Field Theory Models Research Articles

Spinor-Vector Duality and the Swampland

The Swampland Program aims to address the question, “when does an effective field theory model of quantum gravity have an ultraviolet complete embedding in string theory?”, and can be regarded as a bottom-up approach for investigations of quantum gravity. An alternative top-down approach aims to explore the imprints and the constraints imposed by string-theory dualities and symmetries on the effective field theory representations of quantum gravity. The most celebrated example of this approach is mirror symmetry. Mirror symmetry was first observed in worldsheet contructions of string compactifications. It was completely unexpected from the effective field theory point of view, and its implications in that context were astounding. In terms of the moduli parameters of toroidally compactified Narain spaces, mirror symmetry can be regarded as arising from mappings of the moduli of the internal compactified space. Spinor-vector duality, which was discovered in worldsheet constructions of string vacua, is an extension of mirror symmetry that arises from mappings of the Wilson line moduli and provide a probe to constrain and explore the moduli spaces of (2, 0) string compactifications. Mirror symmetry and spinor-vector duality are mere two examples of a much wider symmetry structure, whose implications have yet to be unravelled. A mapping between supersymmetric and non-supersymmetric vacua is briefly discussed. T-duality is another important property of string theory and can be thought of as phase-space duality in compact space. I propose that manifest phase-space duality and the related equivalence postulate of quantum mechanics provide the background independent overarching principles underlying quantum gravity.

Entanglement Hamiltonians: From Field Theory to Lattice Models and Experiments

AbstractResults about entanglement (or modular) Hamiltonians of quantum many‐body systems in field theory and statistical mechanics models, and recent applications in the context of quantum information and quantum simulation, are reviewed. In the first part of the review, what is known about entanglement Hamiltonians of ground states (vacua) in quantum field theory is summarized, based on the Bisognano–Wichmann theorem and its extension to conformal field theory. This is complemented with a more rigorous mathematical discussion of the Bisognano–Wichmann theorem, within the framework of Tomita–Takesaki theorem of modular groups. The second part of the review is devoted to lattice models. There, exactly soluble cases are first considered and then the discussion is extended to non‐integrable models, whose entanglement Hamiltonian is often well captured by the lattice version of the Bisognano–Wichmann theorem. In the last part of the review, recently developed applications in quantum information processing that rely upon the specific properties of entanglement Hamiltonians in many‐body systems are summarized. These include protocols to measure entanglement spectra, and schemes to perform state tomography.

Minimal models of field theories: SDYM and SDGR

There exists a natural L∞-algebra or Q-manifold that can be associated to any (gauge) field theory. Perturbatively, it can be obtained by reducing the L∞-algebra behind the jet space BV-BRST formulation to its minimal model. We explicitly construct the minimal models of self-dual Yang-Mills and self-dual gravity theories, which also represents their equations of motion as Free Differential Algebras. The minimal model regains all relevant information about the field theory, e.g. actions, charges, anomalies, can be understood in terms of the corresponding Q-cohomology.

Minimal models of field theories: Chiral higher spin gravity

There exists a unique class of local higher spin gravities with propagating massless fields in $4d$---chiral higher spin gravity. Originally, it was formulated in the light-cone gauge. We construct a covariant form of this theory as a free differential algebra up to the next-to-leading order, i.e., at the level of equations of motion. It also contains the recently discovered covariant forms of the higher spin extensions of self-dual Yang-Mills and self-dual gravity, as well as self-dual Yang-Mills and self-dual gravity themselves. From the mathematical viewpoint the result is equivalent to taking the minimal model (in the sense of ${L}_{\ensuremath{\infty}}$-algebras) of the jet-space extension of the BV-BRST formulation of chiral higher spin gravity, thereby, containing also information about (presymplectic AKSZ) action, counterterms, anomalies, etc.

A Valid Quantization of a Half-Harmonic Oscillator Field Theory

The usual full- and half-harmonic oscillators are turned into field theories, and that behavior is examined using canonical and affine quantization. The result leads to a valid affine quantization of the half harmonic oscillator field theory, which points toward further valid quantizations of more realistic field theory models.

Higgs effect without lunch.

Reduction in effective space–time dimensionality can occur in field-theory models more general than the widely studied dimensional reductions based on technically consistent truncations. Situations where wave function factors depend non-trivially on coordinates transverse to the effective lower dimension can give rise to unusual patterns of gauge symmetry breaking. Leading-order gauge modes can be left massless, but naturally occurring Stueckelberg modes can couple importantly at quartic order and higher, thus generating a ‘covert’ pattern of gauge symmetry breaking. Such a situation is illustrated in a five-dimensional model of scalar electrodynamics in which one spatial dimension is taken to be an interval with Dirichlet/Robin boundary conditions on opposing ends. The Stueckelberg mode remains in the theory as a propagating scalar degree of freedom from a dimensionally reduced perspective, but it is not ‘eaten’ in a mass-generating mechanism. At leading order, it also makes no contribution to the conserved energy; for this reason, it may be called a (non-ghost) ‘phantom’. This simple model illuminates a mechanism which also has been found in gravitational braneworld scenarios.This article is part of the theme issue ‘The future of mathematical cosmology, Volume 2’.

Thirring İnstantonlarının Lyapunov Üstelleri

Recently, nonlinear differential equations corresponding to pure spinor instanton solutions were obtained by using Heisenberg anzat in the 2D Thirring Model, which has been used as a toy model in Quantum field theory. In addition, the evolution of spinor type instanton solutions in phase space was investigated according to the change in the constant parameter β. Spinor instanton dynamics is a special case in which nonlinear terms play an important role. Chaos describes certain nonlinear dynamical systems that depend very precisely on initial conditions. Lyapunov exponents are an important method for measuring stability and deterministic chaos in dynamical systems. Lyapunov exponents characterize and quantify the dynamics of small perturbations of a state or orbit in state space. In this study, Lyapunov spectrum of spinor type instanton solutions was investigated by examining the largest local and global Lyapunov exponents. As a result of the Lyapunov Spectrum, it was determined that the spinor type instanton solutions exhibit chaotic behavior at parameter value β = 2. Periodic and quasi periodic behaviors were detected when the parameter values were β < 2. In cases of β > 2, weak chaotic behaviors were observed. This study demonstrates that Thirring Instantons, which are spinor type instanton solutions, exhibit chaotic properties.

Hyperons, deconfinement, and the speed of sound in neutron stars

The effects of the presence of hyperons and a phase transition to deconfined quark matter on the speed of sound in neutron stars is investigated. For this purpose a composite description consisting of a model of the covariant field theory of hadrons and one for unbound quarks are used. A phase transition with continuous and monotonous variation of the equation of state is assumed. The predictions are contrasted with recent observational data on isolated neutron stars as well as on binary systems. Only one candidate is finally obtained from six different descriptions. According to the present calculations the onset of the hyperons causes the equilibrium speed of sound to exceed the conformal limit. Qualitative agreement with recent work about the influence of the speed of sound on the g-modes of oscillation in neutron stars is obtained.

Entropy of the quantum fluctuations of fermionic instantons in the Universe

The aim of this paper is to study the entropy of quantum fluctuations of fermionic instantons. For this purpose, we focus on the spinor-type instanton solution family of the massless pure fermionic Thirring model because it is a well-known quantized toy model in the quantum field theory since 1958. We calculate the Boltzmann–Gibbs–Shannon (BGS) entropy of the Thirring model by the normalized inner scalogram (NIS) and find that the entropy of quantum fluctuations of Thirring fermionic instantons increase slightly just after the big bang. This result leads us to discuss the relation between the increasing entropy in the Universe due to quantum fluctuations of the fermionic Thirring instantons during the creation of fermionic type particles.

Multiparticle amplitudes in a scalar EFT

At sufficiently high energies the production of a very large number of particles is kinematically allowed. However, it is well-known that already in the simplest case of a weakly-coupled massive λφ4 theory, n-particle amplitudes become non-perturbative in the limit where n scales with energy. In this case, the effective expansion parameter, λn, is no longer small and the perturbative approach breaks down. In general, the associated n-particle production rates were argued to be described by an exponential that, depending on the specifics of the underlying Quantum Field Theory model, could be either growing or decaying in the large-n regime. We investigate such processes in general settings of Effective Field Theory (EFT), involving arbitrary higher-dimensional operators of φ. We perform the resummation of all leading loop corrections arising from EFT vertices for amplitudes at the multiparticle threshold. We find that the net effect of higher-dimensional operators amounts to an exponentially growing factor. We show that if an exponential growth was already generated by the renormalizable interactions, it would then be further enhanced by the EFT contributions. On the other hand, if the multiparticle rates computed in the renormalizable part of the theory were suppressed, this suppression would not be lifted in the EFT.

Decision Field Theory: Equivalence with probit models and guidance for identifiability

We examine identifiability and distinguishability in Decision Field Theory (DFT) models and highlight pitfalls and how to avoid them. In the past literature, the models’ parameters have been put forward as being able to capture the psychological processes in a decision maker’s mind during deliberation. DFT models have been widely used to analyse human decision making behaviour, and many empirical applications in the choice modelling domain rely solely on data concerning the observed final choice. This raises the question if such data are rich enough to allow for the identification of the model’s parameters. Insight into identifiability and distinguishability is crucial as it allows the researcher to determine which behavioural and psychological conclusions can or cannot be drawn from the estimated DFT model and how a DFT model can be specified in such a way that resulting parameters have meaningful interpretations. In this paper, we address this issue. To do this, we first show which specifications of DFT are equivalent to conventional probit models. Then, building on this equivalence result, we apply established analytical methods to highlight and explain the identification and distinguishability issues that arise when estimating DFT models on conventional choice data. We find evidence that some of the DFT models’ special cases suffer from identifiability issues. Our results warrant caution when DFT models are used to infer psychological processes and human behaviour from conventional choice data, and they help researchers choose the correct specification of DFT models.

A prototypical nonlinear second-class system and its BFFT constraints Abelianization

We apply the Batalin–Fradkin–Fradkina–Tyutin formalism to a prototypical second-class system, aiming to convert its constraints from second class to first class. The proposed system admits a consistent initial set of second-class constraints and an open potential function providing room for feasible applications to field theory and mechanical models. The constraints can be arbitrarily nonlinear, broadly generalizing previously known cases. We obtain a sufficient condition for which a simple closed expression for the Abelian converted constraints and modified involutive Hamiltonian can be achieved. As an explicit example, we discuss a spontaneous Lorentz symmetry breaking vectorial model, obtaining the full first-class Abelianized constraints in closed form and the corresponding involutive Hamiltonian.

Color-flavor reflection in the continuum limit of two-dimensional lattice gauge theories with scalar fields.

We address the interplay between local and global symmetries in determining the continuum limit of two-dimensional lattice scalar theories characterized by SO(N_{c}) gauge symmetry and non-Abelian O(N_{f}) global invariance. We argue that, when a quartic interaction is present, the continuum limit of these models corresponds in some cases to the gauged nonlinear σ model field theory associated with the real Grassmannian manifold SO(N_{f})/(SO(N_{c})×SO(N_{f}-N_{c})), which is characterized by the invariance under the color-flavor reflection N_{c}↔N_{f}-N_{c}. Monte Carlo simulations and finite-size scaling analyses, performed for N_{f}=7 and several values of N_{c}, confirm the emergence of the color-flavor reflection symmetry in the scaling limit and support the identification of the continuum limit.

On the spacetime structure of infrared divergencies in QED

We investigate analytic properties of string-integrated massless correlation functions and propagators with emphasis on their infrared behaviour. These are relevant in various models of quantum field theory with massless fields, including QED.

Spacetime symmetric qubit regularization of the asymptotically free two-dimensional O(4) model

We explore if space-time symmetric lattice field theory models with a finite Hilbert space per lattice site can reproduce asymptotic freedom in the two-dimensional $O(4)$ model. We focus on a simple class of such models with a five dimensional local Hilbert space. We demonstrate how even the simplest model reproduces asymptotic freedom within the D-theory formalism but at the cost of increasing the size of the Hilbert space through coupling several layers of a two-dimensional lattice. We then argue that qubit regularization can be viewed as an effective field theory (EFT) even if the continuum limit cannot be reached, as long as we can tune the model close enough to the continuum limit where perturbation theory, or other analytical techniques, become viable. We construct a simple lattice model on a single layer with a four dimensional local Hilbert space that acts like an excellent EFT of the original theory.

Analyzing Cathode and Anode Spot Movements of Atmospheric Arc Plasma in Parallel Electrodes Using Thermal Field Theory and Thermal Nonequilibrium Model

It is necessary to elucidate the mechanism of atmospheric arc plasma movement and the variation in its physical properties for constructing an accurate virtual model while using digital twin technology to design a next‐generation direct current circuit breaker. In this study, the calculation setting for considering the thermal nonequilibrium effect on an electrode surface was established. Moreover, the thermal field theory was employed for simulating the cathode spot movement and a thermal nonequilibrium model was implemented for analyzing the triggering factor of the re‐strike phenomenon occurrence on the anode surface. It was found that heavy particles (ions and neutral particles) were transported forward by the cathode jet and not only caused an increment in the electrical conductivity on the anode surface, but also increased the electric field between the arc column and the anode surface. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Hybrid Field Theory and Particle Simulation Model of Polyelectrolyte–Surfactant Coacervation

Hybrid Field Theory and Particle Simulation Model of Polyelectrolyte–Surfactant Coacervation

Analytical model and general calculation procedure for wrinkled membrane parameters

The existing buckling theory and tension field theory for wrinkled membranes cannot systematically and conveniently acquire the parametric descriptions of wrinkles considering the prestress and deflection effects. Therefore, this paper proposes a mechanical model with the prestress and deflection based on Föppl–von Kármán equations with a modification parameter considering the contribution of membrane bending stiffness. The nonlinear buckling finite element analysis and experiments in the literature are introduced to determine the key parameters as 0.5. Besides, the results also verify the proposed mechanical model has the accurate predictive ability for stress and configuration parameters of wrinkles. Then, a general calculation procedure for wrinkle parameters of complex membranes is established based on the proposed analytical model and tension field theory. It can be divided into three steps, wrinkle discrimination, finite element model modification and wrinkle parameters calculation. Lastly, the rectangular membrane under different shear loads and the hexagonal membrane with tensile loads are investigated to clarify the proposed calculation procedure. The principles in this work can provide a more effective avenue for the accurate analysis of wrinkle behavior in the membrane structure.

A Modified Compression Field Theory Based Analytical Model of RC Slab-Column Joint without Punching Shear Reinforcement

RC slab–column structures are widely used because of the advantages of small space occupation for horizontal members, easy construction and good economy. However, slab–column joints are prone to punching shear failures, which deteriorates structural safety. This paper provides an analytical model to predict the punching shear capacity of the RC slab–column joint. A database of 251 test results is established for the shear punching capacity of slab–column joints without punching shear reinforcement. The performance of existing design codes in predicting the shear resistance of slab–column joints is investigated and compared based on the database. Then, based on the modified compression field theory (MCFT) model, an equation for calculating the punching shear resistance of slab–column joints without punching shear reinforcement is established. The prediction results of the analytical model are enhanced by using the regression analysis method. The model proposed in this paper is based on both reliable theoretical and the summary of a large number of test results, which has higher prediction accuracy than the design codes.

A mixed elliptic-parabolic boundary value problem coupling a harmonic-like map with a nonlinear spinor

Abstract In this paper, we solve a new elliptic-parabolic system arising in geometric analysis that is motivated by the nonlinear supersymmetric sigma model of quantum field theory. The corresponding action functional involves two fields, a map from a Riemann surface into a Riemannian manifold and a spinor coupled to the map. The first field has to satisfy a second-order elliptic system, which we turn into a parabolic system so as to apply heat flow techniques. The spinor, however, satisfies a first-order Dirac-type equation. We carry that equation as a nonlinear constraint along the flow. With this novel scheme, in more technical terms, we can show the existence of Dirac-harmonic maps from a compact spin Riemann surface with smooth boundary to a general compact Riemannian manifold via a heat flow method when a Dirichlet boundary condition is imposed on the map and a chiral boundary condition on the spinor.