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DOE OSTI2025

String-based model with Hagedorn temperature of 𝑇 𝐻 ∼ 300 MeV describes the spectrum of mesons and glueballs

We consider the thermodynamics of a color-confined phase of quantum chromodynamics (QCD) and pure gauge theory within a string-inspired corresponding to a physical spatial dimension, 𝑑 = 3. We show that the physical mass spectrum of massive mesons—in both the strange and nonstrange sectors separately—is reasonably well described and extended by the exponential mass spectrum of open strings, 𝜌⁡(𝑚), characterized by a unique Hagedorn temperature 𝑇 𝐻 = $\sqrt3⁢𝜎/2⁢𝜋$, expressed by the string tension 𝜎. This 𝑇 𝐻 is the value appropriate for 𝑑 = 3 spatial dimensions and is of the order of 𝑇 𝐻 ∼ 300 MeV for typical values of the string tension. It is much larger than the values of 𝑇 𝐻 which have been phenomenologically extracted so far to describe the meson spectrum. Glueball states in pure gauge theory, modeled by closed strings, exhibit a similarly large Hagedorn temperature, highlighting a universal feature of the exponential spectrum. We further analyze the thermodynamic properties of the equation of state at finite temperature and demonstrate that, in the confined phase, the string models agree with lattice QCD results. This lends further support to the recent interpretation of the QCD phase diagram that incorporates strings as relevant degrees of freedom.

Phase transitions↗

DOE OSTI2020

Cosmic filaments from cosmic strings

Cosmic strings are generically predicted in many extensions of the Standard Model of particle physics. In this work, we propose a new avenue for detecting cosmic strings through their effect on the filamentary structure in the cosmic web. Using cosmological simulations of the density wake from a cosmic string, we examine a variety of filament structure probes. We show that the largest effect of the cosmic string is an overdensity in the filament distribution around the string wake. The signal from the overdensity is stronger at higher redshift and more robust with a wider field. We analyze the spatial distribution of filaments from a publicly available catalog of filaments built from Sloan digital sky survey galaxies. With existing data, we find no evidence for the presence of a cosmic string wake with string tension parameter $\textit{Gμ}$ above 5 × 10 –6 . However, we project WFIRST will be able to detect a signal from such a wake at the 99% confidence level at redshift $\textit{z}$ = 2, with significantly higher confidence and the possibility of probing lower tensions ($\textit{Gμ}$ ~ 10 –6 ), at $\textit{z}$ = 10. The sensitivity of this method is not competitive with constraints derived from the cosmic microwave background. However, it provides an independent discovery channel at low redshift, which could be a smoking gun in scenarios in which the cosmic microwave background bound can be weakened.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1985

Gravitational lensing effects of vacuum strings - Exact solutions

Exact interior and exterior solutions to Einstein's field equations are derived for vacuum strings. The exterior solution for a uniform density vacuum string corresponds to a conical space while the interior solution is that of a spherical cap. For Mu equals 0-1/4 the external metric is ds-squared = -dt-squared + dr-squared + (1-4 Mu)-squared r-squared dphi-squared + dz-squared, where Mu is the mass per unit length in the string in Planck masses per Planck length. A maximum mass per unit length for a string is 6.73 x 10 to the 27th g/cm. It is shown that strings cause temperature fluctuations in the cosmic microwave background and produce equal brightness double QSO images separated by up to several minutes of arc. Formulae for lensing probabilities, image splittings, and time delays are derived for strings in a realistic cosmological setting. String searches using ST, the VLA, and the COBE satellite are discussed.

Gott, J. R., III↗

NASA NTRS2002

String Stability of a Linear Formation Flight Control System

String stability analysis of an autonomous formation flight system was performed using linear and nonlinear simulations. String stability is a measure of how position errors propagate from one vehicle to another in a cascaded system. In the formation flight system considered here, each i(sup th) aircraft uses information from itself and the preceding ((i-1)(sup th)) aircraft to track a commanded relative position. A possible solution for meeting performance requirements with such a system is to allow string instability. This paper explores two results of string instability and outlines analysis techniques for string unstable systems. The three analysis techniques presented here are: linear, nonlinear formation performance, and ride quality. The linear technique was developed from a worst-case scenario and could be applied to the design of a string unstable controller. The nonlinear formation performance and ride quality analysis techniques both use nonlinear formation simulation. Three of the four formation-controller gain-sets analyzed in this paper were limited more by ride quality than by performance. Formations of up to seven aircraft in a cascaded formation could be used in the presence of light gusts with this string unstable system.

Allen, Michael J.↗

NASA NTRS2015

The String Stability of a Trajectory-Based Interval Management Algorithm in the Midterm Airspace

NASA's first Air Traffic Management (ATM) Technology Demonstration (ATD-1) was created to facilitate the transition of mature ATM technologies from the laboratory to operational use. The technologies selected for demonstration are the Traffic Management Advisor with Terminal Metering (TMA-TM), which provides precise time-based scheduling in the terminal airspace; Controller Managed Spacing (CMS), which provides terminal controllers with decision support tools enabling precise schedule conformance; and Interval Management (IM), which consists of flight deck automation that enables aircraft to achieve or maintain a precise spacing interval behind a target aircraft. As the percentage of IM equipped aircraft increases, controllers may provide IM clearances to sequences, or strings, of IM-equipped aircraft. It is important for these strings to maintain stable performance. This paper describes an analytic analysis of the string stability of the latest version of NASA's IM algorithm and a fast-time simulation designed to characterize the string performance of the IM algorithm. The analytic analysis showed that the spacing algorithm has stable poles, indicating that a spacing error perturbation will be reduced as a function of string position. The fast-time simulation investigated IM operations at two airports using constraints associated with the midterm airspace, including limited information of the target aircraft's intended speed profile and limited information of the wind forecast on the target aircraft's route. The results of the fast-time simulation demonstrated that the performance of the spacing algorithm is acceptable for strings of moderate length; however, there is some degradation in IM performance as a function of string position.

Swieringa, Kurt A.↗

DOE OSTI2025

How to falsify string theory at a collider

The string landscape accommodates a broad range of possible effective field theories. This poses a challenge for extracting verifiable predictions as well as falsifiable signatures of string theory. Motivated by these considerations, in this work we observe that all known stringy standard models support only low-dimensional representations of the gauge group. While it is in principle possible to produce contrived models with higher-dimensional representations, these generically appear in a tower of states with lighter ones in lower-dimensional representations, i.e., not in isolation. With this in mind, we consider the phenomenologically well-motivated scenario given by adding a single Majorana field in a real, 𝑛-dimensional representation of 𝑆⁢𝑈⁢(2) 𝐿 with 𝑛≥5 and nothing else . This scenario is not realized in any known string construction, and we conjecture that this is true of string theory in general. Detection of this scenario would thus amount to falsifying the (known) string landscape. We recast existing LHC searches for new electroweak states to extract updated bounds on this class of scenarios. Improved limits from future colliders and dark matter detection experiments provide additional routes to potentially falsifying string theory.

extensions of fermion sector↗

DOE OSTI2021

Heisenberg spin chain as a worldsheet coordinate for lightcone quantized string

Although the energy spectrum of the Heisenberg spin chain on a circle defined by H = 1 4 Σ k = 1 M σ k x σ k + 1 x + σ k y σ k + 1 y + Δ σ k z σ k + 1 z is well known for any fixed M, the boundary conditions vary according to whether Mϵ 4N + r, where r = -1,0,1,2, and also according to the parity of the number of overturned spins in the state, In string theory all these cases must be allowed because interactions involve a string with M spins breaking into strings with M 1 < M and M - M 1 spins (or vice versa). We organize the energy spectrum and degeneracies of H in the case Δ = 0 where the system is equivalent to a system of free fermions. In spite of the multiplicity of special cases, in the limit M → ∞ the spectrum is that of a free compactified worldsheet field. Such a field can be interpreted as a compact transverse string coordinate x(σ) ≡ x(σ) + R 0 . We construct the bosonization formulas explicitly in all separate cases, and for each sector give the Virasoro conformal generators in both fermionic and bosonic formulations. Furthermore from calculations in the literature for selected classes of excited states, there is strong evidence that the only change for Δ ≠ 0 is a change in the compactification radius R 0 → R Δ . As Δ→ -1 this radius goes to infinity, giving a concrete example of noncompact space emerging from a discrete dynamical system. Finally we apply our work to construct the three string vertex implied by a string whose bosonic coordinates emerge from this mechanism.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Factorization of chiral string amplitudes

We re-examine a closed-string model defined by altering the boundary conditions for one handedness of two-dimensional propagators in otherwise-standard string theory. We evaluate the amplitudes using Kawai-Lewellen-Tye factorization into open-string amplitudes. The only modification to standard string theory is effectively that the spacetime Minkowski metric changes overall sign in one open-string factor. This cancels all but a finite number of states: as found in earlier approaches, with enough supersymmetry (e.g., type II) the tree amplitudes reproduce those of the massless truncation of ordinary string theory. However, we now find for the other cases that additional fields, formerly thought to be auxiliary, describe new spin-2 states at the two adjacent mass levels (tachyonic and tardyonic). The tachyon is always a ghost, but can be avoided in the heterotic case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Segmented strings in AdS 3

We study segmented strings in flat space and in AdS 3 . In flat space, these well known classical motions describe strings which at any instant of time are piecewise linear. In AdS 3 , the worldsheet is composed of faces each of which is a region bounded by null geodesics in an AdS 2 subspace of AdS 3 . The time evolution can be described by specifying the null geodesic motion of kinks in the string at which two segments are joined. The outcome of collisions of kinks on the worldsheet can be worked out essentially using considerations of causality. We study several examples of closed segmented strings in AdS 3 and find an unexpected quasi-periodic behavior. Here, we also work out a WKB analysis of quantum states of yo-yo strings in AdS 5 and find a logarithmic term reminiscent of the logarithmic twist of string states on the leading Regge trajectory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

THE FLOW AROUND A COSMIC STRING. I. HYDRODYNAMIC SOLUTION

Cosmic strings are linear topological defects which are hypothesized to be produced during inflation. Most searches for strings have relied on the string’s lensing of background galaxies or the cosmic microwave background. In this paper, I obtained a solution for the supersonic flow of collisional gas past the cosmic string which has two planar shocks with a shock compression ratio that depends on the angle defect of the string and its speed. The shocks result in the compression and heating of the gas and, given favorable conditions, particle acceleration. Gas heating and over-density in an unusual wedge shape can be detected by observing the Hi line at high redshifts. Particle acceleration can occur in the present-day universe when the string crosses the hot gas contained in galaxy clusters and, since the consequences of such a collision persist for cosmological timescales, could be located by looking at unusual large-scale radio sources situated on a single spatial plane.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Axion string dynamics I: 2+1D

If the axion exists and if the initial axion field value is uncorrelated at causally disconnected points, then it should be possible to predict the efficiency of cosmological axion production, relating the axionic dark matter density to the axion mass. The main obstacle to making this prediction is correctly treating the axion string cores. We develop a new algorithm for treating the axionic string cores correctly in 2+1 dimensions. When the axionic string cores are given their full physical string tension, axion production is about twice as efficient as in previous simulations. We argue that the string network in 2+1 dimensions should behave very differently than in 3+1 dimensions, so this result cannot be simply carried over to the physical case. We outline how to extend our method to 3+1D axion string dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Voltage-Matched Strings using 3-Terminal Tandems: Fundamentals and End Losses

Strings constructed from 3-terminal tandem (3TT) cells can provide some of the performance benefits of voltage-matching with less cell complexity than strings based on 4-terminal tandem cells. However, the circuitry for a 3TT string can become more complex, making circuit analysis more challenging. Here we illustrate the essential features of single-polarity voltage-matched (VM) 3TT strings using representative examples. End losses are intrinsic to this type of string, but can be reduced by minimizing m and n in the Vtop/Vbot VM ratio m/n, and further mitigated by increasing the string length. This analysis agrees with preliminary experimental results.

3TT↗

DOE OSTI2014

TeV-Scale Strings

This article discusses the status of string physics where the string tension is around the TeV scale. Here, the article covers model building basics for perturbative strings, based on D-brane configurations. The effective low energy physics description of such string constructions is analyzed: how anomaly cancellation is implemented, how fast proton decay is avoided and how D-brane models lead to additional Z' particles. This review also discusses direct search bounds for strings at the TeV scale, as well as theoretical issues with model building related to flavor physics and axions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Gravitational waves from cosmic superstrings and gauge strings

Abstract We perform a phenomenological comparison of the gravitational wave (GW) spectrum expected from cosmic gauge string networks and superstring networks comprised of multiple string types. We show how violations of scaling behavior and the evolution of the number of relativistic degrees of freedom in the early Universe affect the GW spectrum. We derive simple analytical expressions for the GW spectrum from superstrings and gauge strings that are valid for all frequencies relevant to pulsar timing arrays (PTAs) and laser interferometers. We analyze the latest data from PTAs and show that superstring networks are consistent with 32 nHz data from NANOGrav, but are excluded by 3.2 nHz data at 3σunless the string couplingg s <0.2 or the strings evolve in only about 10% of the volume of the higher-dimensional space. We also point out that while gauge string networks are excluded by NANOGrav-15 data at 3σ, they are completely compatible with EPTA and PPTA data. Finally, we study correlations between GW signals at PTAs and laser interferometers.

Physics↗

DOE OSTI2015

Role of string-like collective atomic motion on diffusion and structural relaxation in glass forming Cu-Zr alloys

We investigate Cu-Zr liquid alloys using molecular dynamics simulation and well-accepted embedded atom method potentials over a wide range of chemical composition and temperature as model metallic glass-forming (GF) liquids. As with other types of GF materials, the dynamics of these complex liquids are characterized by “dynamic heterogeneity” in the form of transient polymeric clusters of highly mobile atoms that are composed in turn of atomic clusters exhibiting string-like cooperative motion. In accordance with the string model of relaxation, an extension of the Adam-Gibbs (AG) model, changes in the activation free energy ΔG{sub a} with temperature of both the Cu and Zr diffusion coefficients D, and the alpha structural relaxation time τ{sub α} can be described to a good approximation by changes in the average string length, L. In particular, we confirm that the strings are a concrete realization of the abstract “cooperatively rearranging regions” of AG. We also find coexisting clusters of relatively “immobile” atoms that exhibit predominantly icosahedral local packing rather than the low symmetry packing of “mobile” atoms. These two distinct types of dynamic heterogeneity are then associated with different fluid structural states. Glass-forming liquids are thus analogous to polycrystalline materials where the icosahedrally packed regions correspond to crystal grains, and the strings reside in the relatively disordered grain boundary-like regions exterior to these locally well-ordered regions. A dynamic equilibrium between localized (“immobile”) and wandering (“mobile”) particles exists in the liquid so that the dynamic heterogeneity can be considered to be type of self-assembly process. We also characterize changes in the local atomic free volume in the course of string-like atomic motion to better understand the initiation and propagation of these fluid excitations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

Cosmic microwave background constraints for global strings and global monopoles

We present the first cosmic microwave background (CMB) power spectra from numerical simulations of the global O( N ) linear σ-model, with N =2,3, which have global strings and monopoles as topological defects. In order to compute the CMB power spectra we compute the unequal time correlators (UETCs) of the energy-momentum tensor, showing that they fall off at high wave number faster than naive estimates based on the geometry of the defects, indicating non-trivial (anti-)correlations between the defects and the surrounding Goldstone boson field. We obtain source functions for Einstein-Boltzmann solvers from the UETCs, using a recently developed method that improves the modelling at the radiation-matter transition. We show that the interpolation function that mimics the transition is similar to other defect models, but not identical, confirming the non-universality of the interpolation function. The CMB power spectra for global strings and global monopoles have the same overall shape as those obtained using the non-linear σ-model approximation, which is well captured by a large- N calculation. However, the amplitudes are larger than the large- N calculation would naively predict, and in the case of global strings much larger: a factor of 20 at the peak. Finally we compare the CMB power spectra with the latest CMB data in other to put limits on the allowed contribution to the temperature power spectrum at multipole l = 10 of 1.7% for global strings and 2.4% for global monopoles. These limits correspond to symmetry-breaking scales of 2.9× 10{sup 15} GeV (6.3× 10{sup 14} GeV with the expected logarithmic scaling of the effective string tension between the simulation time and decoupling) and 6.4× 10{sup 15} GeV respectively. The bound on global strings is a significant one for the ultra-light axion scenario with axion masses m {sub a} ∼< 10{sup −28} eV . These upper limits indicate that gravitational waves from global topological defects will not be observable at the gravitational wave observatory LISA.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Signatures of primordial energy injection from axion strings

Axion strings are horizon-size topological defects that may be produced in the early Universe. Ultralight axion-like particles may form strings that persist to temperatures below that of big bang nucleosynthesis. Such strings have been considered previously as sources of gravitational waves and cosmic microwave background (CMB) polarization rotation. In this work we show, through analytic arguments and dedicated adaptive mesh refinement cosmological simulations, that axion strings deposit a subdominant fraction of their energy into high-energy Standard Model (SM) final states, for example, by the direct production of heavy radial modes that subsequently decay to SM particles. This high-energy SM radiation is absorbed by the primordial plasma, leading to novel signatures in precision big bang nucleosynthesis, the CMB power spectrum, and gamma-ray surveys. In particular, we show that CMB power spectrum data constrains axion strings with decay constants f a ≲ 10 12 GeV , up to model dependence on the ultraviolet completion, for axion masses m a ≲ 10 − 29 eV ; future CMB surveys could find striking evidence of axion strings with lower decay constants. Published by the American Physical Society 2024

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Thermal nature of confining strings

We investigate the quantum statistical properties of the confining string connecting a static fermion-antifermion pair in the massive Schwinger model. By analyzing the reduced density matrix of the subsystem located in between the fermion and antifermion, we demonstrate that as the interfermion separation approaches the string-breaking distance, the overlap between the microscopic density matrix and an effective thermal density matrix exhibits a pronounced, narrow peak, approaching unity at the onset of string breaking. This behavior reveals that the confining flux tube evolves toward a genuinely thermal state as the separation between the charges grows, even in the absence of an external heat bath. In other words, one cannot tell whether a reduced state of the subsystem arises from a surrounding heat bath or from entanglement with the rest of the system. The entanglement spectrum near the critical string-breaking distance exhibits a rapid transition from the dominance of a single state describing the confining electric string towards a strongly entangled state containing virtual fermion-antifermion pairs. Our findings establish a quantitative link between confinement, entanglement, and emergent thermality, and suggest that string breaking corresponds to a microscopic thermalization transition within the flux tube.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗