Samuel W. MacDowell

Spontaneous compactification of supergravity in one loop

Abstract We consider the spontaneous compactification of N = 2, D = 5 supergravity in which the compact subspace is S 1 , at one loop. Supersymmetry resolves ambiguities in the boundary conditions imposed on the dynamical fields, encountered in previous treatments. One cannot achieve self-consistent compactification without breaking global supersymmetry.

Gravity with extra gauge symmetry

Abstract In addition to the tangent space Lorentz gauge invariance, we introduce an extra gauge principle in the gauge formulation of gravity, in any dimension. The connection ω ij μ , which starts out as an elementary field, undergoes a gauge transformation which mixes tangent space indices ( i , j ) with base indices ( μ ). The equations of motion determine ω ij μ as the sum of usual riemannian connection and a completely antisymmetric torsion piece. In 11 dimensions our theory reproduces the bosonic sector of supergravity if we identify torsion with the 3-index gauge potential A μυλ . This generalizes Englerts recent observation, since in our formulation torsion = A μυλ for any field configuration, not just a solution.

Algebraic approach to supergravity in superspace

Abstract The methods of algebraic geometry are used to construct supergravity theories in a homogeneous superspace OSp( N |4) with structure group Sl(2C) ⊗ O N and base supermanifold the coset space OSp ( N |4)/( Sl (2 C )⊗ O N ). The nature and origin of the supersymmetry transformations is completely elucidated. The equations of motion for O 1 and O 2 supergravity are obtained, as the realization of this symmetry on the space-time components h μ of the “supervierbein”.

Supergeometry of the coupled Yang-Mills/supergravity system in ten dimensions

Abstract Supergravity coupled to supersymmetric Yang-Mills theory in ten dimensions is constructed using the bundle of frames approach to superspace. The structure group Spin(9, 1) of simple supergravity is enlarged to Spin (9, 1) × G where G is the internal symmetry group, while the super-Yang-Mills spinor field generates additional torsion. The possibility of this coupling is traced to the fact that given the constraints on the spinorial torsion components, the Bianchi identities do not imply the complete transformation laws and equations of motion for the Fermi fields. The Chern-Simons form associated with the Yang-Mills connection arises from a constraint implied by the Bianchi identities.

Spinor theory of general relativity without elementary gravitons

Abstract We propose a generally covariant and locally Lorentz invariant theory of a Majorana spinor field ψ μ α . Our theory has no elementary spin-2 quanta, but does reproduce Einsteins general relativity as a classical solution. We compare this situation to the possibility of finding classical monopoles in a gauge theory, even though no such elementary object is introduced at the outset.

ELECTROWEAK VORTICES AND GAUGE EQUIVALENCE

Vortex configurations in the electroweak gauge theory are investigated. Two gauge-inequivalent solutions of the field equations, the Z and W vortices, have previously been found. They correspond to embeddings of the Abelian Nielsen-Olesen vortex solution into a U(1) subgroup of SU(2)×U(1). It is shown here that any electroweak vortex solution can be mapped into a solution of the same energy with a vanishing upper component of the Higgs field. The correspondence is a gauge equivalence for all vortex solutions except those for which the winding numbers of the upper and lower Higgs components add to zero. This class of solutions, which includes the W vortex, corresponds to a singular solution in the one-component gauge. The results, combined with numerical investigations, provide an argument against the existence of other vortex solutions in the gauge-Higgs sector of the Standard Model.

Realization of the discrete series of unitary representations of Sl(2,R) in terms of creation and annihilation operators

A basis for the Hilbert space of the discrete series of unitary representations of Sl(2,R) is constructed as a complete set of coherent states of pairs of particle–antiparticle creation operators. The integer q specifying an irreducible representation is the eigenvalue of the charge operator. Representations with charges ∓q are equivalent.

Instability of a Nielsen-Olesen vortex embedded in the electroweak theory

The stability of an abelian (Nielsen-Olesen) vortex embedded in the electroweak theory against W production is investigated in a gauge defined by the condition of a single-component Higgs field. The model is characterized by the parameters β = \(\left( {\frac{{M_H }}{{M_Z }}} \right)^2\)and γ = cost2Ow where Ow is the weak mixing angle. It is shown that the equations for Ws in the background of the Nielsen-Olesen vortex have no solutions in the linear approximation. A necessary condition for the nonlinear equations to have a solution in the region of parameter space where the abelian vortex is classically unstable is that the Ws be produced in a state of angular momentum m such that 0 > m > -2n. The integer n is defined by the phase of the Higgs field, exp(⇌ It is shown that, in the region of parameter space (β, γ) where the nonlinear equations have a solution with energy lower than that of the abelian vortex, this vortex is a saddle point of the energy in the space of classical field configurations. Solutions for a set of values of the parameters β and y in this region were obtained numerically for the case -m = n = 1. The possibility of existence of a stationary state for n = 1 with Ws in the state m = -1 was investigated. The boundary conditions for the Euler-Lagrange equations required to make the energy finite cannot be satisfied at r = 0. For these values of n and m the possibility of a finite-energy stationary state defined in terms of distributions is discussed.

Existence of lattice structures in a class of magnetic phase transitions

Abstract A class of models described in terms of a charged field ψ in interaction with a uniform magnetic field is considered. They generalize the Ginzburg-Landau theory of type II superconductivity to non-local quartic interactions. If the strength of this interaction is sufficiently large this system undergoes a magnetic phase transition to a phase with lattice structure. It is shown that near the critical field the extrema of the action are obtained for ψ expressed in terms of the Jacobi function ι1(z | τ) where τ = τR + iτI for some τ on the line τ R = 0 or τ R = 1 2 . For rotational invariant kernels the action as a function of τ is modular invariant and the line τ R = 1 2 is equivalent to the boundary of moduli space. The actual configuration giving the minimum of the action depends on the particular form of the kernel.

Responsabilidade social dos cientistas: natureza das ciências exatas

As ciencias exatas, isto e, as ciencias fisicas surgiram com base em precisas observacoes astronomicas de Ticho Brahe e da introducao, por Galileu, do metodo experimental como seu alicerce. Suas investigacoes levaram a formulacao do principio da inercia como fundamento da cinematica. A filosofia natural, que as precedeu, procurava entender e explicar os fenomenos naturais de um modo essencialmente qualitativo.