Chiral String Research Articles

Dynamics and properties of chiral cosmic strings in Minkowski space

AbstractChiral cosmic strings are produced naturally at the end of inflation in super-symmetric models where the symmetry is broken via a D-term. Consequently insuch theories, where both inflation and cosmic strings contribute to the densityand CMBR (microwave background) perturbations, it is necessary to understandthe evolution of chiral cosmic string networks. We study the dynamics of chiralcosmic strings in Minkowski space and comment on a number of differences withthose of Nambu-Goto strings. To do this we follow the work of Carter and Pe-ter who showed that the equations of motion for chiral cosmic strings reduce to awave equation and two constraints, only one of which is different from the familiarNambu-Goto constraints. We study chiral string loop solutions consisting of manyharmonics and determine their self-intersection probabilities, and comment on thepossible cosmological significance of these results. 1 Introduction In the last few years many high accuracy calculations have been made of cosmologicalconsequences of Nambu-Goto (NG) cosmic strings [1, 2, 3, 4]. Indeed, such predictionswere recently compared to the Boomerang data [5, 6, 7]. There are good reasons whymost studies of the cosmological effects of topological defects (see [8, 9] for a summary)have concentrated on NG strings: these are the simplest type of cosmic string, and theirequations of motion (at least in Minkowski space) can be solved exactly. On a lattice onecan use the highly efficient Smith-Vilenkin algorithm [10]; and in fact some of the recentpredictions are based on Minkowski space codes of NG network evolution [3, 7].

LOOP VARIABLES AND GLOBAL CHARACTERIZATION OF CONICAL SPACE–TIMES

Using the loop variable approach we describe the global aspects of the space–time of N parallel chiral cosmic strings with one of them moving relative to the others. Particular results in the framework of (2 + 1)-dimensional gravity are given.

Discrete torsion in non-geometric orbifolds and their open-string descendants

We discuss some Z N L × Z N R orbifold compactifications of the type IIB superstring to D=4,6 dimensions and their type I descendants. Although the Z N L × Z N R generators act asymmetrically on the chiral string modes, they result into left–right symmetric models that admit sensible unorientable reductions. We carefully work out the phases that appear in the modular transformations of the chiral amplitudes and identify the possibility of introducing discrete torsion. We propose a simplifying ansatz for the construction of the open-string descendants in which the transverse-channel Klein-bottle, annulus and Möbius-strip amplitudes are numerically identical in the proper parametrization of the world-sheet. A simple variant of the ansatz for the Z 2 L × Z 2 R orbifold gives rise to models with supersymmetry breaking in the open-string sector.

Dynamics and integrability property of the chiral string model

The effect of fermionic string conductivity by purely right (or purely left) moving “zero modes” is shown to be governed by a simple Lagrangian characterizing a certain “chiral” (null current carrying) string model whose dynamical equations of motion turn out to be explicitly integrable in a flat spacetime background.

More on the similarity between D=5 simple supergravity and M theory

It has been known that D=5 simple supergravity resembles D=11 supergravity in many respects. We present their further resemblances in (1) the duality groups upon dimensional reduction, and (2) the worldsheet structure of the solitonic string of the D=5 supergravity. We show that the D=3, G 2(+2)/ SO(4) (bosonic) nonlinear sigma model is obtained by using Freudenthal's construction in parallel to the derivation of the D=3, E 8(+8)/ SO(16) sigma model from D=11 supergravity. The zero modes of the string solution with unbroken (4,0) supersymmetry consist of three (non-chiral) scalars, four Majorana-Weyl spinors of the same chirality and one chiral scalar, which suggests a duality to a certain six-dimensional chiral string theory. The worldsheet gravitational anomaly indicates a quantum correction to the Bianchi identity for the dualized two-form gauge field in the bulk just like the M5-brane case.

Large N phases of chiral QCD 2

A matrix model is constructed which describes a chiral version of the large NU (N) gauge theory on a two-dimensional sphere of area A. This theory has three separate phases. The large area phase describes the associated chiral string theory. An exact expression for the free energy in the large area phase is used to derive a remarkably simple formula for the number of topologically inequivalent covering maps of a sphere with fixed branch points and degree n.

Spinning strings as torsion line spacetime defects

A consistent description of spinning strings with dislocations (chiral strings) as a missing part of the spacetime manifold (spacetime defect) is achieved by introducing a line of torsion along the string. Also, the definition of a spin-dislocation tensor associated with the chiral string allows its interpretation in the context of the Einstein--Cartan theory of gravitation. Some generalizations, as well as the Dirac equations, are briefly discussed. In particular, we argue that the behaviour of the fermions near the chiral string can be used to test the torsion hypothesis.

Spinning strings and cosmic dislocations.

It is shown that the 1+2 gravity spinning particle metric, when lifted to 1+3 dimensions in a boost-covariant way, gives rise to a chiral conical space-time which includes as particular cases the space-time of a spinning string and two space-times that can be associated with the chiral string with a lightlike phase and the twisted string recently discovered by Bekenstein. Some gravitational effects are briefly discussed and a possibility for a new type of anyon is mentioned.

FUNDAMENTAL CHIRAL STRINGS

The problem of the non-uniqueness of the string theory in the space Rd-1,1 with d ≤ 10 and the procedure of the compactification and the deompactification are discussed. We consider a compact bosonic string defined as a closed string moving in the Lorentizian torus T25,1 and introduce fundamental chiral bosonic string (FCBS) as a universal cover of a compact string. It is shown that the Fock spaces of any standard strings are embedded into the Fock space of FCBS.

CHIRAL (SUPER) STRING ACTIONS

We present a covariant action describing chiral bosonic string theories in space-time dimensions d<26 and a covariant (1, 0) supersymmetric action describing heterotic string theories in space-time of dimension d<10. The anomaly cancellation conditions are found. In the four-dimensional case the supersymmetric action corresponds to the SO(44) heterotic string theory.

Covariant quantization of chiral bosons and anomaly cancellation

A bosonic string with D spacetime dimensions, R right-moving internal scalars and L left-moving ones can be quantized canonically and is free from local anomaliesif R= L=26− D. Actions for such string theories can be written using Siegel's action for chiral bosons, but anomaly cancellation requires D=0, R= L=26. An action is presented that describes chiral string theories provided R= L=26− D and the physical spectrum is shown to be identical to that of the canonically constructed theory. Supersymmetry, curved backgrounds and global anomalies are briefly discussed.

A FUNCTIONAL LIGHT-CONE GAUGE CONSTRUCTION OF A BOSONIC STRING COMPACTIFIED ON A TORUS

The closed bosonic string compactified on a torus is decomposed into two open strings corresponding to left and right movers respectively. Multiloop amplitudes are expressed as a product of a holomorphic and an anti-holomorphic function of the moduli of the world-sheet Riemann surface. Such a product is obtained by analytically continuing left and right open string amplitudes such that one is the complex conjugate of the other. A justification for this analytic continuation is provided using a second quantized field theory of strings. The extra parameters needed for complexification are shown to arise from the constraint expressing invariance under choice of origin for string parametrization. The chiral string is discussed.

Chiral four-dimensional heterotic strings from self-dual lattices

It is shown how our previous work on lattice constructions of ten-dimensional heterotic strings can be applied to four dimensions. The construction is based on an extension of Narain's lattices by including the bosonized world-sheet fermions and ghosts, and uses conformal field theory as its starting point. A natural embedding of all these theories in the bosonic string is automatically provided. Large numbers of chiral string theories with and without N = 1 supersymmetry can be constructed. Many features of their spectra have a simple interpretation in terms of properties of even self-dual lattices. In particular we find an intriguing relation between extended supersymmetry and exceptional groups.