String Action Research Articles

Confinement and screening via holographic Wilson loops

Abstract We present the holographic dual to a family of $$ \mathcal{N} $$ N = 1 SCFTs in four dimensions, deformed by a VEV leading to a gapped system. We calculate Wilson loops in this system containing adjoint, bifundamental, and fundamental matter. We calculate the quark-antiquark energy E in terms of their separation L, finding an approximate analytic expression for E(L). This expression shows the transition between conformal, confining, and screened behaviors. Interesting phenomenology is discussed in a variety of examples. The tool used is the minimization of the F1 string action, for which the code used is made publicly available.

Global aspects of 3-form gauge theory: implications for axion-Yang-Mills systems

We investigate the proposition that axion-Yang-Mills systems are characterized by a 3-form gauge theory in the deep infrared regime. This hypothesis is rigorously examined by initially developing a systematic framework for analyzing 3-form gauge theory coupled to an axion, specifically focusing on its global properties. The theory consists of a BF term deformed by marginal and irrelevant operators and describes a network of vacua separated by domain walls converging at the junction of an axion string. It encompasses 0- and 3-form spontaneously broken global symmetries. Utilizing this framework, in conjunction with effective field theory techniques and ’t Hooft anomaly-matching conditions, we argue that the 3-form gauge theory faithfully captures the infrared physics of the axion-Yang-Mills system. The ultraviolet theory is an SU(N) Yang-Mills theory endowed with a massless Dirac fermion coupled to a complex scalar and is characterized by chiral and genuine ℤm1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbb{Z}}_m^{(1)} $$\\end{document} 1-form center symmetries, with a mixed anomaly between them. It features two scales: the vev of the complex scalar, v, and the strong-coupling scale, Λ, with Λ ≪ v. Below v, the fermion decouples and a U(1)(2) 2-form winding symmetry emerge, while the 1-form symmetry is enhanced to ℤN1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbb{Z}}_N^{(1)} $$\\end{document}. As we flow below Λ, matching the mixed anomaly necessitates introducing a dynamical 3-form gauge field of U(1)(2), which appears as the incarnation of a long-range tail of the color field. The infrared theory possesses spontaneously broken chiral and emergent 3-form global symmetries. It passes several checks, among which: it displays the expected restructuring in the hadronic sector upon transition between the vacua, and it is consistent under the gauging of the genuine ℤm1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbb{Z}}_m^{(1)} $$\\end{document} ⊂ ℤN1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbb{Z}}_N^{(1)} $$\\end{document} symmetry.

Induced domain walls of QCD axion, and gravitational waves

We show that heavy axion domain walls induce domain walls of the QCD axion through a mixing between the heavy axion and the QCD axion, even when the pre-inflationary initial condition is assumed for the QCD axion. The induced domain walls arise because the effective θ parameter changes across the heavy axion domain walls, shifting the potential minimum of the QCD axion. When the heavy axion domain walls collapse, the induced QCD axion domain walls collapse as well. This novel mechanism for producing the QCD axions can explain dark matter even with the axion decay constant as small as 𝒪(109) GeV. In particular, this scenario requires domain wall collapse near the QCD crossover, potentially accounting for the stochastic gravitational wave background suggested by recent pulsar timing array observations, including NANOGrav. Using this mechanism, it is also possible to easily create induced domain walls for string axions or axions with a large decay constant, which would otherwise be challenging. We also comment on the implications for cosmic birefringence using induced axion domain walls.

Non-relativistic expansion of open strings and D-branes

We expand the relativistic open bosonic string in powers of 1/c2 where c is the speed of light. We perform this expansion to next-to-leading order in 1/c2 and relate our results to known descriptions of non-relativistic open strings obtained by taking limits. Just as for closed strings the non-relativistic expansion is well-defined if the open string winds a circle in the target space. This direction must satisfy Dirichlet boundary conditions. It is shown that the endpoints of the open string behave as Bargmann particles in the non-relativistic regime. These open strings end on nrDp-branes with p ≤ 24. When these nrDp-branes do not fluctuate they correspond to (p + 1)-dimensional Newton-Cartan submanifolds of the target space. When we include fluctuations and worldvolume gauge fields their dynamics is described by a non-relativistic version of the DBI action whose form we derive from symmetry considerations. The worldvolume gauge field and scalar field of a nrD24-brane make up the field content of Galilean electrodynamics (GED), and the effective theory on the nrD24-brane is precisely a non-linear version of GED. We generalise these results to actions for any nrDp-brane by demanding that they have the same target space gauge symmetries that the non-relativistic open and closed string actions have. Finally, we show that the nrDp-brane action is transverse T-duality covariant. Our results agree with the findings of Gomis, Yan and Yu in [1].

Towards a Surreal Super p-Branes

In this work, it is proved that it makes sense to pursue the idea of de veloping a theory of surreal super p-branes. One uses the fact that the real numbers are contained in the surreal number set and therefore at the classical level all functions in the string action, or in general in the p-brane action, can be considered as quantities build in terms of the fundamental blocks of dyadic rational fractions. However, a partial basic formalism is only presented. Therefore, this work can be considered as a progress report, which, in a sense, may motivate, among other things, the introduction of an approach in which relativistic tops and p-branes are combined.

Cosmological dynamics of string theory axion strings

The quantum chromodynamics (QCD) axion may solve the strong CP problem and explain the dark matter (DM) abundance of our Universe. The axion was originally proposed to arise as the pseudo-Nambu-Goldstone boson of global U(1)PQ Peccei-Quinn (PQ) symmetry breaking, but axions also arise generically in string theory as zero modes of higher-dimensional gauge fields. In this work we show that string theory axions behave fundamentally differently from field theory axions in the early Universe. Field theory axions may form axion strings if the PQ phase transition takes place after inflation. In contrast, we show that string theory axions do not generically form axion strings. In special inflationary paradigms, such as D-brane inflation, string theory axion strings may form; however, their tension is parametrically larger than that of field theory axion strings. We then show that such QCD axion strings overproduce the DM abundance for all allowed QCD axion masses and are thus ruled out, except in scenarios with large warping. A loop-hole to this conclusion arises in the axiverse, where an axion string could be composed of multiple different axion mass eigenstates; a heavier eigenstate could collapse the network earlier, allowing for the QCD axion to produce the correct DM abundance and also generating observable gravitational wave signals. Published by the American Physical Society 2024

Axion string source modeling

In this paper, we investigate the effect of the string radius of curvature RGaussian on the massive and massless scalar radiation emitted from collisions of traveling waves propagating along an axion (global cosmic) string. We construct initial conditions for two colliding Gaussians and perform parameter scans over their amplitude A and standard deviation σd. We show that these collisions emit isotropic bursts of massless radiation and that the energy emitted via this channel obeys a power law ∼∝Aγ, where the coefficient γ depends on the regime of A/δ and δ is the string width. Massive radiation is exponentially suppressed ∼∝e−ζRGaussian in the quasilinear regime σd≫δ and exhibits power-law decay ∼∝RGaussian−γ′ in the nonlinear regime σd≲2δ, with different ζ and γ′ in different regimes of RGaussian. In this nonlinear regime, massive particle radiation can comprise up to 50% of the total energy emitted. Drawing on a known parallel between axion radiation from global strings and gravitational radiation from Abelian-Higgs strings, this suggests that massive particle radiation may become significant with respect to the massless (gravitational) channel for such nonlinear burst signals. For all configurations studied, we obtain a spectral index q≳1 for the axion radiation, where q→1 as A increases; i.e., a higher proportion of radiation is emitted in high-frequency modes. Published by the American Physical Society 2024

Gravitational axiverse spectroscopy: seeing the forest for the axions

We consider inflationary models with multiple spectator axions coupled to dark gauge sectors via Chern-Simons (CS) terms. The energy injection into Abelian gauge fields from the axions engenders a multi-peak profile for scalar and tensor spectra. We highlight the constraining power of CMB spectral distortions on the scalar signal and discuss the conditions under which spectator sectors can account for the recently observed stochastic gravitational wave (GW) background in the nHz range. Given the tantalizing prospect of a multi-peak “GW forest” spanning several decades in frequency, we elaborate on possible ultraviolet origins of the spectator models from Type IIB orientifolds. String compactifications generically produce a multitude of axions, the “Axiverse”, from dimensional reduction of p-form gauge fields. The CS coupling of such axions to dark gauge fields in the worldvolume theory of D7-branes can be tuned via multiple brane wrappings and/or quantized gauge field strengths. If string axions coupled to Abelian gauge fields undergo slow-roll during inflation, they produce GW signals with peaked frequency distribution whose magnitude depends on the details of the compactification. We discuss the restrictions on spectator models from consistency and control requirements of the string compactification and thereby motivate models that may live in the string landscape as opposed to the swampland.

Numerical investigation of wellbore damage due to drill string lateral vibration

During drilling operations, cyclic loading is exerted on the wellbore wall by the vibrations of the drill string. This loading could lead to rock fatigue, which in turn might result in wellbore failure. In this study, a numerical model is developed to simulate the effects of repeated loading on rock fatigue and failure. The simulation is based on an elasto-plastic constitutive model coupled with a damage mechanics approach, which allows us to examine the wellbore instability due to drill string vibrations. The model is verified with the existing data in the literature related to experiments on impact of a steel ball against a curved wall. The findings indicate that cyclic loading increases the development of plastic strain around the wellbore significantly compared to static conditions, promoting rock fatigue. Furthermore, the cyclic loading expands the radius of the yielded zone substantially, a critical factor for maintaining wellbore integrity. The proposed model can be used to evaluate the wellbore stability under repetitive loading caused by the drill string action.

The quality/cosmology tension for a post-inflation QCD axion

It is difficult to construct a post-inflation QCD axion model that solves the axion quality problem (and hence the Strong CP problem) without introducing a cosmological disaster. In a post-inflation axion model, the axion field value is randomized during the Peccei-Quinn phase transition, and axion domain walls form at the QCD phase transition. We emphasize that the gauge equivalence of all minima of the axion potential (i.e., domain wall number equals one) is insufficient to solve the cosmological domain wall problem. The axion string on which a domain wall ends must exist as an individual object (as opposed to a multi-string state), and it must be produced in the early universe. These conditions are often not satisfied in concrete models. Post-inflation axion models also face a potential problem from fractionally charged relics; solving this problem often leads to low-energy Landau poles for Standard Model gauge couplings, reintroducing the quality problem. We study several examples, finding that models that solve the quality problem face cosmological problems, and vice versa. This is not a no-go theorem; nonetheless, we argue that it is much more difficult than generally appreciated to find a viable post-inflation QCD axion model. Successful examples may have a nonstandard cosmological history (e.g., multiple types of cosmic axion strings of different tensions), undermining the widespread expectation that the post-inflation QCD axion scenario predicts a unique mass for axion dark matter.

Primordial black holes from axion domain wall collapse

The QCD axion can solve the Strong CP Problem and be the dark matter of our universe. If the PQ symmetry breaking scale associated with the axion is below the inflationary reheating temperature, axion strings and domain walls populate the universe. Most of these strings and walls decay away into axion dark matter, but a small subset of the walls will be self-enclosed surfaces that are not attached to any strings. These enclosed walls can collapse in on themselves, compressing a large amount of energy into a small volume and potentially forming primordial black holes (PBHs). We study the number density and dynamics of these self-enclosed walls, taking into account their size distribution, Hubble expansion, asphericities, and all stages of domain wall dynamics using a combination of semi-analytic and numerical approaches. We find that axion models with a high axion decay constant fa, such as those of interest in early matter-dominated cosmologies, yield a PBH abundance potentially observable by future gravitational lensing surveys. We note that the formalism developed here is also useful for predicting relic PBH abundances in other models that exhibit unstable domain walls.

Action of the Axial U(1) Non-Invertible Symmetry on the ’t Hooft Line Operator: A Lattice Gauge Theory Study

Abstract We study how the symmetry operator of the axial $U(1)$ non-invertible symmetry acts on the ’t Hooft line operator in the $U(1)$ gauge theory by employing the modified Villain-type lattice formulation. We model the axial anomaly by a compact scalar boson, the “QED axion”. For the gauge invariance, the simple ’t Hooft line operator, which is defined by a line integral of the dual $U(1)$ gauge potential, must be “dressed” by the scalar and $U(1)$ gauge fields. A careful consideration on the basis of the anomalous Ward–Takahashi identity containing the ’t Hooft operator with the dressing factor and a precise definition of the symmetry operator on the lattice shows that the symmetry operator leaves no effect when it sweeps out a ’t Hooft loop operator. This result appears inequivalent with the phenomenon concluded in the continuum theory. In an appendix, we demonstrate that the half-space gauging of the magnetic $\mathbb {Z}_N$ 1-form symmetry, when formulated in an appropriate lattice framework, leads to the same conclusion as above. A similar result is obtained for the axion string operator.

Ultrahigh frequency primordial gravitational waves beyond the kHz: The case of cosmic strings

We investigate gravitational-wave backgrounds (GWBs) of primordial origin that would manifest only at ultrahigh frequencies, from kilohertz to 100 gigahertz, and leave no signal at LIGO, the Einstein Telescope, the Cosmic Explorer, LISA, or pulsar-timing arrays. We focus on GWBs produced by cosmic strings and make predictions for the GW spectra scanning over high-energy scale (beyond 1010 GeV) particle physics parameters. Signals from local string networks can easily be as large as the big bang nucleosynthesis/cosmic microwave background bounds, with a characteristic strain as high as 10−26 in the 10 kHz band, offering prospects to probe grand unification physics in the 1014–1017 GeV energy range. In comparison, GWB from axionic strings is suppressed (with maximal characteristic strain ∼10−31) due to the early matter era induced by the associated heavy axions. We estimate the needed reach of hypothetical futuristic GW detectors to probe such GWB and, therefore, the corresponding high-energy physics processes. Beyond the information of the symmetry-breaking scale, the high-frequency spectrum encodes the microscopic structure of the strings through the position of the UV cutoffs associated with cusps and kinks, as well as potential information about friction forces on the string. The IR slope, on the other hand, reflects the physics responsible for the decay of the string network. We discuss possible strategies for reconstructing the scalar potential, particularly the scalar self-coupling, from the measurement of the UV cutoff of the GW spectrum. Published by the American Physical Society 2024

Zero modes of massive fermions delocalize from axion strings

Massless chiral excitations can arise from the interactions between a fermion and an axion string, propagating along the string and allowing it to superconduct. The properties of these excitations, or zero modes, dictate how the string interacts with light and can thus have important phenomenological consequences. In this paper, we add a nowhere-vanishing Dirac mass for the fermion in the usual model of axion electrodynamics. We find that the zero modes exhibit an interesting phase structure in which they delocalize from the string’s core as the mass increases, up until a critical value past which they disappear. We study this structure from an analytic perspective, with explicit numerical solutions, and via anomaly inflow arguments. Finally, we derive the two-dimensional effective theory of the zero mode and its interactions with the four-dimensional gauge field and show how this effective theory breaks down as the zero modes delocalize.

Quantization of Axion-Gauge Couplings and Noninvertible Higher Symmetries.

We derive model-independent quantization conditions on the axion couplings (sometimes known as the anomaly coefficients) to the standard model gauge group [SU(3)×SU(2)×U(1)_{Y}]/Z_{q} with q=1, 2, 3, 6. Using these quantization conditions, we prove that any QCD axion model to the right of the E/N=8/3 line on the |g_{aγγ}|-m_{a} plot must necessarily face the axion domain wall problem in a postinflationary scenario. We further demonstrate the higher-group and noninvertible global symmetries in the standard model coupled to a single axion. These generalized global symmetries lead to universal bounds on the axion string tension and the monopole mass. If the axion were discovered in the future, our quantization conditions could be used to constrain the global form of the standard model gauge group.

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 fa≲1012 GeV, up to model dependence on the ultraviolet completion, for axion masses ma≲10−29 eV; future CMB surveys could find striking evidence of axion strings with lower decay constants. Published by the American Physical Society 2024

Pulsating strings in I-brane background

We study pulsating strings both on a single stack of NS5-branes and two orthogonal stacks of NS5-branes (the so called I-brane) by using the Polyakov form of the fundamental string action. For the I-brane background, by using a symmetry that decouples the two spheres from the flat geometry, we study pulsating solutions of the string when it pulsates on both the spheres independently and simultaneously. We finally derive the energy of pulsating strings as a function of adiabatic invariant oscillation number in these cases and studied some limiting cases in detail.

Massless fermions and superconductivity of string-wall composites

An axion cosmic string is known to be a chiral superconductor when the axion couples to an electrically charged fermion. After the QCD phase transition, a QCD axion string is attached by N domain walls. We would like to elucidate the fate of massless fermions on a global string after domain walls attached not only in the axion model but also in general models having string-wall composites. We investigate the Dirac equation under various string-wall composite backgrounds both in the axion(-like) models and in the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 supersymmetry inspired Abelian-Higgs models. We give an answer to the elementary question of whether massless fermions exist, and if so, where they are localized. The answer depends on fermion/boson masses in the models, and the massless fermion can be localized either on the string, on one of the domain walls, or in one of the vacua. We find analytic solutions for the fermion zero mode function by which we prove the existence of the massless fermion on the string-wall composites. We also show supercurrents flowing along the string-wall composites and anomalous electric currents flowing in from outside.

Stochastic gravitational wave background from early dark energy

We study the production of stochastic gravitational wave background in early dark energy (EDE) models. It is generated by resonant amplification of scalar field fluctuations, which can easily take place for typical EDE potential based on the string axion or α-attractor model. The resultant spectrum of gravitational wave background is computed by performing 3D lattice simulations. We show that, specifically in some class of a generalized α-attractor EDE model, a significant amount of gravitational waves can be produced via tachyonic instability with a peak around femto-Hz frequency range. Models predicting such gravitational waves can be constrained by cosmic microwave background observations.

Non-invertible Gauss law and axions

In axion-Maxwell theory at the minimal axion-photon coupling, we find non-invertible 0- and 1-form global symmetries arising from the naive shift and center symmetries. Since the Gauss law is anomalous, there is no conserved, gauge-invariant, and quantized electric charge. Rather, using half higher gauging, we find a non-invertible Gauss law associated with a non-invertible 1-form global symmetry, which is related to the Page charge. These symmetries act invertibly on the axion field and Wilson line, but non-invertibly on the monopoles and axion strings, leading to selection rules related to the Witten effect. We also derive various crossing relations between the defects. The non-invertible 0- and 1-form global symmetries mix with other invertible symmetries in a way reminiscent of a higher-group symmetry. Using this non-invertible higher symmetry structure, we derive universal inequalities on the energy scales where different infrared symmetries emerge in any renormalization group flow to the axion-Maxwell theory. Finally, we discuss implications for the Weak Gravity Conjecture and the Completeness Hypothesis in quantum gravity.