Chiral String Research Articles

Massive Strings from a Field Theory with Ghosts.

In this Letter, we present the α^{'}-exact background equations of motion of the bosonic chiral string (also known as Hohm-Siegel-Zwiebach model), with the spin-two ghost fields integrated out. This is the first instance of a world sheet model in which all corrections are fully determined in a generic curved spacetime. As a concrete cross-check, we find complete agreement between all three-point and a sample of four-point tree-level scattering amplitudes computed using field theory methods and the chiral string prescription. These equations of motion provide a field theoretical shortcut to compute world sheet correlators in conventional bosonic strings (with an arbitrary number of massless and mass-level-one states) and outline a new perspective on massive resonances in string theory.

Massive ambitwistor-strings; twistorial models

Ambitwistor-strings are chiral strings whose targets are spaces of complex massless particles, and whose correlation functions directly lead to simple, compact formulae for scattering amplitudes and loop integrands for massless gauge and gravity theories. This article extends the framework to massive particles in 4d, obtained via a symmetry reduction of higher dimensional massless models based on twistors. The target space of the resulting models turns out to be the phase space of 4d massive particles in a twistorial representation, and the worldsheet theory agrees with the two-twistor string previously introduced by the authors. The paper has been written so as to be largely self-contained. We discuss two interesting classes of massive theories in detail. For gauge theories, the reduction procedure is explicitly adapted to supersymmetric gauge theories on the Coulomb branch. For supergravity theories, the reduction is adapted to give theories obtained via Cremmer, Scherk & Schwartz (CSS) reduction, with broken supersymmetry and massive multiplets. The reduction procedure gives explicit and systematic rules to obtain amplitudes for all these theories and their amplitudes from two compact master formulae that have their origins in 6d based on the polarized scattering equations; in the CSS case the formulae are new, and in both cases their derivation is systematic. The freedom to include mass allows the definition of a loop insertion operator, thereby extending the formulae to 1-loop. Unlike the massless 4d twistorial models, these all display a perfect double copy structure, here incorporating massive particles in the relationship between gauge theory and CSS supergravity amplitudes.

From Twistor-Particle Models to Massive Amplitudes

In his twistor-particle programme of the 1970's, Roger Penrose introduced a representation of the massive particle phase space in terms of a pair of twistors subject to an internal symmetry group. Here we use this representation to introduce a chiral string whose target is a complexification of this space, extended so as to incorporate supersymmetry. We show that the gauge anomalies associated to the internal symmetry group vanish only for maximal supersymmetry, and that correlators in these string models describe amplitudes involving massive particles with manifest supersymmetry. The models and amplitude formulae exhibit a double copy structure from gauge theory on the Coulomb branch to gravity, although the graviton remains massless. The formulae are closely related to those obtained earlier by the authors expressed in terms of the polarised scattering equations.

Green-Schwarz and pure spinor formulations of chiral strings

Bosonic and RNS chiral strings have been defined from a singular gauge fixing of the respective Polyakov and spinning string actions, enforcing, among other things, the finite nature of their physical spectra. Except for the heterotic case, the tensionless limits of such chiral models have been shown to describe the same field theories predicted by their ambitwistor analogues. In this paper, we study the Green-Schwarz formulation for Type II and heterotic superstrings in a singular gauge. After performing a light-cone gauge analysis, their physical spectra are shown to match those of RNS chiral strings, and their respective tensionless limits are found to describe the same field theories predicted by RNS ambitwistor strings. Their pure spinor counterparts are then introduced by making use of the Oda-Tonin method. In doing so, symmetries hidden in the pure spinor ambitwistor string action become manifest, proposals motivating the sectorized pure spinor BRST charges find simple grounds, and integrated vertex operators emerge naturally.

Ambitwistor strings in six and five dimensions

Ambitwistor strings are chiral (holomorphic) strings whose target is the space of complex null geodesics, ambitwistor space. We introduce twistor representations of ambitwistor space in 6 and 5 dimensions. In 6d the twistor representation is naturally conformally invariant. Anomaly cancellation leads to models that describe biadjoint scalar amplitudes and certain conformally invariant gauge and gravity theories, respectively of 4th and 6th order. There are three such models, reflecting triality for the conformal group SO(8) associated to these 6d models. On reduction to five dimensions, gauge anomaly cancellation requires supersymmetry and the resulting models describe maximally supersymmetric Yang-Mills and gravity. The twistor representation of these ambitwistor strings lead to formulæ for maximally supersymmetric gauge and gravity amplitudes based on the polarized scattering equations in 5d, found earlier by the first two authors.

Closed Strings in the Skyrme Gauge Model

In the framework of the skyrme gauge SU(2) model, closed chiral strings (vortices) are considered, whose closure radius a is considered large in comparison with the characteristic size of the vortex determined by the parameters of the model. In this approximation, it is possible to find the chiral and gauge fields inside the vortex, estimate its radius and energy as functions of the topological charge Q.

Bosonic sectorized strings and the (DF)2 theory

In this work, we investigate the bosonic chiral string in the sectorized inter- pretation, computing its spectrum, kinetic action and 3-point amplitudes. As expected, the bosonic ambitwistor string is recovered in the tensionless limit. We also consider an extension of the bosonic model with current algebras. In that case, we compute the effective action and show that it is essentially the same as the action of the mass-deformed (DF )2 theory found by Johansson and Nohle. Aspects which might seem somewhat contrived in the original construction — such as the inclusion of a scalar transforming in some real representation of the gauge group — are shown to follow very naturally from the worldsheet formulation of the theory.

Chiral strings, the sectorized description and their integrated vertex operators

A chiral string can be seen as an ordinary string in a singular gauge for the worldsheet metric and has the ambitwistor string as its tensionless limit. As proposed by Siegel, there is a one-parameter (β) gauge family interpolating between the chiral limit and the usual conformal gauge in string theory. This idea was used to compute scattering amplitudes of tensile chiral strings, which are given by standard string amplitudes with modified (β-dependent) antiholomorphic propagators. Due to the absence of a sensible definition of the integrated vertex operator, there is still no ordinary prescription for higher than 3-point amplitude computations directly from the chiral model. The exception is the tensionless limit. In this work this gap will be filled. Starting with a chiral string action, the integrated vertex operator is defined, relying on the so-called sectorized interpretation. As it turns out, this construction effectively emulates a left/right factorization of the scattering ampli- tude and introduces a relative sign flip in the propagator for the sector-split target space coordinates. N -point tree-level amplitudes can be easily shown to coincide with the results of Siegel et al.

Chiral strings, topological branes, and a generalised Weyl-invariance

We introduce a sigma model Lagrangian generalising a number of new and old models which can be thought of as chiral, including the Schild string, ambitwistor strings, and the recently introduced tensionless AdS twistor strings. This “chiral sigma model” describes maps from a [Formula: see text]-brane worldvolume into a symplectic space and is manifestly invariant under diffeomorphisms as well as under a “generalised Weyl invariance” acting on space–time coordinates and worldvolume fields simultaneously. Construction of the Batalin–Vilkovisky master action leads to a BRST operator under which the gauge-fixed action is BRST-exact; we discuss whether this implies that the chiral brane sigma model defines a topological field theory.

Aspects of nonsupersymmetric string phenomenology

We consider a big class of chiral four-dimensional string models which bear [Formula: see text] gauge symmetry. Supersymmetry (SUSY) is spontaneously broken via the Scherk–Schwarz mechanism associated with two large internal dimensions. We study two central issues in nonsupersymmetric string phenomenology: the suppression of the cosmological constant and the decompactification problem. We identify a subclass of chiral nonsupersymmetric models with fermion–boson degeneracy leading to exponentially suppressed cosmological constant. In addition, we propose a novel solution to the decompactification problem related to the cancellation of the linear growth of the gauge part of the thresholds with a similar growth of the universal part. We show that the proposed mechanism resolves the decompactification problem related to the non-Abelian gauge couplings in approximately 40% of the models under consideration.

Collisions of cosmic strings with chiral currents

We present an analytic study of cosmic superconducting chiral string collisions in Minkowski space, applying the kinematic constraints that arise from the relevant generalization of the Nambu-Goto action. In particular, we revisit the solution for chiral superconducting cosmic strings and demonstrate that Y junction production for such strings is possible. We consider the collision of chiral current-carrying straight strings and obtain the region in angle-velocity space that allows the production of string junctions. This study contributes to the understanding of the complex evolution of chiral superconducting string networks.

Intersecting branes, Higgs sector, and chirality from mathcal{N} = 4 SYM with soft SUSY breaking

We consider SU(N ) mathcal{N} = 4 super Yang-Mills with cubic and quadratic soft SUSY breaking potential, such that the global SU(4)R is broken to SU(3) or further. As shown recently, this set-up supports a rich set of non-trivial vacua with the geometry of self-intersecting SU(3) branes in 6 extra dimensions. The zero modes on these branes can be interpreted as 3 generations of bosonic and chiral fermionic strings connecting the branes at their intersections. Here, we uncover a large class of exact solutions consisting of branes connected by Higgs condensates, leading to Yukawa couplings between the chiral fermionic zero modes. Under certain decoupling conditions, the backreaction of the Higgs on the branes vanishes exactly. The resulting physics is that of a spontaneously broken chiral gauge theory on branes with fluxes. In particular, we identify combined brane plus Higgs configurations which lead to gauge fields that couple to chiral fermions at low energy. This turns out to be quite close to the Standard Model and its constructions via branes in string theory. As a by-product, we construct a G2-brane solution corresponding to a squashed fuzzy coadjoint orbit of G2.

Classification of non-Riemannian doubled-yet-gauged spacetime

Assuming mathbf {O}(D,D) covariant fields as the ‘fundamental’ variables, double field theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such non-Riemannian spacetimes in terms of two non-negative integers, (n,bar{n}), 0le n+bar{n}le D. Upon these backgrounds, strings become chiral and anti-chiral over n and bar{n} directions, respectively, while particles and strings are frozen over the n+bar{n} directions. In particular, we identify (0, 0) as Riemannian manifolds, (1, 0) as non-relativistic spacetime, (1, 1) as Gomis–Ooguri non-relativistic string, (D{-1},0) as ultra-relativistic Carroll geometry, and (D, 0) as Siegel’s chiral string. Combined with a covariant Kaluza–Klein ansatz which we further spell, (0, 1) leads to Newton–Cartan gravity. Alternative to the conventional string compactifications on small manifolds, non-Riemannian spacetime such as D=10, (3, 3) may open a new scheme for the dimensional reduction from ten to four.

Elementary supramolecular strings in solutions of chiral trifluoroacetylated amino alcohols

IR spectroscopy is applied to studying the effect of nonpolar and low-polar solvents on the molecular structure of solid-state quasi-one-dimensional strings formed through the chiral self-assembly from solutions of trifluoroacetylated homochiral amino alcohols (TFAAA). It is experimentally confirmed that in stable two-phase string/solvent gels and respective xerogels, solid-phase strings contain no solvent molecules as a structural element, experiencing, however, a weak disturbing influence of solvent molecules. It is shown that the process of spontaneous self-assembly of chiral strings in solutions is accompanied by the formation of a complex system of hydrogen bonds involving the C=O, N–H, and O–H functional groups of dissolved TFAAA molecules and by the displacement of solvent molecules to the periphery of the resulting quasi-one-dimensional strings. The results of the present work, together with data obtained by other experimental methods, indicate that TFAAA-based elementary strings have diameters of 1–2 nm, being crystalline, molecularly thin, quasi-one-dimensional objects. The amplitude of the thermally activated bending vibrations (transverse phonons) of elementary strings is sufficient to cause the entanglement of elementary strings, which leads to the formation of larger diameter supercoiled strings.

Supercoiling as a Physical Process Providing Formation of Macroscopic Anisometric Supramolecular Structures.

Solutions of chiral and achiral trifluoroacetyl amino alcohols (TFAAA) contain anisometric structures with a diameter <1 nm and length ~7 nm. In homochiral solutions and xerogels, chiral TFAAA form strings with a diameter of ~30-100 nm and length more than ~1 μ, and achiral TFAAA condensate into isometric granule with diameter of ~1 μ. We conclude that molecular chirality determines helicity of strings within tens of nanometers or more. Stabilization of supramolecular structure of strings is presumably achieved via their supercoiling.

Generation of optical vorticity from topological defects

The propagation of an electromagnetic wave along a chiral string (or screw dislocation) is studied. Adopting the formalism of differential forms, it is shown that the singular torsion of the defect is responsible for quantized modes. Moreover, it is demonstrated that the modes thus obtained have well defined orbital angular momentum, opening the possibility for applications relevant both for cosmology and for optics.

Structural transitions in chiral solutions and a microscopic model of a chiral string

Homochiral solutions of trifluoroacetylaminoalcohols (TFAAAs) are investigated. It is established that TFAAA molecules aggregate into submicroscopic string with long-range order and helical symmetry, followed by successive formation, through supercoiling, of alternating chiral phases (elementary strings combine into microscopic due to the van der Waals interaction), observed as a structural transition with a width of 20–40°C. A microscopic model of a string is proposed, which takes into account that the stereospecificity of the multicenter interaction (complementarity) imposed by chirality leads to a stacking compact molecular packing (submicroscopic or elementary) of strings with a long-range order.

String fluid in local equilibrium

We study the solutions of string fluid equations under the assumption of a local equilibrium which was previously obtained in the context of the kinetic theory. We show that the fluid can be foliated into noninteracting submanifolds whose equations of motion are exactly that of the wiggly strings considered previously by Vilenkin and Carter. In a special case of negligible statistical variance in either the left- or the right-moving directions of microscopic strings, the submanifolds are described by the action of a null-current-carrying chiral string. When both variances vanish the submanifolds are described by the Nambu-Goto action and the string fluid reduces to the string dust introduced by Stachel.

Initiation of the formation of chiral strings: Dimension of formation domain, microstructure, and nucleation mechanism

The initiation of the formation of strings in low-concentration chiral solutions was experimentally studied. The domains of initiation were classified according to dimensions: (0–3)D. The dipole-dipole mechanism of the formation of anisotropic nucleation in a mesophase was considered. The role of dispersion interactions in the assembly of supramolecular stacks was estimated at ∼0.3–0.4 eV. The threshold values of string formation in chiral mixtures were determined. A phenomenon of the formation of paired strings was established and characterized.

Formation of chiral strings under various macroscopic conditions

It has been established that the growth rate of strings decreases exponentially with time in a closed capillary and increases in inverse proportion to the time remaining until dryout in a drying solution drop. The obtained time dependences indicate that strings are formed simultaneously from a small number of nucleations, and the dissolved substance is condensed on the edge of a growing string, thus confirming the inertness of its side surface; when a solution contains a condensed nonstring phase, its concentration is low, and it does not produce any effect on the kinetics of the growth of strings.