Special Gauge Research Articles

Higgs branch of 6D (1, 0) SCFTs and little string theories with Dynkin DE-type SUSY enhancement

We detail the Higgs branches of 6D (1, 0) superconformal field theories (SCFTs) and little string theories (LSTs) that exhibit supersymmetry-enhancing Higgs branch renormalization group flows to the 6D (2, 0) SCFTs and LSTs of type DE. Generically, such theories are geometrically engineered in F-theory via a configuration of (−2)-curves, arranged in an (affine) DE-type Dynkin diagram, and supporting special unitary gauge algebras; this describes the effective field theory on the tensor branch of the SCFT. For the Higgsable to D-type (2, 0) SCFTs/LSTs, there generically also exists a type IIA brane description, involving a Neveu-Schwarz orientifold plane, which allows for the derivation of a magnetic quiver for the Higgs branch. These are 3D N=4 unitary-orthosymplectic quivers whose Coulomb branch is isomorphic to the Higgs branch of the 6D theories. From this magnetic quiver, together with an extended quiver subtraction algorithm that we explain, the foliation structure of the Higgs branch as a symplectic singularity is unveiled. For this class of 6D SCFTs, we observe a simple rule, which we refer to as “slice subtraction,” to read off the transverse slice in the foliation from the tensor branch. Based on this slice subtraction observation, we conjecture the transverse slices in the Higgsable to E-type (2, 0) Hasse diagram, where the SCFTs lack any known magnetic quiver for their Higgs branches. Published by the American Physical Society 2024

Gravitational corrections to the two-loop beta function in a non-Abelian gauge theory

This paper investigates the coupling of massive fermions to gravity within the context of a non-Abelian gauge theory, utilizing the effective field theory framework for quantum gravity. Specifically, we calculate the two-loop beta function of the gauge coupling constant in a non-Abelian gauge theory, employing the one-graviton exchange approximation. Our findings reveal that gravitational corrections may lead to a nontrivial UV fixed point in the beta function of the gauge coupling constant, contingent upon the specific gauge group and the quantity of fermions involved. Published by the American Physical Society 2024

Gauge-independent transition dividing the confinement phase in the lattice SU(2) gauge-adjoint scalar model

The lattice SU(2) gauge-scalar model with the scalar field in the adjoint representation of the gauge group has two completely separated confinement and Higgs phases according to the preceding studies based on numerical simulations that have been performed in the specific gauge fixing based on the conventional understanding of the Brout-Englert-Higgs mechanism. In this paper, we reexamine this phase structure in a gauge-independent way based on the numerical simulations performed without any gauge fixing. This is motivated to confirm the recently proposed gauge-independent Brout-Englert-Higgs mechanism for generating the mass of the gauge field without relying on any spontaneous symmetry breaking. For this purpose, we investigate correlations between gauge-invariant operators obtained by combining the original adjoint scalar field and the new field called the color-direction field which is constructed from the gauge field based on the gauge-covariant decomposition of the gauge field due to Cho-Duan-Ge-Shabanov and Faddeev-Niemi. Consequently, we reproduce gauge independently the transition line separating the confinement phase and the Higgs phase, and show surprisingly the existence of a new transition line that completely divides the confinement phase into two parts. Finally, we discuss the physical meaning of the new transition and the implications of the confinement mechanism. Published by the American Physical Society 2024

Probing bad theories with the dualization algorithm. Part II.

We continue our analysis of bad theories initiated in [1], focusing on quiver theories with bad unitary and special unitary gauge groups in three dimensions. By extending the dualization algorithm we prove that the partition function of bad linear quivers can be written as a distribution, given by a sum of terms involving a product of delta functions times the partition function of a good quiver theory. We describe in detail the good quiver theories appearing in the partition function of the bad theory and discuss the brane interpretation of our result. We also discuss in detail the lift of these theories to 4d quivers with symplectic gauge groups, in which our results can be recovered by studying the Higgsing triggered by the expectation value for certain chiral operators. The paper is accompanied by a Mathematica file which implements the algorithm for an arbitrary unitary bad linear quiver.

Holography for Sp(2Nc) gauge dynamics: from composite Higgs to technicolour

We study Sp(2Nc) gauge dynamics with two Dirac fermion flavours in the fundamental representation. These strongly coupled systems underlie some composite Higgs models with a global symmetry breaking pattern SU(4)→Sp(4), leading to a light quartet of pseudo-Goldstone bosons that can play the role of the Higgs. Including four-fermion interactions can rotate the vacuum to a technicolour breaking pattern. Using gauge/gravity duality, we study the underlying gauge dynamics. Our model incorporates the Nc-specific running of the fermion anomalous dimension and can thus distinguish between specific gauge groups. We determine the bound-state spectrum of the UV SU(4)→Sp(4) symmetry breaking model, also including fermion masses and mass splitting, and display the Nc dependence. The inclusion of a four-fermion interaction shows the emergence of three Goldstone bosons on the path to technicolour dynamics.

Superselection-resolved entanglement in lattice gauge theories: a tensor network approach

Lattice gauge theories (LGT) play a central role in modern physics, providing insights into high-energy physics, condensed matter physics, and quantum computation. Due to the nontrivial structure of the Hilbert space of LGT systems, entanglement in such systems is tricky to define. However, when one limits themselves to superselection-resolved entanglement, that is, entanglement corresponding to specific gauge symmetry sectors (commonly denoted as superselection sectors), this problem disappears, and the entanglement becomes well-defined. The study of superselection-resolved entanglement is interesting in LGT for an additional reason: when the gauge symmetry is strictly obeyed, superselection-resolved entanglement becomes the only distillable contribution to the entanglement. In our work, we study the behavior of superselection-resolved entanglement in LGT systems. We employ a tensor network construction for gauge-invariant systems as defined by Zohar and Burrello [1] and find that, in a vast range of cases, the leading term in superselection-resolved entanglement depends on the number of corners in the partition — corner-law entanglement. To our knowledge, this is the first case of such a corner-law being observed in any lattice system.

Vine Copula-Based Multivariate Distribution of Rainfall Intensity, Wind Speed, and Wind Direction for Optimizing Qatari Meteorological Stations

This study employs copula functions to establish the dependency structure of the joint distribution among rainfall intensity, wind speed, and wind direction in Qatar. Based on a Vine Copula, the trivariate distribution between rainfall intensity, wind speed, and wind direction is found to exhibit a root-mean-square error (RMSE) of 0.0072 on the observed vs. modeled cumulative probabilities using ranked normalized observations. It is also found that the winter Shamal winds are most pronounced during rainfall. However, a secondary component of easterly winds known as the Kaus winds is also found to exert an important influence. This wind pattern is observable during rainfall at all the selected stations, albeit with minor variations. It is also found that rainfall stations where the rainfall is obstructed in any way from northwest to north and from east to southeast significantly influence the rainfall measurements. Specific rain gauges in Qatar are found to be situated in disrupted surroundings, such as meteorological stations close to passing traffic, where road spray could infiltrate the rain gauge funnel, impacting the accuracy of rainfall measurements. The study results necessitated the relocation of approximately half of these roadside gauges to mitigate wind-induced biases from road spray. An evaluation of operations is recommended for approximately 80 meteorological stations responsible for measuring rainfall in Qatar. The methodology devised in this study holds potential for application to other Middle Eastern countries and regions with similar climates.

DPSV trick for spherically symmetric backgrounds

We discuss the approach suggested by Deffayet et al. (DPSV) to analysing the linearized perturbations in Horndeski theory in the case of a static, spherically symmetric background. In L3 subclass of Horndeski theories we prove the validity of the DPSV approach by showing that the original method corresponds to a specific gauge choice in the quadratic action for perturbations. We also show that in the case of a spherically symmetric background the DPSV trick does not work in a more general L4 Horndeski theory.

First-order formalism for Alice string

We apply the first-order formalism method to obtaining BPS equations for Alice string. This is done by generalizing the well-known first-order formalism to the case of non-Abelian strings. We do not assume any specific gauge group nor the shape of the kinetic term function, but require only that the fields are axially-symmetric and static. With this formalism we reproduce the BPS equations of SU(2)×U(1) Alice strings (Chatterjee and Nitta, 2017), and present their corresponding numerical solutions.

Exploring Seiberg-like N-alities with eight supercharges

We show that a large subclass of 3d 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} = 4 quiver gauge theories consisting of unitary and special unitary gauge nodes with only fundamental/bifundamental matter have multiple Seiberg-like IR duals. A generic quiver T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{T} $$\\end{document} in this subclass has a non-zero number of balanced special unitary gauge nodes and it is a good theory in the Gaiotto-Witten sense. We refer to this phenomenon as IR N-ality and the set of mutually IR dual theories as the N-al set associated with the quiver T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{T} $$\\end{document}. Starting from T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{T} $$\\end{document}, we construct a sequence of dualities by step-wise implementing a set of quiver mutations which act locally on the gauge nodes. The associated N-al theories can then be read off from this duality sequence. The quiver T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{T} $$\\end{document} generically has an emergent Coulomb branch global symmetry in the IR, such that the rank of the IR symmetry is always greater than the rank visible in the UV. We show that there exists at least one theory in the N-al set for which the rank of the IR symmetry precisely matches the rank of the UV symmetry. In certain special cases that we discuss in this work, the correct emergent symmetry algebra itself may be read off from this preferred theory (or theories) in addition to the correct rank. Finally, we give a recipe for constructing the 3d mirror associated with a given N-al set and show how the emergent Coulomb branch symmetry of T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{T} $$\\end{document} is realized as a UV-manifest Higgs branch symmetry of the 3d mirror. This paper is the second in a series of four papers on 3d 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} = 4 Seiberg-like dualities, preceded by the work [1].

Rainfall prediction for data scares areas using metrological satellites in the case of the Lake Tana sub-basin, Ethiopia

Abstract In African nations with complex topographies, alternative rainfall estimation methods such as satellites are crucial. This study is aimed at predicting the spatial and temporal distribution of rainfall in the Lake Tana sub-basin from 1990 to 2020. A satellite-based rainfall estimate of Climate Hazards Group Infrared Precipitation with Station data (CHIRPS) was used with the same spanning period (1990–2020). The validation process employs point-to-pixel analysis, comparing CHIRPS estimates with observed data at specific gauge stations. The findings showed that CHIRPS had well-estimated rainfall incidence in the highland areas and significantly overestimated it in the lowland areas. The Mann–Kendall trends for January, June, and August indicate decreasing trends, while the Bega and spring seasons show notable declines. Regression analysis reveals a non-significant decrease in annual rainfall with the highest rainfall in the summer and relatively dry winters. In addition, the coefficient of variation value of 26.37% suggests a moderate level of variability around the mean annual rainfall. In conclusion, the CHIRPS satellite exhibited varied performance across the Tana Sub-basin, with site-specific discrepancies and notable inaccuracies at certain stations. The study underscores the importance of considering local factors and topography in satellite-based rainfall assessments, providing valuable insights for agricultural planning in the region.

New Classification Method for Equivalence Classes on S1/Z2 and T2/Z3 Orbifolds

Abstract In 5D and 6D U(N) and SU(N) gauge theories compactified on S1/Z2 and T2/Z3 orbifolds, we propose a new method to classify the equivalence classes (ECs) of boundary conditions (BCs) without depending on the structure of gauge transformations. Some of the BCs are connected through gauge transformations and constitute ECs, each of which contains physically equivalent BCs. Previous methods for classifying ECs have been used for specific gauge transformations. In this paper, we show that a geometric property of orbifolds significantly narrows down the possibilities of connecting BCs and completes the classification of ECs.

Ordered exponential and its features in Yang–Mills effective action

In this paper, we discuss some non-trivial relations for ordered exponentials on smooth Riemannian manifolds. As an example of application, we study the dependence of the four-dimensional quantum Yang–Mills effective action on the special gauge transformation with respect to the background field. Also, we formulate some open questions about a structure of divergences for a special type of regularization in the presence of the background field formalism.

Capillary Schwarz symmetrization in the half-space

AbstractIn this article, we introduce a notion of capillary Schwarz symmetrization in the half-space. It can be viewed as the counterpart of the classical Schwarz symmetrization in the framework of capillary problem in the half-space. A key ingredient is a special anisotropic gauge, which enables us to transform the capillary symmetrization to the convex symmetrization introduced in Alvino et al.https:/doi.org/10.1016/S0294-1449(97)80147-3.

Compression and Fatigue Testing of High-Strength Thin Metal Sheets by Using an Anti-Buckling Device

BackgroundThe modelling of the sheet metal forming operations requires accurate and precise data of the material plastic behaviour along non-proportional strain paths. However, the buckling phenomenon severely limits the compressive strain range that could be used to deform thin metal sheets.ObjectiveThe main aim of this paper was to propose an effective device, that enables to determine of accurate stress-strain characteristics of thin metal sheet specimens subjected to axial deformation without buckling and with a special emphasis on friction correction.MethodsIn this paper, an anti-buckling fixture was proposed to assess the deformation characteristics of X10CrMoVNb9-1 (P91) power engineering steel, and DP500 and DP980 dual-phase steels, under compression loading. The fixture enables monitoring of the friction between the specimen and supporting blocks during the test, and thus the precise stress response of the material could be determined.ResultsThe effectiveness of the fixture was evaluated under tension–compression cyclic loading and during the compression tests in which high-strength thin metal sheets were successfully deformed up to 10% without specimen buckling. Furthermore, the successful determination of a friction force variation between supporting blocks and the specimen during tests enabled to determine an actual force acting on the specimen.ConclusionsThe proposed testing fixture was successfully assessed during the compression and cyclic tension–compression of high-strength thin metal sheets as no buckling was observed. Its advantage lies in adapting to change its length with specimen elongation or shrinkage during a test. The friction force generated from a movement of both parts of the device could be effectively monitored by the special strain gauge system during testing and thus its impact on the stress-strain characteristics could be successfully eliminated.

Development of Automatic Inspection Systems for WRS2020 Plant Disaster Prevention Challenge Using Image Processing

In this article, an approach used for the inspection tasks in the WRS2020 Plant Disaster Prevention Challenge is explained. The tasks were categorized into three categories: reading pressure gauges, inspecting rust on a tank, and inspecting cracks in a tank. For reading pressure gauges, the “you only look once” algorithm was used to focus on a specific pressure gauge and check the pressure gauge range strings on the gauge using optical character recognition algorithm. Finally, a previously learned classifier was used to read the values shown in the gauge. For rust inspection, image processes were used to focus on a target plate that may be rusted for rust detection. In particular, it was necessary to report the rust area and distribution type. Thus, the pixel ratio and grouping of rust were used to count the rust. The approach for crack inspection was similar to that for rust. The target plate was focused on first, and then the length of the crack was measured using image processing. Its width was not measured but was calculated using the crack area and length. For each system developed to approach each task, the results of the preliminary experiment and those of WRS2020 are shown. Finally, the approaches are summarized, and planned future work is discussed.

Symmetry fractionalization in the gauge mean-field theory of quantum spin ice

Symmetry fractionalization is a ubiquitous feature of topologically ordered states that can be used to classify different symmetry-enriched topological phases and reveal some of their unique experimental signatures. Despite its vast popularity, there is currently no available framework to study symmetry fractionalization of quantum spin ice (QSI) -- a $U(1)$ quantum spin liquid (QSL) on the pyrochlore lattice supporting emergent photons -- within the most widely used theoretical framework to describe it, gauge mean-field theory (GMFT). In this work, we provide an extension of GMFT that allows for the classification of space-time symmetry fractionalization. The construction classifies all GMFT Ans\"atze that yield physical wavefunctions invariant under given symmetries and a specific low-energy gauge structure. As an application of the framework, we first show that the only two Ans\"atze with emergent $U(1)$ gauge fields that respect all space-group symmetries are the well-known 0- and $\pi$-flux states. We then showcase how the framework may describe QSLs beyond the currently known ones by classifying chiral $U(1)$ QSI. We find two new states described by $\pi/2$- and $3\pi/2$-fluxes of the emergent gauge field threading the hexagonal plaquettes of the pyrochlore lattice. We finally discuss how the different ways translation symmetries fractionalize for all these states lead to unique experimentally relevant signatures and compute their respective inelastic neutron scattering cross-section to illustrate the argument.

Профіль ободу коліс пасажирського вагонa для умов спільної експлуатації на українських і європейських залізницях

The relevance of this work stems from the urgent need for the modern development of the Ukrainian railway transport and the acceleration of Ukraine's integration into the European railway transportation. Currently, the most effective way to travel across borders between countries with different track gauges is the use of gauge-changeable wheelsets, a system that can change from one gauge to another when moving through special gauge changing facilities. The use of cars with gauge-changeable wheelsets on the Ukrainian and European railways calls for assuring a good compatibility of the wheel-rail pair on tracks of both gauges. The goal of this work was to develop a unified wheel profile for the operation on the domestic and European railways and predict the safety of cars with that wheel profile, the ride quality, and processes of wheel-rail dynamic interaction for tracks with different parameters. Use was made of methods of deformable solid mechanics, statistical dynamics, and numerical integration. A family of wheel profiles was constructed, and the effectiveness of their use in passenger car wheelsets on the Ukrainian (1520 mm gauge) and European (1435 mm gauge) railways was evaluated. For each profile, the spatial problem of wheel?rail contact was solved, and the interaction parameters were analyzed, including the dimensions and location of the contact patches. Calculations were also made for a car negotiating a circular curve of a small radius (R = 300 m) and moving at different speeds on tangent track sections. The choice among the constructed profiles was made according to two criteria: wheel flange wear and car dynamic stability. Based on the studies conducted, a new wear-resistant wheel profile, ITM-73EP, was proposed. Its use in gauge-changeable wheelsets of passenger cars will provide reasonable indices of wheel–rail interaction both on the Ukrainian and on the European railways without sacrificing car dynamic performance.

Correction: Two field-theoretic viewpoints on the Fukaya-Morse A∞ category

We study an enhanced version of the Morse degeneration of Fukaya $A_\infty$ category with higher compositions given by counts of gradient flow trees. The enhancement consists in allowing morphisms from an object to itself to be chains on the manifold. Higher compositions correspond to counting Morse trees passing through a given set of chains. We provide two viewpoints on the construction and on the proof of the $A_\infty$ relations for the composition maps. One viewpoint is via an effective action for the $BF$ theory computed in a special gauge. The other is via higher topological quantum mechanics.

Unified theory of thermodynamics and stochastic thermodynamics for nonlinear Langevin systems driven by non-conservative forces

We construct a unified theory of thermodynamics and stochastic thermodynamics for classical nonequilibrium systems driven by non-conservative forces, using the recently developed covariant Ito-Langevin theory. The thermodynamic forces are split into a conservative part and a non-conservative part. Thermodynamic functions are defined using the reference conservative system. Work and heat are partitioned into excess parts and house-keeping parts, which are due to, respectively, conservative forces and non-conservative forces. Excess entropy production (EP) and house-keeping EP are analogously defined. The splitting of thermodynamic forces is subjected to an arbitrariness resembling a gauge symmetry, with each gauge defining a reference conservative Langevin system. In the special Gibbs gauge, the nonequilibrium steady state (NESS) is characterized by Gibbs canonical distribution, the excess heat agrees with that defined by Hatano and Sasa, and the excess EP agrees with that of Glansdorff and Prigogine, i.e., it is the time rate of the second-order variation of system entropy near the NESS. Adopting the Gibbs gauge, and focusing on the excess parts of thermodynamic quantities, a complete analogy between thermodynamics of non-conservative systems and that of conservative systems is established. One important consequence of this analogy is that both the free energy and excess EP are minimized at NESS. Our theory therefore constitutes a statistical foundation both for the steady-state thermodynamics theory due to Sasa and Tasaki and for the stability theory of NESS due to Glansdorff and Prigogine. These results are valid even if the system is far from equilibrium. By studying detailed fluctuation theorem, we find striking differences between systems with symmetric kinetic matrices and those with asymmetric kinetic matrices. For systems with asymmetric kinetic matrices, the total EP is the sum of house-keeping EP, excess EP, and pumped entropy. Entropy pumping is an exchange of entropy between the system and environment without necessarily involving dissipation. In the presence of entropy pumping, the system may behave as either a demon or an antidemon. Fluctuation theorems and work relations are derived both for total work and for excess work. For systems with symmetric kinetic matrices, there is no entropy pumping, yet in the Gibbs gauge, the excess work and house-keeping work each satisfies a separate fluctuation theorem. We illustrate our theory using many concrete examples.