Conformal invariance,current algebra and modular invariance

A large class of conformally invariant models in two dimensions is realised by constraining free fermion theories. The Fock spaces of the constrained theories are described, using the representation theory of affine Kac-Moody algebras. The results are extended to superconformally invariant theories. Projections of the models, producing consistent two-dimensional field theories, are discussed.     

Two-loop modular invariance and spin-statistics

Within the context of a class of fermionic closed string theories I explicitly show some relationships between two-loop modular invariance, factorization, correct spin-statistics and the existence of a massless gravity multiplet.     

Multiloop modular invariance and the cosmological constant

In any ten-dimensional string model with space-time fermions, the cosmological constant vanishes identically, provided that only the transverse degrees of freedom contribute to all loop orders. The proof relies on an elementary application of the theory of induced representations of the modular group.     

Theta functions,modular invariance,and strings

We use Quillen's theorem and algebraic geometry to investigate the modular transformation properties of some quantities of interest in string theory. In particular, we show that the spin structure dependence of the chiral Dirac determinant on a Riemann surface is given by Riemann's theta function. We use this result to investigate the modular invariance of multiloop heterotic string amplitudes.     

Unitarity and modular invariance as constraints on four-dimensional superstrings

It is shown that the requirements of space-time factorization for vertices and one-loop modular invariance guarantee higher-loop modular invariance (as it is presently understood) in the context of string models built out of free fermion fields, either twisted or untwisted. The general solution satisfying these requirements is derived and their relation to the conservation of quantum numbers at general fermionic vertices is discussed. A number of models are discussed using a diagrammatic notation. The natural occurrence in such models of spinor representations which have features in common with the observed quark-lepton multiplets is noted.     

Duality and modular invariance in rational conformal field theories

We investigate the polynomial equations which should be satisfied by the duality data for a rational conformal field theory. We show that by these duality data we can construct some vector spaces which are isomorphic to the spaces of conformal blocks. One can construct explicitly the inner product for the former if one deals with a unitary theory. These vector spaces endowed with an inner product are the algebraic reminiscences of the Hilbert spaces in a Chern-Simons theory. As by-products, we show that the polynomial equations involving the modular transformations for the one-point blocks on the torus are not independent. We discuss the solution of structure constants for a physical theory. Making some assumption, we obtain a neat solution. And this solution in turn implies that the quantum groups of the left sector and of the right sector must be the same, although the chiral algebras need not be the same. Some examples are given. Finally, we discuss the reconstruction of the quantum group in a rational conformal theory.     

A modular subgroup invariance in a four-dimensional string

A four-dimensional closed supersymmetric string theory is constructed from the left-moving Neveu-Schwarz bosonic string and the right-moving superstring. The gauge group [SU(2)]⁶ arises from an algebraic compactification involving a new affine Kac-Moody construction in terms of Neveu-Schwarz operators. The theory is Lorentz-invariant, tachyon-free and has four-point one-loop amplitudes invariant under a subgroup of the modular group.     

Cosmic strings and domain walls

Phase transitions in the early universe can give rise to microscopic topological defects: vacuum domain walls, strings, walls bounded by strings, and monopoles connected by strings. This article reviews the formation, physical properties and the cosmological evolution of various defects. A particular attention is paid to strings and their cosmological consequences, including the string scenario of galaxy formation and possible observational effects of strings.     

Spin-polarised currents and magnetic domain walls

Electrical currents flowing in ferromagnetic materials are spin-polarised as a result of the spin-dependent band structure. When the spatial direction of the polarisation changes, in a domain structure, the electrons must somehow accommodate the necessary change in direction of their spin angular momentum as they pass through the wall. Reflection, scattering, or a transfer of angular momentum onto the lattice are all possible outcomes, depending on the circumstances. This gives rise to a variety of different physical effects, most importantly a contribution to the electrical resistance caused by the wall, and a motion of the wall driven by the spin-polarised current.

Historical and recent research on these topics is reviewed.

Spin-polarised currents and magnetic domain walls

All authors

C. H. Marrows

https://doi.org/10.1080/00018730500442209

Published online:

19 February 2007

Table     

Domains and domain walls in multiferroics

Multiferroics are gathering solid-state matter in which several types of orders are simultaneously allowed, as ferroelectricity, ferromagnetism (or antiferromagnetism), ferroelasticity, or ferrotoroidicity. Among all, the ferroelectric/ferromagnetic couple is the most intensively studied because of potential applications in novel low-power magnetoelectric devices. Switching of one order thanks to the other necessarily proceeds via the nucleation and growth of coupled domains. This review is an introduction to the basics of ferroelectric/ferromagnetic domain formation and to the recent microscopy techniques devoted to domains imaging, providing new insights into the archetypal multiferroic domain morphologies. Some relevant examples are also given to illustrate some of the unexpected properties of domain walls, as well as the way these domain walls can be manipulated altogether thanks to various types of magnetoelectric coupling.     

Topological structures on domain walls

The possibility that a symmetry which is preserved in the vacuum might be broken in the interior of a domain wall is discussed. The simplest field theory example is explored in detail. The possibility that unexpected topological structures could then arise is illustrated with some examples. If the broken symmetry is electromagnetism, the domain wall becomes superconducting, a phenomenon which was discovered in the context of cosmic strings.     

New massive gravity domain walls

The properties of the asymptotic AdS₃${\mathit{AdS}}_3$ space–times representing flat domain walls (DW's) solutions of the new massive 3D gravity with scalar matter are studied. Our analysis is based on first order BPS-like equations involving an appropriate superpotential. The Brown–York boundary stress-tensor is used for the calculation of DW's tensions as well as of the CFT₂${\mathit{CFT}}_2$ central charges. The holographic renormalization group flows and the phase transitions in specific deformed CFT₂${\mathit{CFT}}_2$ dual to 3D massive gravity model with quadratic superpotential are discussed.     

Leptogenesis with left-right domain walls

The presence of domain walls separating regions of unbrokenSU(2)_L andSU(2)_R is shown to provide necessary conditions for leptogenesis which converts later to the observed baryon asymmetry. The strength of lepton number violation is related to the Majorana neutrino mass and hence related to current bounds on light neutrino masses. Thus the observed neutrino masses and the baryon asymmetry can be used to constrain the scale of left-right symmetry breaking.