Gauge String Research Articles

Gravitational waves from cosmic superstrings and gauge strings

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 3σ unless the string coupling gs< 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.

Gauged global strings

We investigate the string solutions and cosmological implications of the gauge U(1)Z × global U(1)PQ model. With two hierarchical symmetry-breaking scales, the model exhibits three distinct string solutions: a conventional global string, a global string with a heavy core, and a gauge string as a bound state of the two global strings. This model reveals rich phenomenological implications in cosmology. During the evolution of the universe, these three types of strings can form a Y-junction configuration. Intriguingly, when incorporating this model with the QCD axion framework, the heavy-core global strings emit more axion particles compared to conventional axion cosmic strings due to their higher tension. This radiation significantly enhances the QCD axion dark matter abundance, thereby opening up the QCD axion mass window. Consequently, axions with masses exceeding ~ 10−5 eV have the potential to constitute the whole dark matter abundance. Furthermore, in contrast to conventional gauge strings, the gauge strings in this model exhibit a distinctive behavior by radiating axions.

Causality in string field theory

In this letter, we will investigate causality in string field theory using pp-wave light-cone gauge string field theory. We will generalise the Ramsey scheme to string field theory, and use it to analyze string field theoretical processes. An explicit characteristic function for interactive string field theory will be built using this string field theoretical Ramsey scheme. The average of the difference between the initial and final values of any operator described in string field theory will be obtained using this characteristic function. We will use the quantum information theoretical technique based on quantum Fisher information to extract information about such string field theoretical processes.

Anomalous U(1) gauge bosons and string physics at the forward physics facility

We show that experiments at the Forward Physics Facility, planned to operate near the ATLAS interaction point during the LHC high-luminosity era, will be able to probe predictions of Little String Theory by searching for anomalous U(1) gauge bosons living in the bulk. The interaction of the abelian broken gauge symmetry with the Standard Model is generated at the one-loop level through kinetic mixing with the photon. Gauge invariant generation of mass for the U(1) gauge boson proceeds via the Higgs mechanism in spontaneous symmetry breaking, or else through anomaly-cancellation appealing to Stückelberg-mass terms. We demonstrate that FASER2 will be able to probe string scales over roughly two orders of magnitude: 105≲Ms/TeV≲107.

Spectral form factor for free large N gauge theory and strings

We investigate the spectral form factor in two different systems, free large N gauge theories and highly excited string gas. In both cases, after a rapid decay of the spectral form factor at early time, new contributions come in, preventing the spectral form factor from ever becoming exponentially small. We consider U(N) gauge theories with only adjoint matter and compute the spectral form factor using a matrix integral of the thermal holonomy U. The new saddles differ from the early time saddle by preserving certain subgroups of the center symmetry. For a gas of strings, the short time decay of the spectral form factor is governed by the continuous Hagedorn density of states, which can be associated to the thermal winding mode with winding number ±1. We show that the rise of the spectral form factor comes from other winding modes that also carry momentum along the time direction. We speculate on the existence of a family of classical solutions for these string modes, similar to the Horowitz-Polchinski solution.We review a similar problem for black holes. In particular, we examine the Kontsevich-Segal criterion on complex black holes that contribute to the spectral form factor. In the canonical ensemble quantity Z(β + it), the black hole becomes unallowed at t ~ mathcal{O} (β). A way to avoid this is to consider the microcanonical ensemble, where the black hole stays allowable.

Size Matters: Historical String Lengths and Possible Tunings of the Chitarrone or Theorbo

What was considered the "normal" size for the Italian theorbo or chitarrone upon its creation in the 17th century, and why should 21st century players like us embrace the historical size? This research tackles the question from several different angles: description in historical texts, surviving instruments, the optimal string gauge and tension, and tone comparison. The study finds the vast majority of surviving chitarroni to have a stopped string length around 88-89cm, with some exceeding 90cm and very few falling short of 80cm. This sparks the question of whether smaller instruments required a different tuning. Upon comparing with lute family instruments from the same era, the logical conclusion is that smaller instruments with string lengths around 76cm most probably did not need to have a double re-entrant tuning which is the standard tuning for all solo chitarrone music. When comparing a large instrument (95cm) and a small instrument (76cm, with single re-entrant tuning), one can hear that they perform very different roles as continuo instruments, and are not mutually replaceable. As modern-day lutenists, one should really embrace the large size if one wishes to play the chitarrone, and develop a technique to suit the instrument, instead of scaling down the instrument to suit the technique. Menglin Gao has been a recorder player, a countertenor, and now a theorbist, studying at the Royal Conservatoire of the Hague. He is the founder and director of the Shanghai Camerata, an early music ensemble based in Shanghai, China.

Numerical and experimental assessment of string gauge influence on guitar tone

String gauge is known for affecting a guitar's tone, playability and volume. It is often a subject of debate between younger players and becomes a staple and signature of older ones. The choice between the heavier or lighter strings is usually made based on personal taste and practical reasons. Although string gauge is intuitively associated with fatter or thinner sound, physics behind string vibration do not necessarily confirm this assumption. In the study, the impact of string gauge on the guitar's tone is assessed in several ways. A numerical study is carried out, introducing a time-domain dynamic analysis of a coupled string-structure system. A basic experimental study is also performed to validate the numerical results. The study is focused on estimation of the three aspects of sound—harmonic composition, sustain and volume—and how they are affected by the guitar's string gauge.

Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond N-ality

We study a 3d lattice gauge theory with gauge group U(1)N−1 ⋊ SN, which is obtained by gauging the SN global symmetry of a pure U(1)N−1 gauge theory, and we call it the semi-Abelian gauge theory. We compute mass gaps and string tensions for both theories using the monopole-gas description. We find that the effective potential receives equal contributions at leading order from monopoles associated with the entire SU(N) root system. Even though the center symmetry of the semi-Abelian gauge theory is given by ℤN, we observe that the string tensions do not obey the N-ality rule and carry more detailed information on the representations of the gauge group. We find that this refinement is due to the presence of non-invertible topological lines as a remnant of U(1)N−1 one-form symmetry in the original Abelian lattice theory. Upon adding charged particles corresponding to W-bosons, such non-invertible symmetries are explicitly broken so that the N-ality rule should emerge in the deep infrared regime.

Volumes And Random Matrices

AbstractThis article is an introduction to newly discovered relations between volumes of moduli spaces of Riemann surfaces or super Riemann surfaces, simple models of gravity or supergravity in two dimensions, and random matrix ensembles. (The article is based on a lecture at the conference on the Mathematics of Gauge Theory and String Theory, University of Auckland, January 2020)

The duality between F-theory and the heterotic string in $$D=8$$ with two Wilson lines

We construct non-geometric string compactifications by using the F-theory dual of the heterotic string compactified on a two-torus with two Wilson line parameters, together with a close connection between modular forms and the equations for certain K3 surfaces of Picard rank $16$. We construct explicit Weierstrass models for all inequivalent Jacobian elliptic fibrations supported on this family of K3 surfaces and express their parameters in terms of modular forms generalizing Siegel modular forms. In this way, we find a complete list of all dual non-geometric compactifications obtained by the partial higgsing of the heterotic string gauge algebra using two Wilson line parameters.

Lattice Gauge Theories and String Dynamics in Rydberg Atom Quantum Simulators

Gauge theories are the cornerstone of our understanding of fundamental interactions among particles. Their properties are often probed in dynamical experiments, such as those performed at ion colliders and high-intensity laser facilities. Describing the evolution of these strongly coupled systems is a formidable challenge for classical computers, and represents one of the key open quests for quantum simulation approaches to particle physics phenomena. Here, we show how recent experiments done on Rydberg atom chains naturally realize the real-time dynamics of a lattice gauge theory at system sizes at the boundary of classical computational methods. We prove that the constrained Hamiltonian dynamics induced by strong Rydberg interactions maps exactly onto the one of a $U(1)$ lattice gauge theory. Building on this correspondence, we show that the recently observed anomalously slow dynamics corresponds to a string-inversion mechanism, reminiscent of the string-breaking typically observed in gauge theories. This underlies the generality of this slow dynamics, which we illustrate in the context of one-dimensional quantum electrodynamics on the lattice. Within the same platform, we propose a set of experiments that generically show long-lived oscillations, including the evolution of particle-antiparticle pairs. Our work shows that the state of the art for quantum simulation of lattice gauge theories is at 51 qubits, and connects the recently observed slow dynamics in atomic systems to archetypal phenomena in particle physics

ESR and Radiocarbon Dating of Gut Strings from Early Plucked Instruments

Early European plucked instruments have recently experienced a great revival, but a few aspects remain unknown (e.g., the gauge of gut strings). Here we report, for the first time, that the electron spin resonance (ESR) signal intensity of oxidized iron, Fe(III), from gut strings at g = 2 increases linearly with age within a few hundred years. The signal increase in the remaining old strings on early instruments can be used to judge if they are as old as or younger than the instrument. Obtaining the authenticity information of gut strings contributes to the revival of the old instruments and the music.

α′-Corrections to DBI action via T-duality constraint

It is known that Dp-brane effective action at the leading order of α′ in flat space–time which is given by DBI action, transforms to Dp−1-brane effective action under standard T-duality transformations of the open string gauge bosons and transverse scalar fields. Extending this duality to order α′, one may find corrections to the DBI action which include the second fundamental form Ω and the covariant derivative of gauge field strength DF, as well as the corrections to the T-duality transformations. Using this idea, up to two parameters, we have found all 81 covariant couplings of DFDF and ΩΩ with zero, two, four and six F's. The four gauge field couplings that the T-duality constraint fixes are consistent with the known couplings in the literature.

Cello in the Baroque, part 1

The article was based on a fragment of the author’s doctoral dissertation entitled The birth of cello as a solo instrument – instruments, practice, and selected literature examples (Academy of Music in Łódź, chapter The evolution of cello in the 17th century) and consists of two parts. The first part outlines of the evolution of cello from its birth in the 16th century to the 18th century (the text is supplemented with illustrations), whereas the second part describes the role and use of cello in music of that period. The introduction to the article includes a critical reference to the list of academic and popular science publications therein, in Polish and other languages, touching on the cello issue in the 17th and 18th centuries. The historical part touches on the circumstances of how the violin family emerged with a special attention paid to bass representatives of that group of instruments. Following a detailed analysis of preserved instruments, their reliable copies, luthier publications, illustrations and treatises from that period, the author discussed the construction of the earlies cellos. Apart from data concerning sizes and scale length of these instruments, the article includes information about their body, neck, fingerboard (with slope angle), bridge and tailpiece, materials they were made of, and types and gauge of strings used at that time. It also describes cello tuning methods. Moreover, the author mentions different types of cello (piccolo, da spalla, basse de violon) and different ways of how it was held. A separate issue are the bows, especially types of bows, their evolution and ways of holding. This part of the article is concluded with a list of different names of bass variants of the violin used in the 16th and 17th centuries before the name cello/violoncello finally settled. The second part of the article elaborates on the most important functions of cello: as a consort instrument, a universal continuo instrument or a solo instrument. Cello (along with viola da gamba or dulcian/bassoon) managed especially well as a melodic instrument co-rendering the continuo parts, and the result was that the basso continuo became the most important domain of cello in the Baroque, having a significant influence on the shape of playing technique and performance practice of that instrument. As one of melodic bass instruments, cello performed an important role in shaping the concertante style, along with the violin, shawm/oboe, cornet or flute. It was that practice combined with the improvisation practice developed simultaneously (which also influenced the development of the instrument itself) that the idea to write first autonomous compositions for the cello (solo, chamber or with basso continuo) emerged from at the end of the 17th century. Continuation of this article, which shall be devoted to Baroque works for the cello and their composers, will be published in the following issue of “Notes Muzyczny”.

Influence of damping and nonlinearity in plucked strings: Why do light-gauge strings sound brighter?

When monofilament nylon strings of different tensions are used on a plucked instrument like the guitar or lute, it is readily observed that a lower-tension string tends to give a brighter sound. The elementary linear theory of a plucked string predicts no such effect. Linear theory can be extended to include bending stiffness and frequencydependent damping: Detailed measurements on a range of nylon strings are analysed to enable this extended model to be made quantitatively accurate. It is shown that a small influence of the string gauge is predicted, but synthesis based on this model does not match measurements or perceived differences of sound quality. Two nonlinear effects are then explored. The familiar effect of coupling between transverse and axial vibration in the string is shown to account for some observed features, but still does not explain the large difference of sound. The evidence from measurements strongly suggests that the mechanism responsible for the sound differences involves nonlinear interaction between the string and other parts of the structure, such as the frets. Because a lower-tension string tends to be played at larger amplitude, such buzzing interactions are more likely to occur. Implications for makers and players of instruments like the lute are discussed.

Many-Body Chern Numbers of ν = 1/3 and 1/2 States on Various Lattices

For various two dimensional lattices such as honeycomb, kagome, and square-octagon, gauge conventions (string gauge) realizing minimum magnetic fluxes that are consistent with the lattice periodicity are explicitly given. Then many-body interactions of lattice fermions are projected into the Hofstadter bands to form pseudopotentials. By using these pseudopotentials, degenerate many-body ground states are numerically obtained. We further formulate a scheme to calculate the Chern number of the ground state multiplet by the pseudopotentials. For the filling factor of the lowest Landau level, $\nu=1/3$, a simple scaling form of the energy gap are numerially obtained and the ground state is unique except the three-fold topological degeneracy. This is a quantum liquid, which can be lattice analogue of the Laughlin state. For the $\nu=1/2$ case, validity of the composite fermion picture is discussed in relation to the existence of the Fermi surface. Effects of disorder are also described.

The physics of unwound and wound strings on the electric guitar applied to the pitch intervals produced by tremolo/vibrato arm systems.

The physics of wound and unwound strings on the electric guitar are presented here, and the pitch intervals produced by the movements of a Fender Stratocaster tremolo unit are explained. Predicted changes in pitch sensitivity of different strings are given, and experimentally verified, for changes in saddle height, the distance of string free to move behind the nut and ratio of diameters/masses of the core and windings of wound strings. Also, it is shown that changes to the gauge of strings (assuming the string tension is sufficient for linear behaviour and in absence of changes to other construction details) don’t alter the pitch intervals produced by a given angle of tremolo arm use assuming the instrument is set up with the same sounding pitches and starting bridge angle. It is demonstrated that it not possible to equalise the relative sensitivity of unwound steel stings on a Fender Stratocaster type tremolo unit through string construction techniques. The ratio of core to winding mass in the string, on the other hand, was found to be a very powerful design parameter for choosing the sensitivity of the string to tremolo arm use and standard pitch bends. For instance, the pitch intervals produced by operation of tremolo arm for wound strings may be made to approximately match that for one of the unwound strings if they share very similar core gauges (assuming the winding masses are chosen to give approximately the same tension at their sounding pitches). Such a design, only available currently by custom order, also delivers the optimum equalisation in sensitivity of strings for standard string bends (due to these also being produced by altering the length of the string to generate changes in tension and therefore pitch).

Holographic corrections to meson scattering amplitudes

We compute meson scattering amplitudes using the holographic duality between confining gauge theories and string theory, in order to consider holographic corrections to the Veneziano amplitude and associated higher-point functions. The generic nature of such computations is explained, thanks to the well-understood nature of confining string backgrounds, and two different examples of the calculation in given backgrounds are used to illustrate the details. The effect we discover, whilst only qualitative, is re-obtainable in many such examples, in four-point but also higher point amplitudes.

Worldsheet theory of light-cone gauge noncritical strings on higher genus Riemann surfaces

It is possible to formulate light-cone gauge string field theory in noncritical dimensions. Such a theory corresponds to conformal gauge worldsheet theory with nonstandard longitudinal part. We study the longitudinal part of the worldsheet theory on higher genus Riemann surfaces. The results in this paper shall be used to study the dimensional regularization of light-cone gauge string field theory.

Gauge theory and string topology

Given a principal bundle over a closed manifold, \(G \rightarrow P \rightarrow M\), let \(P^{Ad} \rightarrow M\) be the associated adjoint bundle. Gruher and Salvatore (Proc Lond Math Soc 96(3), 78106 2008) showed that the Thom spectrum \((P^\mathrm{Ad})^{-TM}\) is a ring spectrum whose corresponding product in homology is a Chas-Sullivan type string topology product. We refer to this spectrum as the “string topology spectrum of P”, \( \mathcal {S}(P)\). In the universal case when P is contractible, \(\mathcal {S}(P) \simeq LM^{-TM}\) where LM is the free loop space of the manifold. This ring spectrum was introduced by the authors in Cohen et al. (Math Annalen 324, 773–798 2002) as a homotopy theoretic realization of the Chas-Sullivan string topology of M. The main purpose of this paper is to introduce an action of the gauge group of the principal bundle, \(\mathcal {G}(P)\) on the string topology spectrum \(\mathcal {S}(P)\), and to study this action in detail. Indeed we study the entire group of units and the induced representation \(\mathcal {G}(P) \rightarrow GL_1(\mathcal {S}(P))\). We show that this group of units is the group of homotopy automorphisms of the fiberwise suspension spectrum of P. More generally we describe the homotopy type of the group of homotopy automorphisms of any E-line bundle for any ring spectrum E. We import some of the basic ideas of gauge theory, such as the action of the gauge group on the space of connections to the setting of E-line bundles over a manifold and do explicit calculations. We end by discussing a functorial perspective, which describes a sense in which the string topology spectrum \(\mathcal {S}(P)\) of a principal bundle is the “linearization” of the gauge group \(\mathcal {G}(P)\).