Dimensional Field Research Articles

Three dimensional topological quantum field theory from [formula omitted] and U(1|1) Chern–Simons theory

We introduce an unrolled quantization UqE(gl(1|1)) of the complex Lie superalgebra gl(1|1) and use its categories of weight modules to construct and study new three dimensional non-semisimple topological quantum field theories. These theories are defined on categories of cobordisms which are decorated by ribbon graphs and cohomology classes and take values in categories of graded super vector spaces. Computations in these theories are enabled by a detailed study of the representation theory of UqE(gl(1|1)). We argue that by restricting to subcategories of integral weight modules we obtain topological quantum field theories which are mathematical models of Chern–Simons theories with gauge supergroups psl(1|1) and U(1|1) coupled to background flat C×-connections, as studied in the physics literature by Rozansky–Saleur and Mikhaylov. In particular, we match Verlinde formulae and mapping class group actions on state spaces of non-generic tori with results in the physics literature. We also obtain explicit descriptions of state spaces of generic surfaces, including their graded dimensions, which go beyond results in the physics literature.

5d 2-Chern-Simons Theory and 3d Integrable Field Theories

The 4-dimensional semi-holomorphic Chern-Simons theory of Costello and Yamazaki provides a gauge-theoretic origin for the Lax connection of 2-dimensional integrable field theories. The purpose of this paper is to extend this framework to the setting of 3-dimensional integrable field theories by considering a 5-dimensional semi-holomorphic higher Chern-Simons theory for a higher connection (A, B) on R3×CP1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^3 \ imes \\mathbb {C}P^1$$\\end{document}. The input data for this theory are the choice of a meromorphic 1-form ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} on CP1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {C}P^1$$\\end{document} and a strict Lie 2-group with cyclic structure on its underlying Lie 2-algebra. Integrable field theories on R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^3$$\\end{document} are constructed by imposing suitable boundary conditions on the connection (A, B) at the 3-dimensional defects located at the poles of ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} and choosing certain admissible meromorphic solutions of the bulk equations of motion. The latter provides a natural notion of higher Lax connection for 3-dimensional integrable field theories, including a 2-form component B which can be integrated over Cauchy surfaces to produce conserved charges. As a first application of this approach, we show how to construct a generalization of Ward’s (2+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2+1)$$\\end{document}-dimensional integrable chiral model from a suitable choice of data in the 5-dimensional theory.

Trace anomalies and the graviton-dilaton amplitude

We consider 3+1 dimensional Quantum Field Theories (QFTs) coupled to the dilaton and the graviton. We show that the graviton-dilaton scattering amplitude receives a universal contribution which is helicity flipping and is proportional to ∆c − ∆a along any RG flow, where ∆c and ∆a are the differences of the UV and IR c- and a-trace anomalies respectively. This allows us to relate ∆c − ∆a to spinning massive states in the spectrum of the QFT. We test our predictions in two simple examples: in the theory of a massive free scalar and in the theory of a massive Dirac fermion (a more complicated example is provided in a companion paper [1]). We discuss possible applications.

Some lower dimensional quantum field theories reduced from Chern-Simons gauge theories

We study symmetry reductions in the context of Euclidean Chern-Simons gauge theories to obtain lower dimensional field theories. Symmetry reduction in certain gauge theories is a common tool for obtaining explicit soliton solutions. Although pure Chern-Simons theories do not admit solitonic solutions, symmetry reduction still leads to interesting results. We establish relations at the semiclassical regime between pure Chern-Simons theories on S3 and the reduced quantum field theories, based on actions obtained by the symmetry reduction of the Chern-Simons action, spherical symmetry being the prominent one. We also discuss symmetry reductions of Chern-Simons theories on the disk, yielding a topological theory in two dimensions, which signals a curious relationship between symmetry reductions and the boundary conformal field theories. Finally, we study the Chern-Simons-Higgs instantons and show that under certain circumstances, the reduced action can formally be viewed as the action of a supersymmetric quantum mechanical model. We discuss the extent to which the reduced actions have a fermionic nature at the level of the partition function. Published by the American Physical Society 2024

Entanglement in ( 1+1 )-dimensional free scalar field theory: Tiptoeing between continuum and discrete formulations

We review some classic works on ground state entanglement entropy in (1+1)-dimensional free scalar field theory. We point out identifications between the methods for the calculation of entanglement entropy and we show how the formalism developed for the discretized theory can be utilized in order to obtain results in the continuous theory. We specify the entanglement spectrum and we calculate the entanglement entropy for the theory defined on an interval of finite length L. Finally, we derive the modular Hamiltonian directly, without using the modular flow, via the continuum limit of the expressions obtained in the discretized theory. In a specific coordinate system, the modular Hamiltonian assumes the form of a free field Hamiltonian on the Rindler wedge. Published by the American Physical Society 2024

Off-shell pion properties: Electromagnetic form factors and light-front wave functions

The off-shell pion electromagnetic form factors are explored with corresponding off-shell light-front wave functions modeled by constituent quark and antiquark. We apply the Mandelstam approach for the microscopic computation of the form factors relating the model parameters with the pion decay constant and charge radius. Analyzing the existing data on the cross sections for the Sullivan process, H1(e,e′,π+)n [H. P. Blok (Jefferson Lab Fπ Collaboration), Charged pion form factor between Q2=0.60, and 2.45 GeV2. I. Measurements of the cross section for the H1(e,e′π+)n reaction, .], we extract the off-shell pion form factor using the relation derived from the generalized Ward-Takahashi identity for the pion electromagnetic current. They are compared with our previous results [H.-M. Choi , Pion off-shell electromagnetic form factors: Data extraction and model analysis, .] from exactly solvable manifestly covariant model of a (3+1)-dimensional fermion field theory. We find that the adopted constituent quark model reproduces the extracted off-shell form factor F1(Q2,t) from the experimental data within a few percent difference and matches well with our previous theoretical simulation which exhibits a variation of about 10% for the extracted off-shell pion form factor g(Q2,t). We also identify the pion valence parton distribution function (PDF) and transverse momentum distribution (TMD) in terms of the light-front wave function and discuss their off-shell properties. Published by the American Physical Society 2024

Influence of field mass and acceleration on entanglement generation

We explore the entanglement dynamics of two detectors undergoing uniform acceleration and circular motion within a massive scalar field, while also investigating the influence of the anti-Unruh effect on entanglement harvesting. Contrary to the conventional understanding of the weak anti-Unruh effect, where entanglement typically increases, we observe that the maximum entanglement between detectors does not exhibit a strict monotonic dependence on detector acceleration. Particularly at low accelerations, fluctuations in the entanglement maxima show a strong correlation with fluctuations in detector transition rates. We also find that the maximum entanglement of detectors tends to increase with smaller field mass. Novelly, our findings indicate the absence of a strong anti-Unruh effect in (3+1)-dimensional massive scalar fields. Instead, thermal effects arising from acceleration contribute to a decrease in the detector entanglement maximum.

Higher-order-operator corrections to phase-transition parameters in dimensional reduction

The dynamics of phase transitions (PT) in quantum field theories at finite temperature is most accurately described within the framework of dimensional reduction. In this framework, thermodynamic quantities are computed within the 3-dimensional effective field theory (EFT) that results from integrating out the high-temperature Matsubara modes. However, strong-enough PTs, observable in gravitational wave (GW) detectors, occur often nearby the limit of validity of the EFT, where effective operators can no longer be neglected. Here, we perform a quantitative analysis of the impact of these interactions on the determination of PT parameters. We find that they allow for strong PTs in a wider region of parameter space, and that both the peak frequency and the amplitude of the resulting GW power spectrum can change by more than one order of magnitude when they are included. As a byproduct of this work, we derive equations for computing the bounce solution in the presence of higher-derivative terms, consistently with the EFT power counting.

Three-Dimensional Lorentz-Invariant Velocities

Lorentz invariance underlies special relativity, and the energy formula and relative velocity formula are well known to be invariant under a Lorentz transformation. Here, we determine the functional forms in terms of four arbitrary functions for those three dimensional velocity fields that are automatically invariant under the most general fully three-dimensional Lorentz transformation. For general three-dimensional motion, using rectangular Cartesian coordinates (x,y,z), we determine the first-order partial differential equations for the three velocity components u(x,y,z,t), v(x,y,z,t) and w(x,y,z,t) in the x−, y− and z−directions respectively. These partial differential equations and the associated partial differential relations connecting energy and momentum are fully compatible with the Lorentz-invariant energy–momentum relations and appear not to have been given previously in the literature. We determine the spatial and temporal dependence of the functional forms for those three-dimensional velocity fields that are automatically invariant under three-dimensional Lorentz transformations. An interesting special case gives rise to families of particle paths for which the magnitude of the velocity is the speed of light. This is indicative of the abundant possibilities existing in the “fast lane”.

Accelerating Kaluza–Klein black hole and Kerr/CFT correspondence

We construct a new solution in the Einstein–Maxwell-dilaton theory describing accelerating, charged, and rotating black hole, i.e. the accelerating Kaluza–Klein black hole. Some properties the spacetime are discussed, such as the electromagnetic fields, the area-temperature product, and the holography according to Kerr/CFT correspondence. As expected, the macroscopic Bekenstein–Hawking entropy for an extremal accelerating Kaluza–Klein black hole can be recovered by using Cardy formula of a two dimensional conformal field theory. An interesting feature is found, namely the area-temperature product is just the one belongs to the vacuum Einstein seed solution.

Integrability and renormalizability for the fully anisotropic SU(2) principal chiral field and its deformations

For the class of 1 + 1 dimensional field theories referred to as the non-linear sigma models, there is known to be a deep connection between classical integrability and one-loop renormalizability. In this work, the phenomenon is reviewed on the example of the so-called fully anisotropic SU(2) Principal Chiral Field (PCF). Along the way, we discover a new classically integrable four parameter family of sigma models, which is obtained from the fully anisotropic SU(2) PCF by means of the Poisson-Lie deformation. The theory turns out to be one-loop renormalizable and the system of ODEs describing the flow of the four couplings is derived. Also provided are explicit analytical expressions for the full set of functionally independent first integrals (renormalization group invariants).

Bridging two quantum quench problems — local joining quantum quench and Möbius quench — and their holographic dual descriptions

We establish an equivalence between two different quantum quench problems, the joining local quantum quench and the Möbius quench, in the context of (1 + 1)-dimensional conformal field theory (CFT). Here, in the former, two initially decoupled systems (CFTs) on finite intervals are joined at t = 0. In the latter, we consider the system that is initially prepared in the ground state of the regular homogeneous Hamiltonian on a finite interval and, after t = 0, let it time-evolve by the so-called Möbius Hamiltonian that is spatially inhomogeneous. The equivalence allows us to relate the time-dependent physical observables in one of these problems to those in the other. As an application of the equivalence, we construct a holographic dual of the Möbius quench from that of the local quantum quench. The holographic geometry involves an end-of-the-world brane whose profile exhibits non-trivial dynamics.

Generalized entanglement capacity of de Sitter space

Near horizons, quantum fields of low spin exhibit densities of states that behave asymptotically like 1+1 dimensional conformal field theories. In effective field theory, imposing some short-distance cutoff, one can compute thermodynamic quantities associated with the horizon, and the leading cutoff sensitivity of the heat capacity is found to equal to the leading cutoff sensitivity of the entropy. One can also compute contributions to the thermodynamic quantities from the gravitational path integral. For the cosmological horizon of the static patch of de Sitter space, a natural conjecture for the relevant heat capacity is shown to equal the Bekenstein-Hawking entropy. These observations allow us to extend the well-known notion of the generalized entropy to a generalized heat capacity for the static patch of de Sitter (dS). The finiteness of the entropy and the nonvanishing of the generalized heat capacity suggest it is useful to think about dS as a state in a finite dimensional quantum gravity model that is not maximally uncertain. Published by the American Physical Society 2024

Vector magnetic field characteristics of magneto-shape effect with high figure of merit based on fiber optic vernier effect

The vector magnetic field structures utilizing magnetic fluid (MF) mainly rely on the magneto-refractive index effect (MRI), which has the low spatial resolution due to the long sensitive length. In this article, the vector magnetic field characteristics of the magneto-shape effect (MSE) are simulated and experimentally studied based on the fiber optic vernier effect. The high vector magnetic field sensitivity can be achieved under the condition of Φ128*73 μm in the sensitive area by combine the MSE and vernier effect. The distribution of magnetic field on the concavity of MF varies with magnetic field direction, giving rising to MF concavity different deformations. The magnetic field observation structure based on fiber optic vernier effect are fabricated to verify the vector magnetic field characteristics of MSE. The observation structure is subjected to one-dimensional and two-dimensional magnetic field. The test results demonstrate that the magnetic field sensibility can reach 2.36 nm/Gs, 3.88 nm/Gs and 4.52 nm/Gs under 0–55.0 Gs, 55.0–91.7 Gs and 91.7–119.2 Gs in Y direction field. The magnetic field sensibility is 0.91 nm/Gs in Z direction field. The magnetic field direction sensitivity can reach 1.16 nm/° in XY dimensional field. The structure of the MSE is very compact and the size is very small, which is very helpful for detecting the narrow space and gradient magnetic field.

Multi‒scale numerical investigations on the atomization performance of liquid‒liquid pintle injector

Three‒dimensional atomization field of the radial annular slot type liquid‒liquid pintle injector under different total momentum ratio (TMR) is simulated based on the volume of fluid to discrete particle model (VOF to DPM) method and the octree adaptive mesh refinement (AMR). The typical spray morphology of the injector is obtained, the variation of spray angle, breakup length of liquid film, amplitude of disturbance waves before liquid film breaking and its causes are analyzed. The results show that the injector can form a hollow conical spray during operation, and there are two recirculation zones near the inner surface of liquid film. According to the characteristics of the spray morphology, the spray can be divided into four areas: undisturbed liquid film, disturbed liquid film, fluctuating breakup zone and small droplets accumulation zone. The simulated spray angle is close to the model proposed by Heister when TMR is smaller than 0.6 and is close to the model proposed by Boettcher when TMR exceeds 0.6, with the maximum relative error of 9.5%. TMR has little influence on the amplitude of disturbance waves before liquid film breaking, while the breakup length of liquid film increases at first and then decreases with the increase of TMR. The breakup length is relatively large when TMR is close to 1, within the range of 20∼22 mm, while it is relatively small when TMR is far away from 1, within the range of 12∼15mm.

First-order electroweak phase transition at finite density

We study the Electroweak phase transition with the Standard Model effective field theory at finite temperature and finite density. Utilizing the dimensional reduction approach, we construct the tree dimensional thermal effective field theory at finite density and investigate the phase transition dynamics. We evaluate how the results depend on the renormalization scale and the chemical potential. Our results show that, with the tree dimensional thermal effective potential at 2-loop level, we can effectively reduce the theoretical uncertainty in the calculations of the phase transition parameters due to the renormalization scale dependence, and the new physics scale is restricted to be Λ ≲ (770 − 800) GeV by the baryon number washout avoidance condition. Meanwhile, the presence of the chemical potential would affect the phase transition parameter and make the constraints from the baryon number washout avoidance condition more strict, especially for weaker first-order phase transition scenarios at higher new physics scales.

Four loop renormalization in six dimensions using forcer

We employ the algorithm to renormalize a variety of six dimensional field theories to four loops. In order to achieve this we construct the master integrals in six dimensions from their four dimensional counterparts by using the Tarasov method. The ε expansion of the six dimensional masters are determined up to weight 9 where d=6−2ε. By applying the routine the four loop MS¯ renormalization of ϕ3 theory is reproduced before gauge theories are considered. The renormalization of these theories is also determined in the MOM˜ scheme. For instance the absence of ζ4 and ζ6 is confirmed to five loops in the MOM˜ renormalization of ϕ3 theory. We also evaluate the three loop β-function of the gauge coupling in six dimensional QCD. Published by the American Physical Society 2024

Penrose limits of I-branes, twist-compactified D5-branes, and spin chains

In this paper we consider the Penrose limit in the case of two gravity duals. One of them, consists of compactified I-branes [intersecting sets of D5-branes over (1+1) dimensions]. The second consists of D5-branes compactified on a circle. Both compactifications preserve supersymmetry. We find a match of the oscillators and masses of string modes on the resulting pp wave against a spin chain in a (2+1)-dimensional field theory in the first case, and a spin chain in a (1+1)-dimensional field theory in the second. Published by the American Physical Society 2024

Boundary Liouville conformal field theory in four dimensions

Higher dimensional Euclidean Liouville conformal field theories (LCFTs) consist of a log-correlated real scalar field with a background charge and an exponential potential. We analyse the LCFT on a four-dimensional manifold with a boundary. We extend to the boundary, the conformally covariant GJMS operator and the Q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{Q} $$\\end{document}-curvature term in the LCFT action and classify the conformal boundary conditions. Working on a flat space with plate boundary, we calculate the dimensions of the boundary conformal primary operators, the two- and three-point functions of the displacement operator and the boundary conformal anomaly coefficients.

RF-DYNA — Software for optimized random finite element simulation using LS-DYNA

This paper presents a user-friendly software to assign spatially distributed material properties to nonlinear finite element models in LS-DYNA using discretized three dimensional random fields and random variables. The purpose of the software is to enable probabilistic analysis frameworks that incorporate results from LS-DYNA simulations with random material properties. The software leverages the existing well-established deterministic formulation of LS-DYNA by utilizing inbuilt material constitutive laws. K-nearest neighbors spatial interpolation and k-means clustering are implemented to streamline the generation and assignment of random fields to parts in LS-DYNA models. The functionality of the software is demonstrated through real-life safety assessments of two marine structural elements composed of steel-reinforced concrete. Analysis results demonstrated the robustness and efficiency of the software where it can be successfully integrated into analysis frameworks to evaluate the safety of structural members.