Field Theory Research Articles

Seismic response of RC short columns strengthened by high-strength stainless steel wire rope meshes reinforced ECC jacket

A novel strengthening scheme of high-strength stainless steel wire rope (HSSSWR) meshes reinforced engineering cementitious composite (ECC) jacket was used to strengthen the reinforced concrete (RC) short columns in this paper. The seismic performance of short columns after being strengthened was investigated, considering the changes in the strengthening scheme, and the spacing of lateral HSSSWRs. The failure mode, hysteresis behavior, envelope curve, ductility, energy dissipation, stiffness degradation, and strength degradation were introduced specifically based on the analysis of six full-scale short columns. The test results show a significant enhancement in the seismic performance of the strengthened short columns, especially in ductility and energy dissipation, which were increased by 49.4–98.4 %, and 149.3–713.2 %, respectively. The placement of HSSSWRs in ECC jacket proved to be effective in enhancing the strengthening effect of the jacket. A prediction model for the shear capacity of the strengthened columns was proposed using the Modified Compression Field Theory (MCFT), and the predicted results were in good agreement with the test results presented in this paper and in relative study.

Thermodynamic formulation of vacuum energy density in flat spacetime and potential implications for the cosmological constant

We propose a thermodynamical definition of the vacuum energy density ρvac, defined as 〈vac|Tμν|vac〉 = − ρvacgμν, in quantum field theory in flat Minkowski space in D spacetime dimensions, which can be computed in the limit of high temperature, namely in the limit β = 1/T → 0. It takes the form ρvac = const ∙ mD where m is a fundamental mass scale and “const” is a computable constant which can be positive or negative depending on interaction couplings. Due to modular invariance ρvac can also be computed in a different non-thermodynamic channel where one spatial dimension is compactifed on a circle of circumference β and we confirm this modularity for free massive theories for both bosons and fermions for D = 2, 3, 4. We list various properties of ρvac that are generally required, for instance ρvac = 0 for conformal field theories, and others, such as the constraint that ρvac has opposite signs for free bosons verses fermions of the same mass, which is related to constraints from supersymmetry. Using the Thermodynamic Bethe Ansatz we compute ρvac exactly for 2 classes of integrable QFT’s in 2D and interpreting some previously known results. We apply our definition of ρvac to Lattice QCD data with two light quarks (up and down) and one additional massive flavor (the strange quark), and find it is negative, ρvac ≈ − (200 MeV)4. Finally we make some remarks on the Cosmological Constant Problem since ρvac is central to any discussion of it.

Hybrid inflation, reheating and dark radiation in a IIB perturbative moduli stabilization scenario

We study the cosmological implications of an effective field theory model derived within a configuration of D7 brane stacks in the framework of type-IIB string theory. We consider a suitable geometric setup where the Kähler moduli fields are stabilized and the parametric space is constrained so that a de Sitter vacuum is ensured. In addition to the moduli fields we also take into account the usual Higgs and matter fields included in the effective field theory. In this background, we implement the standard hybrid inflation scenario with a singlet scalar field acting as the inflaton and the Higgs states serving as waterfall fields. Radiative corrections and soft supersymmetry breaking terms play an essential role in the realization of a successful inflationary scenario consistent with the present cosmological data. Small tensor-to-scalar ratio values are predicted, which can be probed in future planned experiments. Further constraints on the model’s parameters are derived from bounds on dark radiation which is measured as a contribution to the effective number of neutrino species Neff. In particular, we find an excess of ∆Neff ≤ 0.95 at 2σ confidence level with natural values of the involved couplings.

Relativistic Effects in Ligand Field Theory (I): Optical Properties of d1 Atoms in Oh' Symmetry.

Ligand field theory, which explains the splitting of degenerate nd atomic orbitals due to static electric fields from point-charge ligands, is rederived using Dirac orbitals instead of Schrödinger orbitals, specifically using the nd3/2 and nd5/2 spinors. This formalism is, to some extent, equivalent to incorporating the spin-orbit interaction either in the nd atomic orbitals or in the ligand field orbitals (e.g., the t2g and eg orbitals arising from Oh symmetry). The spin-orbit interaction is of fundamental importance in the description of the magnetic and optical properties of the 4d and 5d transition metal complexes. Algebraic equations for the relativistic energy levels of d1 octahedral complexes as functions of the spin-orbit coupling constant ξnd and the ligand field parameters Dq and Dp are derived. It is demonstrated that these parameters allow a direct link between the ligand field theory and ab initio relativistic calculations, consistent with the emerging ab initio ligand field theory. The spin-orbit coupling constant and ligand field parameters of ReF6 obtained from optical absorption spectra are carefuly in the light of the new theory.

From quantum field theory to the quantum method the inverse problem On the 90th anniversary of the birth of academician L.D. Faddeev

The article is dedicated to the life and work of a theoretical physicist and mathematician, a full member of the USSR Academy of Sciences and RAS L.D. Faddeev (1934−2017), the formation of his scientific school. Faddeev’s works on scattering theory, quantum field theory, classical and quantum theory of integrable systems were included in the golden fund of world science and largely determined the face of modern mathematical physics. The author of the article is an employee of the Laboratory of Mathematical Problems of Physics created by L.D. Faddeev at the St. Petersburg Department of the V.A. Steklov Mathematical Institute of the Russian Academy of Sciences since its foundation.

The NFLikelihood: An unsupervised DNNLikelihood from normalizing flows

We propose the NFLikelihood, an unsupervised version, based on Normalizing Flows, of the DNNLikelihood proposed in [Eur. Phys. J. C 80, 664 (2020)]. We show, through realistic examples, how Autoregressive Flows, based on affine and rational quadratic spline bijectors, are able to learn complicated high-dimensional Likelihoods arising in High Energy Physics (HEP) analyses. We focus on a toy LHC analysis example already considered in the literature and on two Effective Field Theory fits of flavor and electroweak observables, whose samples have been obtained through the HEPFit code. We discuss advantages and disadvantages of the unsupervised approach with respect to the supervised one and discuss a possible interplay between the two.

Analytic soliton solutions to the shallow water dispersive long gravity wave equations: the first integral approach in nonlinear physics

In this article, we investigate the (2+1)-dimensional dispersive long water wave equation and the (1+1)-dimensional Phi-four equation, which describe the behavior of long gravity waves with small amplitudes, long wave propagation in oceans and seas, coastal structures and harbor design, effects of wave motion on sediment transport, quantum field theory, phase transitions of matter, ferromagnetic systems, liquid-gas transitions, and the structure of optical solitons. We use the first integral technique and obtain new and generic solutions for the models under consideration. By setting definite values for the associated parameters, various types of richly structured solitons are generated. The solitons include kink, flat kink, bell-shaped, anti-bell-shaped, and singular kink formations. These solutions allow for a profound understanding of the behavior and properties of the phenomena, offering new insights and potential applications in the associated field. The first integral technique is simpler, directly integrates the models, and the solutions offer clear insights into the underlying phenomena without requiring intermediate steps, making it widely applicable to various other models, including nonlinear equations and those that are challenging to solve using other standard techniques.

Non-relativistic limits of bosonic and heterotic Double Field Theory

The known stringy non-relativistic (NR) limit of the universal NS-NS sector of supergravity has a finite Lagrangian due to non-trivial cancellations of divergent parts coming from the metric and the B-field. We demonstrate that in Double Field Theory (DFT) and generalised geometry these cancellations already happen at the level of the generalised metric, which is convergent in the limit c → ∞, implying that the NR limit can be imposed before solving the strong constraint. We present the c-expansion of the generalised metric, which reproduces the Non-Riemannian formulation of DFT at the (finite) leading order, and the c-expansion of the generalised frame, which contains divergences. We also extend this approach to the non-Abelian gauge field of Heterotic DFT assuming a convergent expansion for the O(D, D + n) generalised metric. From this proposal, we derive a novel c-expansion for the bosonic part of the heterotic supergravity which is, by construction, compatible with O(D, D)-symmetry.

Topological Quantum Field Theories and Homotopy Cobordisms

We construct a category HomCob\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extrm{HomCob}}$$\\end{document} whose objects are homotopically 1-finitely generated topological spaces, and whose morphisms are cofibrant cospans. Given a manifold submanifold pair (M, A), we prove that there exists functors into HomCob\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extrm{HomCob}}$$\\end{document} from the full subgroupoid of the mapping class groupoid MCGMA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{MCG}_{M}^{A}$$\\end{document}, and from the full subgroupoid of the motion groupoid MotMA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{Mot}_{M}^{A}$$\\end{document}, whose objects are homotopically 1-finitely generated. We also construct a family of functors ZG:HomCob→Vect\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extsf{Z}}_G:{\ extrm{HomCob}}\\rightarrow {\ extbf{Vect}}$$\\end{document}, one for each finite group G. These generalise topological quantum field theories previously constructed by Yetter, and an untwisted version of Dijkgraaf–Witten. Given a space X, we prove that ZG(X)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extsf{Z}}_G(X)$$\\end{document} can be expressed as the C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {C}}$$\\end{document}-vector space with basis natural transformation classes of maps from π(X,X0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi (X,X_0)$$\\end{document} to G for some finite representative set of points X0⊂X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_0\\subset X$$\\end{document}, demonstrating that ZG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extsf{Z}}_G$$\\end{document} is explicitly calculable.

Time-Dependent Reliability Analysis of Anhydrite Rock Tunnels under Swelling Conditions: A Study on Stress, Deformation, and Engineering Solutions

This study presents an analytical approach for evaluating the reliability of anhydrite rock tunnels, focusing on their characteristic swelling behavior. Anhydrite rocks, prone to significant expansion upon moisture exposure, pose a challenge in tunnel construction, potentially leading to structural issues such as floor heave and lining damage. To address this, this research develops an elastic swelling analytical solution based on humidity stress field theory, enabling the assessment of time-dependent stress and deformation changes in anhydrite tunnels. The solution’s applicability is demonstrated through its application to the Lirang tunnel. The investigation into the effects of support pressure, swelling time, and reserved deformation on tunnel reliability reveals that circumferential stress at the tunnel wall increases by 13.94% and 21.86% for swelling periods of 30 and 365 days, respectively. Similarly, radial displacement escalates by 22.97% and 35.93% over these periods, highlighting the significant impact of swelling behavior. Using a spreadsheet-based First Order Reliability Method (FORM) for analysis, this study finds that the original design of the Lirang tunnel did not meet the desired reliability standards under swelling conditions. However, strategic adjustments in construction variables, such as increasing support pressure to 1.2 MPa or enhancing reserved deformation to 59 mm, elevated the tunnel’s reliability to meet safety requirements. This research provides a vital framework for assessing and enhancing the reliability of anhydrite rock tunnels, considering the long-term effects of swelling. It underscores the importance of incorporating swelling behavior in the design and construction of tunnels in anhydrite rock formations, offering valuable insights for optimizing tunnel stability in such challenging geological conditions.

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.

Asymptotics for Some Logistic Maps and the Renormalization Group

Abstract We explain the relation between a special case of the logistic map and the renormalization group flow arising in the multiscale analysis of some interesting zero fixed point, asymptotic free quantum field theory models. Using elementary mathematics, we obtain a fine control of the asymptotic dependence of our logistic map iteration on the number of steps or time $n$. We prove that this behavior is independent of the initial state or condition, and also that it only depends on the lowest orders in a polynomial perturbation. In asymptotic free quantum field theory, this amounts to say that knowing the renormalization group $\beta$-function expansion in the coupling constant, up to higher orders, does not improve our knowledge of the asymptotics of the coupling flow. A comparison is made with a similar differential equation in continuous time.

Axion‐Like Interactions and CFT in Topological Matter, Anomaly Sum Rules and the Faraday Effect

AbstractFundamental aspects of chiral anomaly‐driven interactions in conformal field theory (CFT) in four spacetime dimensions are discussed. These interactions find application in very general contexts, from early universe plasma to topological condensed matter. The key shared characteristics of these interactions are outlined, specifically addressing the case of chiral anomalies, both for vector currents and gravitons. In the case of topological materials, the gravitational chiral anomaly is generated by thermal gradients via the (Tolman–Ehrenfest) Luttinger relation. In the CFT framework, a nonlocal effective action, derived through perturbation theory, indicates that the interaction is mediated by excitation in the form of an anomaly pole, which appears in the conformal limit of the vertex. To illustrate this, it is demonstrated how conformal Ward identities (CWIs) in momentum space allow to reconstruct the entire chiral anomaly interaction in its longitudinal and transverse sectors just by inclusion of a pole in the longitudinal sector. Both sectors are coupled in amplitudes with an intermediate chiral fermion or a bilinear Chern–Simons current with intermediate photons. In the presence of fermion mass corrections, the pole transforms into a cut, but the absorption amplitude in the axial‐vector channel satisfies mass‐independent sum rules related to the anomaly in any chiral interaction. The detection of an axion‐like/quasiparticle in these materials may rely on a combined investigation of these sum rules, along with the measurement of the angle of rotation of the plane of polarization of incident light when subjected to a chiral perturbation. This phenomenon serves as an analog of a similar one in ordinary axion physics, in the presence of an axion‐like condensate, which is rederived using axion electrodynamics.

Curvature correlators in nonperturbative 2D Lorentzian quantum gravity

Correlation functions are ubiquitous tools in quantum field theory from both a fundamental and a practical point of view. However, up to now their use in theories of quantum gravity beyond perturbative and asymptotically flat regimes has been limited, due to difficulties associated with diffeomorphism invariance and the dynamical nature of geometry. We present an analysis of a manifestly diffeomorphism-invariant, nonperturbative two-point curvature correlator in two-dimensional Lorentzian quantum gravity. It is based on the recently introduced quantum Ricci curvature and uses a lattice regularization of the full path integral in terms of causal dynamical triangulations. We discuss some of the subtleties and ambiguities in defining connected correlators in theories of dynamical geometry, and provide strong evidence from Monte Carlo simulations that the connected two-point curvature correlator in 2D Lorentzian quantum gravity vanishes. This work paves the way for an analogous investigation in higher dimensions.

Fermionic UV models for neutral triple gauge boson vertices

Searches for anomalous neutral triple gauge boson couplings (NTGCs) provide important tests for the gauge structure of the standard model. In SMEFT (“standard model effective field theory”) NTGCs appear only at the level of dimension-8 operators. While the phenomenology of these operators has been discussed extensively in the literature, renormalizable UV models that can generate these operators are scarce. In this work, we study a variety of extensions of the SM with heavy fermions and calculate their matching to d = 8 NTGC operators. We point out that the complete matching of UV models requires four different CP-conserving d = 8 operators and that the single CPC d = 8 operator, most commonly used by the experimental collaborations, does not describe all possible NTGC form factors. Despite stringent experimental constraints on NTGCs, limits on the scale of UV models are relatively weak, because their contributions are doubly suppressed (being d = 8 and 1-loop). We suggest a series of benchmark UV scenarios suitable for interpreting searches for NTGCs in the upcoming LHC runs, obtain their current limits and provide estimates for the expected sensitivity of the high-luminosity LHC.

Optimization of fluorinated phenyl azides as universal photocrosslinkers for semiconducting polymers

Fluorinated phenyl azides (FPA) enable photo-structuring of π-conjugated polymer films for electronic device applications. Despite their potential, FPAs have faced limitations regarding their crosslinking efficiency, and more importantly, their impact on critical semiconductor properties, such as charge-carrier mobility. Here, we report that azide photolysis and photocrosslinking can achieve unity quantum efficiencies for specific FPAs. This suggests preferential nitrene insertion into unactivated C‒H bonds over benzazirine and ketenimine reactions, which we attribute to rapid interconversion between the initially formed hot states. Furthermore, we establish a structure‒activity relationship for carrier mobility quenching. The binding affinity of FPA crosslinker to polymer π-stacks governs its propensity for mobility quenching in both PM6 and PBDB-T used as model conjugated polymers. This binding affinity can be suppressed by FPA ring substitution, but varies in a non-trivial way with π-stack order. Utilizing the optimal FPA, photocrosslinking enables the fabrication of morphology-stabilized, acceptor-infiltrated donor polymer networks (that is, PBDB-T: ITIC and PM6: Y6) for solar cells. Our findings demonstrate the exceptional potential of the FPA photochemistry and offer a promising approach to address the challenges of modelling realistic molecular interactions in complex polymer morphologies, moving beyond the limitations of Flory‒Huggins mean field theory.

Shear strengthening of self-compacting lightweight concrete beams with steel fibers and unbonded prestressing bars

This study aims to investigate the shear behavior of self-compacting lightweight concrete (SCLC) beams strengthened with steel fibers and unbonded prestressing bars. For this, the experimental program included the use of hooked-end steel fibers with volume fractions of 0.5 %−0.75 %, and high-strength prestressing bars with varying prestressing forces and transverse reinforcement ratios. The addition of steel fibers in SCLC significantly increased the normalized shear capacity of beams, reaching up to 2.50 times higher values, whereas the substitution of normal coarse aggregates with lightweight aggregate resulted in a decrease of up to 10.1 %. The shear strengthening of SCLC beams with unbonded prestressing bars provided a substantial increase in the ultimate shear capacity up to 2.06 times higher than that of beam without reinforcement. Increasing the prestressing force of bars effectively restrained the occurrence of critical shear cracking, consequently enhancing the shear capacity. Utilizing hybrid reinforcement with fibers and prestressing bars resulted in a transition of failure mode from shear to flexural, attributed to the improved shear capacity. For the SCLC beams reinforced with steel fibers, the shear strengths were predicted by previous prediction models. When modifier for lightweight concrete was considered, the Imam’s model most precisely predicted the shear strengths with an average vu/vn ratio of 1.00 and SD of 0.07. The fib model Code, based on the modified compression field theory, provided accurate predictions for the shear capacities of SCLC beams with unbonded prestressing bars, exhibiting an average Vu/Vn ratio of 1.00 and SD of 0.09. The fiber-resisting component was reasonably considered in the model with an average Vu/Vn ratio of 1.02 and SD of 0.07.

Rethinking the Effective Field Theory formulation of Gravity

Rethinking the Effective Field Theory formulation of Gravity

Anomalous U(1) extension of the Standard Model

We present a set of example models in which the Standard Model (SM) symmetry group is extended by a new abelian symmetry. This additional symmetry appears anomalous in the effective low-energy theory; however, the anomalies cancel out when massive chiral fermions not present in the effective low-energy theory are taken into account. These chiral fermions under the new abelian gauge group, are chosen to be vector-like under the SM symmetries, and reside in the same representations as quarks and leptons. This allows us to quantitatively determine the magnitude of tree-level interactions between three vector bosons induced in low-energy effective field theory by the integration of chiral heavy fermions. We also examine the perturbativity constraints of the theory and the ultraviolet cut-off. We conclude by highlighting possible extensions of our work.

Wormholes in the axiverse, and the species scale

We analyze a large class of four-dimensional 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} = 1 low-energy realizations of the axiverse satisfying various quantum gravity constraints. We propose a novel upper bound on the ultimate UV cutoff of the effective theory, namely the species scale, which only depends on data available at the two-derivative level. Its dependence on the moduli fields and the number N of axions matches expectations from other independent considerations. After an assessment of the regime of validity of the effective field theory, we investigate the non-perturbative gravitational effects therein. We identify a set of axionic charges supported by extremal and non-extremal wormhole configurations. We present a universal class of analytic wormhole solutions, explore their deformations, and analyze the relation between wormhole energy scales and the species scale. The connection between these wormholes and a special subclass of BPS fundamental instantons is discussed, and an argument in favor of the genericity of certain axion-dependent effective superpotentials is provided. We find a lower bound increasing with N ≫ 1 on the Gauss-Bonnet coefficient, resulting in an exponential suppression of non-extremal wormhole effects. Our claims are illustrated and tested in concrete string theory models.