Finite Gauge Research Articles

Three-dimensional finite temperature Z2 gauge theory with tensor network scheme

We apply a tensor network scheme to finite temperature Z2 gauge theory in 2+1 dimensions. Finite size scaling analysis with the spatial extension up to Nσ = 4096 at the temporal extension of Nτ = 2, 3, 5 allows us to determine the transition temperature and the critical exponent ν at high level of precision, which shows the consistency with the Svetitsky-Yaffe conjecture.

Magnetic quivers, Higgs branches and 6d mathcal{N} = left(1,kern0.5em 0right) theories

The physics of M5 branes placed near an M9 plane on an A-type ALE singularity exhibits a variety of phenomena that introduce additional massless degrees of freedom. There are tensionless strings whenever two M5 branes coincide or whenever an M5 brane approaches the M9 plane. These systems do not admit a low-energy Lagrangian description so new techniques are desirable to shed light on the physics of these phenomena. The 6-dimensional mathcal{N} = left(1,kern0.5em 0right) world-volume theory on the M5 branes is composed of massless vector, tensor, and hyper multiplets, and has two branches of the vacuum moduli space where either the scalar fields in the tensor or hyper multiplets receive vacuum expectation values. Focusing on the Higgs branch of the low-energy theory, previous works suggest the conjecture that a new Higgs branch arises whenever a BPS-string becomes tensionless. Consequently, a single theory admits a multitude of Higgs branches depending on the types of tensionless strings in the spectrum. The two main phenomena discrete gauging and small E8instanton transition can be treated in a concise and effective manner by means of Coulomb branches of 3-dimensional mathcal{N} = 4 gauge theories. In this paper, a formalism is introduced that allows to derive a novel object from a brane configuration, called the magnetic quiver. The main features are as follows: (i) the 3d Coulomb branch of the magnetic quiver yields the Higgs branch of the 6d system, (ii) all discrete gauging and E8 instanton transitions have an explicit brane realisation, and (iii) exceptional symmetries arise directly from brane configurations. The formalism facilitates the description of Higgs branches at finite and infinite gauge coupling as spaces of dressed monopole operators.

Counting of states in Higgs theories

We enumerate the micro-states in Higgs theories, addressing (i) the number of vacuum states and (ii) the appropriate measure in the quantum path integral. To address (i) we explicitly construct the set of ground state wave-functionals in the field basis focussing on scalar modes $\theta(x)$. Firstly, we show that in the limit in which the gauge coupling is zero, we obtain an infinite set of degenerate ground states at large volume distinguished by $\theta(x)\to\theta(x)+\theta_0$, spontaneously breaking the global symmetry, as is well known. We then show that at finite gauge coupling there is a unique ground state at large volume since the wave-functional only depends on $\nabla\theta$ in the IR, and we explain this at the level of the Lagrangian. Since gauge fields fall off exponentially from sources there are no conserved charges or symmetries in the Higgs phase; so the Higgs mechanism is the removal of symmetry from the theory. We show how physical features of defects, such as cosmic strings in the abelian Higgs model, are best understood in this context. Since there is a unique ground state, we address (ii) whether the path integral is a volume measure for the radial Higgs field $\mathcal{D}\rho\,\rho^{N-1}$ from the $N$ components of the Higgs multiplet, or a line measure $\mathcal{D}\rho$ as the $N-1$ would-be Goldstones can be removed in unitary gauge. We prove that the need to avoid quartic divergences demands a tower of counter terms that resum to exactly give the volume measure. So the size of the Hilbert space in the zero gauge coupling case and finite gauge coupling case are in one-to-one correspondence, despite the degeneracy of the ground state being lifted in the latter. As a cosmological application, we point out that the volume measure can make it exponentially more unlikely in $N(=4)$ for the Standard Model Higgs to relax to the electroweak vacuum in the early universe.

The Bremsstrahlung function of mathcal{N} = 2 SCQCD

For SU(N) superconformal QCD we perform a three-loop calculation of the cusp anomalous dimension for a generalized Maldacena-Wilson operator, using HQET formalism. We obtain an expression that is valid at generic geometric and internal angles and finite gauge group rank N. For equal and opposite angles this expression vanishes, proving that at these points the cusp becomes BPS. From its small angle expansion we derive the corresponding Bremsstrahlung function at three loops, matching the matrix model prediction given in terms of derivatives of the Wilson loop on the ellipsoid. Finally, we discuss possible scenarios at higher loops, with respect to the existence of a universal effective coupling in an integrable subsector of the model.

Remarks on the Green–Schwarz Terms of Six-Dimensional Supergravity Theories

We construct the Green-Schwarz terms of six-dimensional supergravity theories on spacetimes with non-trivial topology and gauge bundle. We prove the cancellation of all global gauge and gravitational anomalies for theories with gauge groups given by products of $U(n)$, $SU(n)$ and $Sp(n)$ factors, as well as for $E_8$. For other gauge groups, anomaly cancellation is equivalent to the triviality of a certain 7-dimensional spin topological field theory. We show in the case of a finite Abelian gauge group that there are residual global anomalies imposing constraints on the 6d supergravity. These constraints are compatible with the known F-theory models. Interestingly, our construction requires that the gravitational anomaly coefficient of the 6d supergravity theory is a characteristic element of the lattice of string charges, a fact true in six-dimensional F-theory compactifications but that until now was lacking a low-energy explanation. We also discover a new anomaly coefficient associated with a torsion characteristic class in theories with a disconnected gauge group.

Dimensional reduction and the equivariant Chern character

We propose a dimensional reduction procedure in the Stolz--Teichner framework of supersymmetric Euclidean field theories (EFTs) that is well-suited in the presence of a finite gauge group or, more generally, for field theories over an orbifold. As an illustration, we give a geometric interpretation of the Chern character for manifolds with an action by a finite group.

Semi-doubled gauged linear sigma model for five-branes of codimension two

We establish a double dualization in two-dimensional supersymmetric gauge theory. We construct a gauged linear sigma model (GLSM) which contains a complex twisted linear superfield coupled to two sets of Abelian vector superfields. In the IR regime, the GLSM provides a string sigma model whose target spaces are a defect NS5-brane, a Kaluza-Klein vortex and an exotic 522-brane. All of them are five-branes of codimension two and are related by T-duality. This model is a natural extension of the GLSM proposed by Tong which gives a sigma model for an H-monopole, i.e., a smeared NS5-brane of codimension three. This is also regarded as an alternative system of the GLSM for exotic five-branes proposed by the present authors. In this analysis, we confirm that the T-duality transformation procedure in terms of the complex twisted linear superfield is applicable to dualize both the real and imaginary parts of the twisted chiral superfield even at the UV level, beyond the IR limit. This indicates that the T-duality transformations at finite gauge couplings can be performed in terms of reducible superfields in the same way as irreducible (twisted) chiral superfields. Furthermore, we study quantum vortex corrections to the GLSM at the UV level. In the IR limit, these corrections are mapped to string worldsheet instanton corrections to the five-branes of codimension two. The result completely agrees with those in double field theory analysis.

Assessment of Stress-Strain Behavior of Corroded Steel Reinforcement Using Digital Image Correlation (DIC)

Abstract Understanding the stress-strain behavior of corroded rebars is essential for understanding the structural behavior of corroding reinforced concrete structures. However, conventional methods of testing have several drawbacks, which have led to differences in opinion among researchers regarding the mechanical behavior of corroded rebars. This article proposes an improved method using Digital Image Correlation (DIC) to assess the stress-strain behavior of corroded rebars. The study is conducted in two phases: (a) development of the testing and evaluation method and (b) determination of the mechanical properties (i.e., yield strength, ultimate strength, and ultimate strain) of naturally corroded cold-twisted deformed (CTD) steel rebars using the developed method. The stress-strain behavior of one pristine plain mild (PM) steel and 13 naturally corroded steel rebars collected from a 15-year-old building are investigated in this study. The experimental results show that the proposed method can provide more accurate estimates of mechanical properties than the conventional methods. The developed method facilitates a better understanding of the stress-strain behavior at the fracture location (FL) and other local points of interest on corroded steel rebars. Because DIC measures local strains, the proposed method is able to measure local strain heterogeneity and therefore distinguish between the effects of geometrical variations from those due to true material degradation. This is in contrast to the conventional methods wherein deformation is measured over a finite gauge length, which results in a measurement of average deformation rather than true local deformation. This study emphasizes the need for measurement of full-field deformation to assess the stress-strain behavior of the corroded rebars with highly uneven cross-sectional area.

Digital quantum simulation of lattice gauge theories in three spatial dimensions

In the present work, we propose a scheme for the digital formulation of lattice gauge theories with dynamical fermions in 3 + 1 dimensions. All interactions are obtained as a stroboscopic sequence of two-body interactions with an auxiliary system. This enables quantum simulations of lattice gauge theories where the magnetic four-body interactions arising in two and more spatial dimensions are obtained without the use of perturbation theory, thus resulting in stronger interactions compared with analogue approaches. The simulation scheme is applicable to lattice gauge theories with either compact or finite gauge groups. The required bounds on the digitization errors in lattice gauge theories, due to the sequential nature of the stroboscopic time evolution, are provided. Furthermore, an implementation of a lattice gauge theory with a non-abelian gauge group, the dihedral group D3, is proposed employing the aforementioned simulation scheme using ultracold atoms in optical lattices.

Chiral and deconfinement phase transitions in QED3 with finite gauge boson mass

Based on the experimental observation that there is a coexisting region between the antiferromagnetic (AF) and d-wave superconducting (dSC) phases, the influences of gauge boson mass m a on chiral symmetry restoration and deconfinement phase transitions in QED3 are investigated simultaneously within a unified framework, i.e., Dyson–Schwinger equations. The results show that the chiral symmetry restoration phase transition in the presence of the gauge boson mass m a is a typical second-order phase transition; the chiral symmetry restoration and deconfinement phase transitions are coincident; the critical number of fermion flavors N c f decreases as the gauge boson mass m a increases, which implies that there exists a boundary that separates the N c f –m a plane into chiral symmetry breaking/confinement region for (N c f , m a ) below the boundary and chiral symmetry restoration/deconfinement region for (N c f , m a ) above it.

Delocalized SYZ mirrors and confronting top\u2013down SU(3)-structure holographic meson masses at finite g and N_c with P(article) D(ata) G(roup) values

Meson spectroscopy at finite gauge coupling – whereat any perturbative QCD computation would break down – and finite number of colors, from a top–down holographic string model, has thus far been entirely missing in the literature. This paper fills this gap. Using the delocalized type IIA SYZ mirror (with SU(3) structure) of the holographic type IIB dual of large-N thermal QCD of Mia et al. (Nucl Phys B 839:187. arXiv:0902.1540 [hep-th], 2010) as constructed in Dhuria and Misra (JHEP 1311:001. arXiv:1306.4339 [hep-th], 2013) at finite coupling and number of colors (N_c = number of D5(overline{D5})-branes wrapping a vanishing two-cycle in the top–down holographic construct of Mia et al. (Nucl Phys B 839:187. arXiv:0902.1540 [hep-th], 2010) = mathcal{O}(1) in the IR in the MQGP limit of Dhuria and Misra (JHEP 1311:001. arXiv:1306.4339 [hep-th], 2013) at the end of a Seiberg-duality cascade), we obtain analytical (not just numerical) expressions for the vector and scalar meson spectra and compare our results with previous calculations of Sakai and Sugimoto (Prog Theor Phys 113:843. doi:10.1143/PTP.113.843. arXiv:hep-th/0412141, 2005) and Dasgupta et al. (JHEP 1507:122. doi:10.1007/JHEP07(2015)122. arXiv:1409.0559 [hep-th], 2015), and we obtain a closer match with the Particle Data Group (PDG) results of Olive et al. (Particle Data Group) (Chin Phys C 38:090001, 2014). Through explicit computations, we verify that the vector and scalar meson spectra obtained by the gravity dual with a black hole for all temperatures (small and large) are nearly isospectral with the spectra obtained by a thermal gravity dual valid for only low temperatures; the isospectrality is much closer for vector mesons than scalar mesons. The black-hole gravity dual (with a horizon radius smaller than the deconfinement scale) also provides the expected large-N suppressed decrease in vector meson mass with increase of temperature.

Stress-strain Analysis of Premolars With Non-carious Cervical Lesions: Influence of Restorative Material, Loading Direction and Mechanical Fatigue.

Noncarious cervical lesions (NCCLs) are characterized by a loss of dental structure at the cementoenamel junction (CEJ) caused by stress, biocorrosion, and attrition. Variations in occlusal loading can promote different stress and strain patterns on the CEJ. Restoration of NCCLs is part of lesion management; however, there is still no conclusive restorative protocol for NCCLs. This study aimed to evaluate the stress and strain distribution of maxillary premolars with NCCLs according to three factors: 1) restorative technique; 2) direction of occlusal loading; and 3) mechanical fatigue. Three-dimensional (3D) finite element analysis (FEA) and strain gauge testing were used to assess stress and strain, respectively. 3D-FEA orthotropic, linear, and elastic models were generated: sound tooth (SO); unrestored NCCL; or NCCL restored with glass ionomer; flowable composite resin; nanofilled composite resin (CR); lithium disilicate ceramic; and nanofilled composite resin core associated with a lithium disilicate laminate (CL). A 150-N compressive static load was applied in two conditions: axially in both cusps (Al); and at a 45° angle to the long axis of the tooth applied to the palatine cusp (Ol). For the experimental tests, specimens were treated as described previously, and one strain gauge was attached to the buccal surface of each tooth to record tooth strains before and after cyclic loading (200,000 cycles, 50 N). FEA showed that the association of NCCL and Ol resulted in higher stress values. CR and CL restorations showed the closest biomechanical behavior to SO for both loading types. Loaded Al or Ol specimens showed higher strain values after mechanical fatigue. Lower stress and strain were observed with Al when compared with Ol. The restoration of NCCLs with composite resin only or associated with ceramic laminates seems to be the best approach because the results for those groups were similar in biomechanical behaviors to sound teeth.

BPS boojums in ${\cal N}=2$ supersymmetric gauge theories I

We study 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) composite solitons of vortex strings, domain walls and boojums in ${\cal N}=2$ supersymmetric Abelian gauge theories in four dimensions. We obtain solutions to the 1/4 BPS equations with the finite gauge coupling constant. To obtain numerical solutions for generic coupling constants, we construct globally correct approximate functions which allow us to easily find fixed points of gradient flow equations. We analytically/numerically confirm that the negative mass of a single boojum appearingat the endpoint of the vortex string on the logarithmically bent domain wall is equal to the half-mass of the 't Hooft-Polyakov monopole. We examine various configurations and clarify how the shape of the boojum depends on the coupling constants and moduli parameters. We also find analytic solutions to the 1/4 BPS equations for specific values of the coupling constants.

External spur gear root bending stress: A comparison of ISO 6336:2006, AGMA 2101-D04, ANSYS finite element analysis and strain gauge techniques

The International Organisation for Standardisation ISO 6336:2006 and the American Gear Manufacturers Association AGMA 2101-D04 are the two most predominant empirically based analytical gear stress analysis methods for establishing contact and root bending stress in involute spur and helical gears. Although based on the same fundamental principles, they have evolved to such an extent that, for various reasons, they are not necessarily in agreement. The use of commercial universal numerical finite element software has become an increasingly popular alternative for gear stress analysis and this research compares the root bending stresses in external spur gears established using ISO 6336:2006, AGMA 2101-D04 and numerical finite element analysis (ANSYS) with experimental strain gauge validation.

Exact BPS domain walls at finite gauge coupling

Bogomol'nyi-Prasad-Sommerfield solitons in models with spontaneously broken gauge symmetry have been intensively studied at infinite gauge coupling limit, where the governing equation -- so-called master equation -- is exactly solvable. Except for a handful of special solutions, the standing impression is that analytic results at finite coupling are generally unavailable. The aim of this paper is to demonstrate, using domain walls in Abelian-Higgs models as the simplest example, that exact solitons at finite gauge coupling can be readily obtained if the number of Higgs fields ($N_F$) is large enough. In particular, we present a family of exact solutions, describing $N$ domain walls at arbitrary positions in models with at least $N_F \geq 2N+1$. We have also found that adding together any pair of solution can produce a new exact solution if the combined tension is below a certain limit.

Biomechanical tools to study dental implants: A literature review

Since 1980, the biomechanical behavior of dental implants has received importance regarding the issue of failure in this rehabilitation system due to occlusal overload. Through bioengineering tools, several studies have been conducted to answer about the influence of different factors on the biological response. Bioengineering tools such as finite element analysis (FEA), strain gauge (SGA), photoelasticity (PEA) and digital image correlation (DIC) are widely inspiring clinical extrapolation of possible solutions in the mechanics of implantology. This study has aimed to investigate the available stress analysis methods to study dental implants’ behavior through a literature review. This review started with a PubMed search from the mostly old studies of each methodology correlated to biomechanical behavior of dental implants used with dental implants studies until 2016. FEA, SGA, PEA and DIC methodologies are capable to elucidate the mechanical behavior of this rehabilitation system. However, the combination of two or more methods gives more detailed explanation and avoids limitations of a single methodology.

New insights into properties of large-N holographic thermal QCD at finite gauge coupling at (the non-conformal/next-to) leading order in N

It is believed that large-N thermal QCD laboratories like strongly coupled QGP (sQGP) require not only a large ‘t Hooft coupling but also a finite gauge coupling (Natsuume, String theory and quark–gluon plasma. arXiv:hep-ph/0701201 , 2007). Unlike almost all top–down holographic models in the literature, holographic large-N thermal QCD models, based on this assumption, therefore necessarily require addressing this limit from M-theory. This was initiated in Dhuria and Misra (JHEP 1311:001, 2013) which presented a local M-theory uplift of the string theoretic dual of large-N thermal QCD-like theories at finite gauge/string coupling of Mia et al. (Nucl. Phys. B 839:187, arXiv:0902.1540 [hep-th], 2010) ( $$g_s\mathop {<}\limits ^{\sim }1$$ as part of the ‘MQGP’ limit of Dhuria and Misra in JHEP 1311:001, arXiv:1306.4339 [hep-th], 2013). Understanding and classifying the properties of systems like sQGP from a top–down holographic model, assuming a finite gauge coupling, have been entirely missing in the literature. In this paper we largely address the following two non-trivial issues pertaining to the same. First, up to LO in N (the number of D3-branes), by calculating the temperature dependence of the thermal (and electrical) conductivity and the consequent deviation from the Wiedemann–Franz law, upon comparison with Garg et al. (Phys. Rev. Lett. 103:096402, 2009), we show that, remarkably, the results qualitatively mimic a 1+1-dimensional Luttinger liquid with impurities. Second, by looking at, respectively, the scalar, vector, and tensor modes of metric perturbations and using the prescription of Kovtun and Starinets (Phys. Rev. D 72:086009, arXiv:hep-th/0506184 , 2005) for constructing appropriate gauge-invariant perturbations, we obtain the non-conformal corrections to the conformal results (but at finite $$g_s$$ ), respectively, for the speed of sound, the shear mode diffusion constant, and the shear viscosity $$\eta $$ (and $$\frac{\eta }{s}$$ ). The new insight gained is that it turns out that these corrections show a partial universality in the sense that at NLO in N the same are given by the product of $$\frac{(g_s M^2)}{N}\ll 1$$ and $$g_s N_f\sim \mathcal{O}(1)$$ , $$N_f$$ being the number of flavor D7-branes and M the number of fractional D3-branes = the number of colors = 3 in the IR after the end of a Seiberg-duality cascade. On the mathematics side, using the results of Ionel and Min-OO (Ill. J. Math. 52, 2008), at LO in N we finish our argument of Dhuria and Misra (Eur. Phys. J. C 75:16, 2015) and show that for a predominantly resolved (resolution > deformation – this paper) or deformed (deformation > resolution – Dhuria and Misra in Eur Phys J C 75(1):16, arXiv:1406.6076 [hep-th], 2015) resolved warped deformed conifold, the local $$T^3$$ of Dhuria and Misra (JHEP 1311:001, arXiv:1306.4339 [hep-th], 2013) in the MQGP limit is the $$T^2$$ -invariant special Lagrangian three-cycle of Ionel and Min-OO (Ill J Math 52(3), 2008) justifying the construction in Dhuria and Misra (JHEP 1311:001, arXiv:1306.4339 [hep-th], 2013) of the delocalized Strominger–Yau–Zaslow Type IIA mirror of the Type IIB background of Mia et al. (Nucl Phys B 839:187, arXiv:0902.1540 [hep-th], 2010).

Finite quantum gauge theories

We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of running gauge coupling constant. The outcome is "a UV finite theory for any gauge interaction". Our calculations are done in D=4, but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite we are able to solve also the Landau pole problems, in particular in QED. Without any potential the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV, nor the singularities in the infrared regime (IR).

Finite gauge transformations and geometry in extended field theory

The recently derived expressions for finite gauge transformations in double field theory with duality group O(d,d) are generalised to give expressions for finite gauge transformations for extended field theories with duality group SL(5,R), SO(5,5) and E6. The generalised metrics are discussed.

Generalized higher gauge theory

We study a generalization of higher gauge theory which makes use of generalized geometry and seems to be closely related to double field theory. The local kinematical data of this theory is captured by morphisms of graded manifolds between the canonical exact Courant Lie 2-algebroid $TM\oplus T^*M$ over some manifold $M$ and a semistrict gauge Lie 2-algebra. We discuss generalized curvatures and their infinitesimal gauge transformations. Finite gauge transformation as well as global kinematical data are then obtained from principal 2-bundles over 2-spaces. As dynamical principle, we consider first the canonical Chern-Simons action for such a gauge theory. We then show that a previously proposed 3-Lie algebra model for the six-dimensional (2,0) theory is very naturally interpreted as a generalized higher gauge theory.