AC susceptibility of thin Pb films in intermediate and mixed state

Thin films of type I superconductors of a thickness comparable or less than a flux penetration length behave like type II superconductors in a mixed state. With decreasing film thickness normal domains carrying a magnetic flux get smaller with smaller number of flux quanta per domain and finally transform into single quantum flux lines, i.e. quantum vortices similar to those found in type II superconductors. We give an evidence of this behavior from the measurements of the nonlinear response of a total magnetic moment to an applied AC magnetic field, directly from the temperature dependence of an AC susceptibility.     

Fermionic vacuum polarization in compactified cosmic string spacetime

We investigate the fermionic condensate and the vacuum expectation value (VEV) of the energy-momentum tensor for a charged massive fermionic field in the geometry of a cosmic string compactified along its axis. In addition, we assume the presence of two types of magnetic fluxes: a flux running along the cosmic string and another enclosed by the compact dimension. These fluxes give rise to Aharanov–Bohm-like effects on the VEVs. The VEVs are decomposed into two parts corresponding to the geometry of a straight cosmic string without compactification plus a topological part induced by the compactification of the string axis. Both contributions are even periodic functions of the magnetic fluxes with period equal to the flux quantum. The vacuum energy density is equal to the radial stress for the parts corresponding to the straight cosmic string and the topological one. Moreover, the axial stress is equal to the energy density for the parts corresponding to the straight cosmic string; however, for massive fermionic fields this does not occur for the topological contributions. With respect to the dependence on the magnetic fluxes, both the fermionic condensate and the vacuum energy density, can be either positive or negative. Moreover, for points near the string, the main contribution to the VEVs comes from the straight cosmic string part, whereas at large distances the topological ones dominate. In addition to the local characteristics of the vacuum state, we also evaluate the part in the topological Casimir energy induced by the string.     

Quantum Processes beyond the Aharonov-Bohm Effect

We consider QED processes in the presence of an infinitely thin and infinitely long straight string with a magnetic flux inside it. The bremsstrahlung from an electron passing by the magnetic string and the electron-positron pair production by a single photon are reviewed. Based on the exact electron and positron solutions of the Dirac equation in the external Aharonov-Bohm potential we present matrix elements for these processes. The dependence of the resulting cross sections on energies, directions, and polarizations of the involved particles is discussed for low energies.     

Berry’s phase for a spin 1/2 particle in the presence of topological defects

The relativistic quantum dynamics of a spinorial quantum particle in the presence of a chiral conical background is investigated. We study the gravitational Berry geometric quantum phase acquired by a spin 1/2 particle in the chiral cosmic string spacetime. We obtain the result that this phase depends on the global features of this spacetime. We also consider the case that a string possesses an internal magnetic flux and obtain the geometric quantum phase in this case. The spacetime of multiple chiral cosmic strings is considered and the relativistic Berry quantum phase is also obtained.     

Confinement of monopole field lines in a superconductor at T ≠ 0

We apply the Bogoliubov-de Gennes equations to the confinement of a monopole-antimonopole pair in a superconductor. This is related to the problem of a quark-antiquark pair bound by a confining string, consisting of a colour-electric flux tube, dual to the magnetic vortex of type-II superconductors. We study the confinement of the field lines due to the superconducting state and calculate the effective potential between the two monopoles. The monopoles can be simulated in a real experiment inserting two long and thin magnetic rods. At short distances the potential is Coulombic and at large distances the potential is linear, as previously determined solving the Ginzburg-Landau equations. The magnetic field lines and the string tension are also studied as a function of the temperature T. Because we take into account the explicit fermionic degrees of freedom, this work may open new perspectives to the breaking of chiral symmetry or to colour superconductivity.     

Spectrum of a particle on a polyhedron enclosing a synthetic magnetic monopole

We consider a single particle hopping on a tight binding lattice formed by the vertices of a regular polyhedron and discuss the effect of a magnetic monopole enclosed in the polyhedron. The presence of the monopole induces phases on the hopping terms, given by Peierls substitution. By requiring the flux through each face of a regular polyhedron to be the same, Dirac’s quantization condition is obtained in this discrete setting. For each regular polyhedron, we calculate the energy spectrum for an arbitrary value of the flux through a Dirac string coming in from one of the faces. We find that the energy levels are degenerate only when the flux through the Dirac string corresponds to a quantized monopole. We show that the degeneracies in the presence of the monopole can be classified using the double group of the symmetry of the polyhedron and label all energy levels with corresponding irreducible representations.     

Time-dependent supergravity solutions in null dilaton background

A class of time dependent pp-waves with NS–NS flux in type IIA string theory is considered. The background preserves 1/4 supersymmetry and may provide a toy model of Big Bang cosmology with nontrivial flux. At the Big Bang singularity in early past, the string theory is strongly coupled and matrix string model can be used to describe the dynamics. We also construct some time dependent supergravity solutions for D-branes and analyze their supersymmetry properties.     

Aharonov-Bohm and non-inertial effects on a Klein-Gordon oscillator with potential in the cosmic string space-time with a spacelike dislocation

In this paper, we investigate the analogue effect to the Aharonov-Bohm effect for bound states in a relativistic quantum system described by the Klein-Gordon oscillator in the cosmic string space-time with a spacelike dislocation. We assume the topological defects have an internal magnetic flux and then analyze the effect on the relativistic energy eigenvalue subject to a Cornell-type potential and subsequently with a Coulomb-type potential. We show the presence of various potential parameters, the torsion parameter as well the cosmic string modify the energy spectrum.     

Quantum and string shape fluctuations in the dual monopole Nambu–Jona–Lasinio model with dual Dirac strings

The magnetic monopole condensate is calculated in the dual Monopole Nambu–Jona–Lasinio model with dual Dirac strings suggested in [1,2] as a functional of the dual Dirac string shape. The calculation is carried out in the tree approximation in the scalar monopole–antimonopole collective excitation field. The integration over quantum fluctuations of the dual–vector monopole–antimonopole collective excitation field around the Abrikosov flux line and string shape fluctuations are performed explicitly. We claim that there are important contributions of quantum and string shape fluctuations to the magnetic monopole condensate. Received: 3 June 1998 / Revised version: 1 September 1998 / Published online: 19 November 1998     

Junctions of three quantum wires and the dissipative Hofstadter model

We study a junction of three quantum wires enclosing a magnetic flux. This is the simplest problem of a quantum junction between Tomonaga-Luttinger liquids in which Fermi statistics enter in a nontrivial way. We present a direct connection between this problem and the dissipative Hofstadter problem, or quantum Brownian motion in two dimensions in a periodic potential and an external magnetic field, which in turn is connected to open string theory in a background electromagnetic field. We find nontrivial fixed points corresponding to a chiral conductance tensor leading to an asymmetric flow of the current.     

M‐strings,elliptic genera and N = 4 string amplitudes

We study mass‐deformed N = 2 gauge theories from various points of view. Their partition functions can be computed via three dual approaches: firstly, (p,q)‐brane webs in type II string theory using Nekrasov's instanton calculus, secondly, the (refined) topological string using the topological vertex formalism and thirdly, M theory via the elliptic genus of certain M‐strings configurations. We argue for a large class of theories that these approaches yield the same gauge theory partition function which we study in detail. To make their modular properties more tangible, we consider a fourth approach by connecting the partition function to the equivariant elliptic genus of ℂ² through a (singular) theta‐transform. This form appears naturally as a specific class of one‐loop scattering amplitudes in type II string theory on T², which we calculate explicitly.     

Exact monodromy group of N = 2 heterotic superstring

We describe an N = 2 heterotic superstring model of rank 3 which is dual to the type II string compactified on a Calabi-Yau manifold with Betti numbers b_1,1 = 2 and b_1,2 = 86. We show that the exact duality symmetry found from the type II realization contains the perturbative duality group of the heterotic model, as well as the exact quantum monodromies of the rigid SU(2) super-Yang-Mills theory. Moreover, it contains a non-perturbative monodromy which is stringy in origin and corresponds roughly to an exchange of the string coupling with the compactification radius.     

A relation between tree amplitudes of closed and open strings

We derive a formula which expresses any closed string tree amplitude in terms of a sum of the products of appropriate open string tree amplitudes. This formula is applicable to the heterotic string as well as to the closed bosonic string and type II superstrings. In particular, we demonstrate its use by showing how to write down, without any direct calculation, all four-point heterotic string tree amplitudes with massless external particles.     

A note on Chern–Simons solitons—A type III vortex from the wall vortex

We study some properties of topological Chern–Simons vortices in 2+1 dimensions. As has already been understood in the past, in the large magnetic flux limit, they are well described by a Chern–Simons domain wall, which has been compactified on a circle with the symmetric phase inside and the asymmetric phase on the outside.Our goal is two-fold. First we want to explore how the tension depends on the magnetic flux discretized by the integer n. The BPS case is already known, but not much has been explored about the non-BPS potentials. A generic renormalizable potential has two dimensionless parameters that can be varied. Variation of only one of them leads to a type I and type II vortex, very similar to the Abrikosov–Nielsen–Olesen (ANO) case. Variation of both the parameters leads to a much richer structure. In particular we have found a new type of vortex, which is type I-like for small flux and then turns type II-like for larger flux. We could tentatively denote it a type III vortex. This results in a stable vortex with number of fluxes which can be greater than one.Our second objective is to study the Maxwell–Chern–Simons theory and understand how the large n limit of the CS vortex is smoothly connected with the large n limit of the ANO vortex.     

Flux expulsion and trapping in rotating discs of type II superconductors

The magnetic flux rotating in step with a type II superconducting disc is measured with orthogonal pick up coils for various previous magnetic histories vs H₀ applied ⊥ to the axis of rotation. For some initial magnetic states, flux expulsion, independent of the rate of rotation, occurs during the initial rotation. A simple model where flux lines leave the specimen against the magnetic pressure in the active region accounts for the observations.     

Electrical and superconducting properties of BiSrCaCuO ceramics superconductors

Electrical and superconducting properties of BiSrCaCuO superconductor prepared by partial melting method were determined to study its superconducting mechanism. Induced voltage of the BiSrCaCuO superconductor was not so significantly dependent upon on the shape and size of the superconductor. Anti-magnetism was less dependent upon the melting and the annealing temperatures. BiSrCaCuO film prepared at 1158 K shows the maximum magnetic susceptibility in this study. Differential conductance behavior of the superconductor with magnetic flux was not well matched by a conventional flux flow model. It suggests that a superconducting mechanism for type II superconductor should be able to explain the fact that magnetic properties arise from the interaction between the trapped magnetic flux and weak link of the superconducting connectors forms in the superconducting material.     

General N=1 supersymmetric flux vacua of massive type IIA string theory

We derive conditions for the existence of four-dimensional N=1 supersymmetric flux vacua of massive type IIA string theory with general supergravity fluxes turned on. For an SU(3) singlet Killing spinor, we show that such flux vacua exist when the internal geometry is nearly K?hler. The geometry is not warped, all the allowed fluxes are proportional to the mass parameter, and the dilaton is fixed by a ratio of (quantized) fluxes. The four-dimensional cosmological constant, while negative, becomes small in the vacuum with the weak string coupling.     

Interactions of strings and D-branes from M theory

We discuss the relation between M theory and type II string theories. We show that, assuming “natural” interactions between membranes and fivebranes in M theory, the known interactions between strings and D-branes in type II string theories arise in appropriate limits. Our discussion of the interactions is purely at the classical level. We remark on issues associated with the M theory approach to enhanced gauge symmetries, which deserve further investigation.     

Generalized Cohomologies and Supersymmetry

We show that the complex cohomologies of Bott, Chern, and Aeppli and the symplectic cohomologies of Tseng and Yau arise in the context of type II string theory. Specifically, they can be used to count a subset of scalar moduli fields in Minkowski compactification with RR fluxes in the presence of either O5/D5 or O6/D6 brane sources, respectively. Further, we introduce a new set of cohomologies within the generalized complex geometry framework which interpolate between these known complex and symplectic cohomologies. The generalized complex cohomologies play the analogous role for counting massless fields for a general supersymmetric Minkowski type II compactification with Ramond–Ramond flux.     

Superstrings on hyperelliptic surfaces and the two-loop vanishing of the cosmological constant

We calculate the supersymmetric type II string partition function in a flat background for the situation where the world-sheet is hyperelliptic. We show explicitly that the contribution to the cosmological constant from hyperelliptic world-surfaces vanishes for genus ⩽ 20. This implies, in particular, that the cosmological constant vanishes completely to two loops. Due to the decoupling of the holomorphic and antiholomorphic sectors, this conclusion holds equally well for the heterotic string.