Field Theory Research Articles

Magnetic Properties in the Spin-3/2 Ashkin-Teller Model from Mean Field Theory

Magnetic Properties in the Spin-3/2 Ashkin-Teller Model from Mean Field Theory

On the analysis and deeper properties of the fractional complex physical models pertaining to nonsingular kernels.

This study solves the coupled fractional differential equations defining the massive Thirring model and the Kundu Eckhaus equation using the Natural transform decomposition method. The massive Thirring model is a dynamic component of quantum field theory, consisting of a coupled nonlinear complex differential equations. Initially, we study the suggested equations under the fractional derivative of Caputo-Fabrizio. The Atangana-Baleanu derivative is then used to evaluate the comparable equations. The results are significant and necessary for exploring a range of physical processes. This paper uses modern approach and the fractional operators in this situation to develop satisfactory approximations to the offered problems. The proposed approach combines the natural transform technique with the efficient Adomian decomposition scheme. Obtaining numerical findings in the form of a fast-converge series significantly improves the scheme's accuracy. Some graphical plot distributions are presented to show that the present approach is very simple and straightforward. We performed a fractional order analysis of assumed phenomena to demonstrate and validate the effectiveness of the future technique. The behaviour of the approximate series solution for several fractional orders is shown visually. Additionally, the nature of the derived outcome has been observed for various fractional orders. The derived results demonstrate how simple and efficient the proposed method is to apply for analysing the behaviour of fractionally-order complex nonlinear differential equations that arise in related fields of engineering and science.

Ax–Kochen–Ershov principles for finitely ramified henselian fields

We study the model theory of finitely ramified henselian valued fields of fixed initial ramification, obtaining versions of the Ax–Kochen–Ershov principle as follows. We identify the induced structure on the residue field and show that once the residue field is endowed with this structure, the theory of the valued field is determined by the theories of the enriched residue field and the value group. Similarly, we show that the existential theory of the valued field is determined by the positive existential theory of the enriched residue field. We also prove that an embedding of finitely ramified henselian valued fields is existentially closed as soon as the induced embeddings of value group and residue field are existentially closed. This last result requires no enrichment of the residue field, in analogy to the corresponding result for model completeness, which holds by results of Ershov and Ziegler.

Nucleon-to- Δ Axial and Pseudoscalar Transition Form Factors

A symmetry-preserving approach to the calculation of baryon properties in relativistic quantum field theory is used to predict all form factors associated with nucleon-to-Δ axial and pseudoscalar transition currents, thereby unifying them with many additional properties of these and other baryons. The new parameter-free predictions can serve as credible benchmarks for use in analyzing existing and anticipated data from worldwide efforts focused on elucidation of ν properties. Published by the American Physical Society 2024

Holography as homotopy

We give an interpretation of holography in the form of the AdS/CFT correspondence in terms of homotopy algebras. A field theory such as a bulk gravity theory can be viewed as a homotopy Lie or L∞ algebra. We extend this dictionary to theories defined on manifolds with a boundary, including the conformal boundary of AdS, taking into account the cyclic structure needed to define an action with the correct boundary terms. Projecting fields to their boundary values then defines a homotopy retract, which in turn implies that the cyclic L∞ algebra of the bulk theory is equivalent, up to homotopy, to a cyclic L∞ algebra on the boundary. The resulting action is the ‘on-shell action’ conventionally computed via Witten diagrams that, according to AdS/CFT, yields the generating functional for the correlation functions of the dual CFT. These results are established with the help of new techniques regarding the homotopy transfer of cyclic L∞ algebras.

Flat-space limit of holographic pseudoentropy in (A)dS spacetimes

The real part of pseudoentropy in conformal field theories is holographically calculated by the area of some extremal spacelike surfaces in the dual de Sitter (dS) and anti–de Sitter (AdS) spacetimes. We show that the flat-space limit of these curves in three-dimensional (A)dS spacetimes is well defined. We find that, if the length of the curves is calculated from the radial coordinate where the retarded time is extremum, then after taking the flat-space limit, the entanglement entropy of the dual theory of three-dimensional flat spacetime is obtained. For dS spacetime, the radial coordinate corresponding to the extremum of retarded time is located inside the cosmological horizon. Our results suggest that, on the field theory side, the entanglement entropy in the dual theory of flat spacetimes should be obtained from the ultrarelativistic limit of pseudoentropy in the dual conformal field theory to (A)dS spacetimes. Published by the American Physical Society 2024

Statistical physics and emergent behaviour: from spin models to cultural complexity. In memory of Ralph Kenna (27.08.1964-26.10.2023)

It’s been sixty years since Ralph’s birth day and soon it will be one year since he left us. Initially, this collection of papers was being prepared as a Festschrift - a birthday greeting, and now it is published in his memory. It is difficult to write this foreword, because Ralph is not only a fellow physicist and a close collaborator, he is a very close friend. It is also difficult to write because, in a short text, it is hard to reflect the versatility of his gifts: from statistical physics to field theory, from the science of complex systems to quantitative methods in social sciences and humanities, from scientometrics to history of physics. This is not a complete list of areas that he enriched thanks to his talent and hard work. What’s more, his activities in scientific research are inseparable from his public activities, be it the protection of historical heritage or the restoration of historical memory in Ireland, his motherland, or the collection of funds for the fight against serious diseases in the UK, where he worked, or his participation in the organisation and evaluation of research work on a pan-European scale. The integrity of his personality is one of those features that first come to mind when we think about him, repeatedly.

Revisiting the Lee-Yang singularities in the four-dimensional Ising model: a tribute to the memory of Ralph Kenna

We have studied numerically the Lee-Yang singularities of the four dimensional Ising model at criticality, which is believed to be in the same universality class as the φ44 scalar field theory. We have focused in the numerical characterization of the logarithmic corrections to the scaling of the zeros of the partition function and its cumulative probability distribution, finding a very good agreement with the predictions of the renormalization group computation on the φ44 scalar field theory. To obtain these results, we have extended a previous study [R. Kenna, C. B. Lang, Nucl. Phys., 1993, B393, 461] in which there were computed numerically the first two zeros for L≤24 lattices, to the computation of the first four zeros for L≤64 lattices.

Revisiting elastic string models of forward interest rates

Twenty five years ago, several authors proposed to describe the forward interest rate curve (FRC) as an elastic string along which idiosyncratic shocks propagate, accounting for the peculiar structure of the return correlation across different maturities. In this paper, we revisit the specific ‘stiff’ elastic string field theory of Baaquie and Bouchaud [Stiff field theory of interest rates and psychological future time. Wilmott Mag., 2004, 2–6] in a way that makes its micro-foundation more transparent. Our model can be interpreted as capturing the effect of market forces that set the rates of nearby tenors in a self-referential fashion. The model is parsimonious and accurately reproduces the whole correlation structure of the FRC over the time period 1994–2023, with an error around 1% and with only one adjustable parameter, the value of which being very stable across the last three decades. The dependence of correlation on time resolution (also called the Epps effect) is also faithfully reproduced within the model and leads to a cross-tenor information propagation time on the order of 30 minutes. Finally, we confirm that the perceived time in interest rate markets is a strongly sub-linear function of real time, as surmised by Baaquie and Bouchaud [Stiff field theory of interest rates and psychological future time. Wilmott Mag., 2004, 2–6]. In fact, our results are fully compatible with hyperbolic discounting, in line with the recent behavioral Finance literature Farmer and Geanakoplos [Hyperbolic Discounting is Rational: Valuing the Far Future with Uncertain Discount Rates, Cowles Foundation Discussion Papers, 2009 (Cowles Foundation for Research in Economics, Yale University)].

Modularity of the Schur index, modular differential equations, and high-temperature asymptotics

In this paper we analytically explore the modularity of the flavored Schur index of 4d N=2 superconformal field theories. We focus on the A1 theories of class-S and N=4 theories with SU(N) gauge group. We work out the modular orbit of the flavored index and defect index, compute the dimension of the space spanned by the orbit, and provide complete basis for computing modular transformation matrices. The dimension obtained from the flavored analysis predicts the minimal order of the unflavored modular differential equation satisfied by the unflavored Schur index. With the help of modularity, we also study analytically the high temperature asymptotics of the Schur index. In the high temperature limit τ→+i0, we identified the (defect) Schur index of the genus-zero A1 theories of class S with the S3 partition function of the SU(2)×U(1)n star-shaped quiver (with Wilson line insertion). In the identification, we observe an interesting relation between the linear-independence of defect indices and the convergence of the Wilson line partition functions. Published by the American Physical Society 2024

Approximate CFTs and random tensor models

A key issue in both the field of quantum chaos and quantum gravity is an effective description of chaotic conformal field theories (CFTs), that is CFTs that have a quantum ergodic limit. We develop a framework incorporating the constraints of conformal symmetry and locality, allowing the definition of ensembles of ‘CFT data’. These ensembles take on the same role as the ensembles of random Hamiltonians in more conventional quantum ergodic phases of many-body quantum systems. To describe individual members of the ensembles, we introduce the notion of approximate CFT, defined as a collection of ‘CFT data’ satisfying the usual CFT constraints approximately, i.e. up to small deviations. We show that they generically exist by providing concrete examples. Ensembles of approximate CFTs are very natural in holography, as every member of the ensemble is indistinguishable from a true CFT for low-energy probes that only have access to information from semi-classical gravity. To specify these ensembles, we impose successively higher moments of the CFT constraints. Lastly, we propose a theory of pure gravity in AdS3 as a random matrix/tensor model implementing approximate CFT constraints. This tensor model is the maximum ignorance ensemble compatible with conformal symmetry, crossing invariance, and a primary gap to the black-hole threshold. The resulting theory is a random matrix/tensor model governed by the Virasoro 6j-symbol.

Dimer piling problems and interacting field theory

The dimer tiling problem asks in how many ways can the edges of a graph be covered by dimers so that each site is covered once. In the special case of a planar graph, this problem has a solution in terms of a free fermionic field theory. We rediscover and explore an expression for the number of coverings of an arbitrary graph by arbitrary objects in terms of an interacting fermionic field theory first proposed by Samuel. Generalizations of the dimer tiling problem, which we call “dimer piling problems,” demand that each site be covered N times by indistinguishable dimers. Our field theory provides a solution of these problems in the large-N limit. We give a similar path integral representation for certain lattice coloring problems. Published by the American Physical Society 2024

Brick wall quantum circuits with global fermionic symmetry

We study brick wall quantum circuits enjoying a global fermionic symmetry. The constituent 2-qubit gate, and its fermionic symmetry, derive from a 2-particle scattering matrix in integrable, supersymmetric quantum field theory in 1+1 dimensions. Our 2-qubit gate, as a function of three free parameters, is of so-called free fermionic or matchgate form, allowing us to derive the spectral structure of both the brick wall unitary U_FUF and its, non-trivial, Hamiltonian limit H_{\gamma}Hγ in closed form. We find that the fermionic symmetry pins H_{\gamma}Hγ to a surface of critical points, whereas breaking that symmetry leads to non-trivial topological phases. We briefly explore quench dynamics for this class of circuits.

Quantum error thresholds for gauge-redundant digitizations of lattice field theories

In the quantum simulation of lattice gauge theories, gauge symmetry can be either fixed or encoded as a redundancy of the Hilbert space. While gauge-fixing reduces the number of qubits, keeping the gauge redundancy can provide code space to mitigate and correct quantum errors by checking and restoring Gauss’s law. In this work, we consider the correctable errors for generic finite gauge groups and design the quantum circuits to detect and correct them. We calculate the error thresholds below which the gauge-redundant digitization with Gauss’s law error correction has better fidelity than the gauge-fixed digitization involving only gauge-invariant states. Our results provide guidance for fault-tolerant quantum simulations of lattice gauge theories. Published by the American Physical Society 2024

Jesus was Married? “SCANDALOUS!” Field Theory in Reporting on a U.S. Religion Scandal

ABSTRACT The scandal story reflects an essential journalistic lens to understand culture; scandals circumscribe attention to the norms, values and expectations of a culture. This study explores the nature of the scandal story through an examination of a case in U.S. journalism: the coverage of the now-disproved “Gospel of Jesus’ Wife.” This study examines the initial 2012 case of an ancient papyrus scrap alleged to prove that the historical Jesus was married, and that over a period of eight years, was disproved to a complicated backstory of cultural misogyny, academic dishonesty, and a con man. Through the lens of field theory, this study aims to explore how scandal stories help shed a light on how a culture informs a newsroom doxa.

The Challenger's Social Skills: Bengkalis Panglong Business

This article focuses on the social skills possessed by the challengers, in this case, charcoal panglong (a place for wood processing and charcoal production) owners, entrepreneurs, and their workers who are able to survive the regulations on the utilization of mangrove forests. The battle in this field began in the days of the Dutch government. The purpose of this study is 1) to reveal how the contestation of stability and change in the charcoal panglong business in Bengkalis. 2) to analyze the social skills possessed by the owner of the charcoal panglong and his workers, hereinafter referred to as challengers, in maintaining the existence of his business until now. The ability to maintain the charcoal panglong business and its business existence. A series of research studies using a qualitative approach, using interviews and observations, were conducted by the author to reveal a series of strategic action fields in the forestry business. The findings obtained show that challengers have always competed with incumbents (mangrove forest policies and regulations) and governance units for a long time. This field contestation has occurred since 1853, starting from the time the Dutch government established a panglong in Bengkalis to meet the demand for wood and charcoal from Singapore and Malaysia. The challenger always maintains its business existence by fulfilling all obligations as a holder of a community forest license granted by the president and also as a charcoal export license holder to Malaysia; of course, to meet these export needs, another skill it has is maintaining a stable supply of charcoal for export. The patron client relationship is one of the challenger's skills in maintaining good relations with the local community and its workers. The market field analysis using Fligstein and McAdam's Field Theory of Strategic Action Field (SAF) helps explore the elements of social skills in SAF so that the structure of stability and change in the forestry charcoal panglong business arena can be illustrated more clearly.

On fusing matrices associated with conformal boundary conditions

In the context of rational conformal field theories (RCFT) we look at the fusing matrices that arise when a topological defect is attached to a conformal boundary condition. We call such junctions open topological defects. One type of fusing matrices arises when two open defects fuse while another arises when an open defect passes through a boundary operator. We use the topological field theory approach to RCFTs based on Frobenius algebra objects in modular tensor categories to describe the general structure associated with such matrices and how to compute them from a given Frobenius algebra object and its representation theory. We illustrate the computational process on the rational free boson theories. Applications to boundary renormalisation group flows are briefly discussed.

Spiral tool path generation method for complex pocket machining based on electrostatic field theory

Spiral tool path generation method for complex pocket machining based on electrostatic field theory

Differential equations for Carrollian amplitudes

Differential equations are powerful tools in the study of correlation functions in conformal field theories (CFTs). Carrollian amplitudes behave as correlation functions of Carrollian CFT that holographically describes asymptotically flat spacetime. We derive linear differential equations satisfied by Carrollian MHV gluon and graviton amplitudes. We obtain non-distributional solutions for both the gluon and graviton cases. We perform various consistency checks for these differential equations, including compatibility with conformal Carrollian symmetries.

Equivalence of field theories: Crane-Yetter and the shadow

Equivalence of field theories: Crane-Yetter and the shadow