interacting system is gauge equivalent to the dynamical system described by the sum of the spacetime, component action for supergravity interacting with the tensor multiplet, and of the purely bosonic string action.

We reproduce Chang’s duality condition in a regularized $\mathrm{}(1+1)\mathrm{}$-dimensional ${\phi }^4$ theory quantized on the light front. The regularization involves higher derivatives in the Lagrangian, renders the model finite in the ultraviolet, and does not require the introduction of a finite size of the system. It is demonstrated that light-front quantization is a natural way to treat systems with higher derivatives. The phase transition is related to the presence of tachyons in the regularized theory. The prospects for computing the critical coupling in this formulation are briefly discussed.

We examine the singularity resolution issue in quantum gravity by studying a new quantization of standard Friedmann-Robertson-Walker geometrodynamics. The quantization procedure is inspired by the loop quantum gravity program, and is based on an alternative to the Schrödinger representation normally used in metric variable quantum cosmology. We show that in this representation for quantum geometrodynamics there exists a densely defined inverse scale factor operator, and that the Hamiltonian constraint acts as a difference operator on the basis states. We find that the cosmological singularity is avoided in the quantum dynamics. We discuss these results with a view to identifying the criteria that constitute “singularity resolution” in quantum gravity.

We evaluate the massless Dirac quasinormal mode frequencies in the Reissner-Nordström black hole spacetime using the Pöshl-Teller potential approximation method. The result shows that positive-charged Dirac field perturbations decay faster than negative-charged field perturbations around positive-charged black holes. A properly charged black hole makes the Dirac field perturbation decay more quickly. The behavior of the Dirac field in the stage of quasinormal ringing is very similar to that of a complex scalar field.

Many candidate fundamental theories contain scalar fields that can acquire spacetime-varying expectation values in a cosmological context. Such scalars typically obey Lorentz-violating effective dispersion relations. We illustrate this fact within a simple supergravity model that also exhibits the observed late-time cosmological acceleration and implies varying electromagnetic couplings.

The recent high precision maps of cosmic microwave anisotropies combined with measurements of the galaxy power spectrum from new large-scale redshift surveys have allowed stringent bounds on the sum of the neutrino masses to be placed. The past analyses, however, have implicitly assumed that the spectrum of primordial density fluctuations is adiabatic and coherent, as predicted in the simplest models of inflation. In this paper, we show that the limits hold even if the assumption on the primordial power spectrum is relaxed to allow for a contribution of nonadiabatic, incoherent fluctuations such as would be predicted by topological defects.

The sum of the CP-violating asymmetries $A\left({\Lambda }_{-}^0\right)$ and $A\left({\Xi }_{-}^{-}\right)$ in hyperon nonleptonic decays is presently being measured by the E871 experiment. We evaluate contributions to the asymmetries induced by chromomagnetic-penguin operators, whose coefficients can be enhanced in certain models of new physics. Incorporating recent information on the strong phases in $\overrightarrow{\Xi }\Lambda \pi$ decay, we show that new-physics contributions to the two asymmetries can be comparable. We explore how the upcoming results of E871 may constrain the coefficients of the operators. We find that its preliminary measurement is already better than the $\epsilon$ parameter of $K-\overline{K}$ mixing in bounding the parity-conserving contributions.

We study the $O\left({\Lambda }_{\mathrm{QCD}}{/m}_b\right)$ corrections to the singly and doubly differential hadronic invariant mass spectra $d\Gamma {/ds}_H$ and $d\Gamma {/ds}_H{\mathrm{dq}}^2$ in $\overline{B}\to X_{u}l{\overline{\nu }}_l$ decays, and discuss the implications for the extraction of the CKM matrix element $|V_{\mathrm{ub}}|.$ Using simple models for the subleading shape functions, the effects of subleading operators are estimated to be at the few percent level for experimentally relevant cuts. The subleading corrections proportional to the leading shape function are larger, but largely cancel in the relation between the hadronic invariant mass spectrum and the photon spectrum in $\overline{B}\to X_s\gamma .$ We also discuss the applicability of the usual prescription of convoluting the partonic level rate with the leading light-cone wave function of the b quark to subleading order.

We develop the concept of quantum phase-space (Wigner) distributions for quarks and gluons in the proton. To appreciate their physical content, we analyze the contraints from special relativity on the interpretation of elastic form factors, and examine the physics of the Feynman parton distributions in the proton’s rest frame. We relate the quark Wigner functions to the transverse-momentum dependent parton distributions and generalized parton distributions, emphasizing the physical role of the skewness parameter. We show that the Wigner functions allow us to visualize quantum quarks and gluons using the language of classical phase space. We present two examples of the quark Wigner distributions and point out some model-independent features.

The production of the standard model Higgs boson (H) plus one jet is compared with that of the lightest scalar Higgs boson ${(h}^0)$ plus one jet and that of the pseudoscalar Higgs boson ${(A}^0)$ plus one jet. The latter particles belong to the minimal supersymmetric model. We include both top and bottom quark loops to lowest order in QCD and investigate the limits of small quark mass and infinite quark mass. We give results for both the CERN Large Hadron Collider and the Fermilab Tevatron.

We discuss the renormalization of the electric charge at the two-loop level in the standard model of the electroweak interactions. We explicitly calculate the expression of the complete on-shell two-loop counterterm using the background field method and discuss the advantages of this computational approach. We consider the related quantity $e^2\left(\mu \right),$ defined in the $\overline{\mathrm{MS}}$ renormalization scheme and present numerical results for different values of the scale μ. We find that the full two-loop electroweak corrections contribute more than ten parts in units ${10}^{-5}$ to the $\Delta \hat{\alpha }{(m}_z^2)$ parameter, obtaining ${\hat{\alpha }}^{-1}{(m}_z)=128.12\mathrm{}\pm 0.05$ for $\Delta {\alpha }_{\mathrm{had}}^{\mathrm{}\left(5\right)\mathrm{}}{(m}_z^2)=0.027\mathrm{}572\pm 0.000359.$

We study soliton solutions of a modified nonlinear Schrödinger (MNLS) equation. Using an ansatz for the time and azimuthal angle dependence previously considered in the studies of the spinning Q balls, we construct multinode solutions of the MNLS equation as well as spinning generalizations.

A supersymmetric string model in the $D=11\mathrm{}$ superspace maximally extended by antisymmetric tensor bosonic coordinates ${\Sigma }^{\left(528\mathrm{}|32\right)}$ is proposed. It possesses 30 $\kappa$ symmetries and 32 target space supersymmetries. The usual preserved supersymmetry–κ-symmetry correspondence suggests that it describes the excitations of a Bogomol’nyi-Prasad-Sommerfield (BPS) state preserving all but two supersymmetries. The model can also be formulated in any ${\Sigma }^{\left(\right[n(n+1\mathrm{})/2\mathrm{}\left]|n\right)}$ superspace, $n=32\mathrm{}$ corresponding to $D=11.\mathrm{}$ It may also be treated as a “higher-spin generalization” of the usual Green-Schwarz superstring. Although the global symmetry of the model is a generalization of the super-Poincaré group ${\Sigma }^{\left(\right[n(n+1\mathrm{})/2\mathrm{}\left]|n\right)}\mathrm{Sp}\left(n\right),$ it may be formulated in terms of constrained $OSp\left(2n|1\right)$ orthosymplectic supertwistors. We work out this supertwistor realization and its Hamiltonian dynamics. We also give the supersymmetric p-brane generalization of the model. In particular, the ${\Sigma }^{\left(528\mathrm{}|32\right)}$ supersymmetric membrane model describes excitations of a $\frac{30}{32}$ BPS state, as the ${\Sigma }^{\left(528\mathrm{}|32\right)}$ supersymmetric string does, while the supersymmetric 3-brane and 5-brane correspond, respectively, to $\frac{28}{32}$ and $\frac{24}{32}$ BPS states.

We study the renormalization of the nonlinear effective $\mathrm{SU}\left(2\right)\mathrm{}$ Lagrangian up to ${O(p}^4)$ with spontaneous symmetry breaking. The Stueckelberg transformation, the background field gauge, the Schwinger proper time and heat kernel method, and the covariant short distance expansion technology guarantee gauge covariance and incorporate the Ward (Slavnov-Taylor) identities in the calculations. A modified power counting rule is introduced to consistently estimate and control the contributions of higher loops and higher-dimension operators. The one-loop renormalization group equations of the effective couplings are provided and analyzed. We find that the difference between the results obtained from the direct method and the renormalization group equation method can be quite large when the Higgs scalar boson is far below its decoupling limit. The exact one-loop calculation of $d_1$ in the renormalizable $\mathrm{SU}\left(2\right)\mathrm{}$ Higgs model is provided to understand such a difference. A better way of calculating at the one-loop level in the framework of the effective theory method is suggested.

It was shown recently that the $\mathrm{SU}\left(2\right)\mathrm{}$ sigma model coupled to gravity has periodic spherically symmetric self-similar solutions for small values of the coupling constant. In this article we extend the analysis of Bizoń, Szybka, and Wasserman to larger values of the coupling constant $(\alpha >~0.426)$ and present numerical evidence for the chaotic solution and the fractal threshold behavior. We explain this phenomenon in terms of horseshoelike dynamics and heteroclinic intersections.

The coupling of gravity to matter is explored in the linearized gravity limit. The usual derivation of gravity-matter couplings within the quantum-field-theoretic framework is reviewed. A number of inconsistencies between this derivation of the couplings and the known results of tidal effects on test particles according to classical general relativity are pointed out. As a step towards resolving these inconsistencies, a general laboratory frame fixed on the worldline of an observer is constructed. In this frame, the dynamics of nonrelativistic test particles in the linearized gravity limit is studied, and their Hamiltonian dynamics is derived. It is shown that for stationary metrics this Hamiltonian reduces to the usual Hamiltonian for nonrelativistic particles undergoing geodesic motion. For nonstationary metrics with long-wavelength gravitational waves present (GWs), it reduces to the Hamiltonian for a nonrelativistic particle undergoing geodesic deviation motion. Arbitrary-wavelength GWs couple to the test particle through a vector-potential-like field $N_a,$ the net result of the tidal forces that the GW induces in the system, namely, a local velocity field on the system induced by tidal effects, as seen by an observer in the general laboratory frame. Effective electric and magnetic fields, which are related to the electric and magnetic parts of the Weyl tensor, are constructed from $N_a$ that obey equations of the same form as Maxwell’s equations. A gedankin gravitational Aharonov-Bohm-type experiment using $N_a$ to measure the interference of quantum test particles is presented.

In this paper we first show that within the Hamiltonian description of general relativity the central charge of a near horizon asymptotic symmetry group is zero, and therefore that the entropy of the system cannot be estimated using Cardy’s formula. This is done by mapping a static black hole to a two-dimensional space. We explain how such a charge can appear only to a static observer who chooses to stay permanently outside the black hole. Then an alternative argument is given for the presence of a universal central charge. Finally, we suggest an effective quantum theory on the horizon that is compatible with the thermodynamic behavior of the black hole.