Two-dimensional Spacetime Research Articles

Z22-graded supersymmetry via superfield on minimal Z22-superspace

Abstract A superfield formalism for the minimal Z2 2-graded version of supersymmetry is developed. This is done by using the recently introduced definition of integration on the minimal Z2 2-superspace. It is shown that one may construct Z2 2-supersymmetric action by the procedure similar to the standard supersymmetry. 
However, the Lagrangian obtained has very general interaction terms, which give rise to a Z2 2-graded extension of many known theories defined in two-dimensional spacetime. 
As an illustration, we will give a Z2 2-extension of the sine-Gordon model different from the one already discussed in the literature.

Connections between kinks with different asymptotics

In this letter, we show how to build bridges between field-theoretic models that have kink solutions with different asymptotic behavior. We study transformational properties of kinks in models with a real scalar field in two-dimensional space-time. We show how to obtain new models with solitons having different asymptotic behavior, using deformations with specific functions. In particular, starting from the well-known model, we obtain kinks with super-exponential, super-super-exponential, power-law, and logarithmic asymptotics. We also comment on how asymptotic behavior of stability potential and zero mode can be obtained for deformed kinks.

A relationship between two-dimensional and four-dimensional space-time by comparing generalized two-dimensional Yang–Mills theory and Maxwell construction

Some important problems in science do not have analytical solutions in four dimensions including QCD, but they are integrable in two dimensions. For many years, scientists have been trying to find a relation between two-dimensional and four-dimensional space-time to explain the real problem in four dimensions by accurately solving the appropriate model in two dimensions. In this paper, an interesting relation between gYM2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$gY M_2$$\\end{document} (generalized two-dimensional Yang–Mills) and Maxwell construction has been found, which can be a starting point for finding more relations between two-dimensional and four-dimensional space-time, so this paper can play an important role in the advancement of science. For this purpose, first, the large-N behavior of the quartic-cubic generalized two-dimensional Yang–Mills U(N) on a sphere is investigated for finite cubic couplings. It is shown that there are two phase transitions one of which is of third order, which is similar to previous papers, and the other one is of second order, which is a novel result. Second, gYM2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$gY M_2$$\\end{document} (for G(z)=zm+λzn;m=4,6;n<m\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ G(z) = z^ m + \\lambda \\, z^n; m = 4, 6; n < m$$\\end{document}) and Maxwell construction are compared with each other and a relationship between two-dimensional space-time, which is integrable, and four-dimensional space-time is obtained.

Modelling and Mitigating Wind Turbine Clutter in Space–Air Bistatic Radar

The extensive deployment of wind farms has significantly impacted the detection capabilities of space–air bistatic radar (SABR) systems. Although space–time adaptive processing techniques are available, their performance is significantly degraded, and even unable to suppress clutter. This paper explores the geometric configuration of the SABR system and the selection of detection areas, establishing a space–time clutter model that addresses the effects of wind turbine clutter (WTC). Expressions for spatial and Doppler frequencies have been derived to deeply analyze the characteristics of clutter spreading. Building on this, the paper extends two-dimensional space–time data to three-dimensional azimuth–elevation–Doppler data. It proposes a three-dimensional space–time multi-beam (STMB) strategy incorporating the Ordering Points to Identify the Clustering Structure (OPTICS) clustering algorithm to suppress WTC effectively. This algorithm selects WTC samples and applies OPTICS clustering to the clutter-suppressed data to achieve this effect. Simulation experiments further verify the effectiveness of the algorithm.

Geometrically constrained localized configurations: First-order framework and analytical solutions

This work deals with the presence of topological structures in models of two real scalar fields in the two-dimensional spacetime. The subject concerns the presence of a geometric constriction, which appears with a modification of the kinetic term of one of the two fields. We elaborate on the construction of a first-order framework, which directly contributes to find analytical solutions. We describe several distinct possibilities, in particular, the case where the first-order equations do not separate. This is much harder, but we use the integrating factor to deal with analytical configurations. The proposed methodology help us deal with localized structures of both the Néel and Bloch type very naturally, and we end the work suggesting some possibilities of applications in distinct areas of nonlinear science.

The Virasoro minimal string

We introduce a critical string theory in two dimensions and demonstrate that this theory, viewed as two-dimensional quantum gravity on the worldsheet, is equivalent to a double-scaled matrix integral. The worldsheet theory consists of Liouville CFT with central charge c≥≥ 25 coupled to timelike Liouville CFT with central charge 26-c. The double-scaled matrix integral has as its leading density of states the universal Cardy density of primaries in a two-dimensional CFT, thus motivating the name Virasoro minimal string. The duality holds for any value of the continuous parameter cc and reduces to the JT gravity/matrix integral duality in the large central charge limit. It thus provides a precise stringy realization of JT gravity. The main observables of the Virasoro minimal string are quantum analogues of the Weil-Petersson volumes, which are computed as absolutely convergent integrals of worldsheet CFT correlators over the moduli space of Riemann surfaces. By exploiting a relation of the Virasoro minimal string to three-dimensional gravity and intersection theory on the moduli space of Riemann surfaces, we are able to give a direct derivation of the duality. We provide many checks, such as explicit numerical - and in special cases, analytic - integration of string diagrams, the identification of the CFT boundary conditions with asymptotic boundaries of the two-dimensional spacetime, and the matching between the leading non-perturbative corrections of the worldsheet theory and the matrix integral. As a byproduct, we discover natural conformal boundary conditions for timelike Liouville CFT.

The discreet charm of the discrete series in dS2

We study quantum field theories placed on a two-dimensional de Sitter spacetime (dS2) with an eye on the group-theoretic organization of single and multi-particle states. We explore the distinguished role of the discrete series unitary irreducible representation (UIR) in the Hilbert space. By employing previous attempts to realize these states in free tachyonic scalar field theories, we propose how the discrete series may contribute to the Källén–Lehmann decomposition of an interacting scalar two-point function. We also study BF gauge theories with SL(N,R) gauge group in dS2 and establish a relation between the discrete series UIRs and the operator content of these theories. Although present at the level of the operators, states carrying discrete series quantum numbers are projected out of the gauge-invariant Hilbert space. This projection is reminiscent of what happens for quantum field theories coupled to semiclassical de Sitter gravity, where we must project onto the subspace of de Sitter invariant states. We discuss how to impose the diffeomorphism constraints on local field-theory operators coupled to two-dimensional gravity in de Sitter, with particular emphasis on the role of contact terms. Finally, we discuss an SYK-type model with a random two-body interaction that encodes an infinite tower of discrete series operators. We speculate on its potential microscopic connection to the SL(N,R) BF theory in the large-N limit.

Surface Properties of Double-Fin Generated Shock-Wave/Boundary-Layer Interactions

Shock-Wave/Boundary-Layer Interaction (SBLI) is ubiquitous in high-speed air vehicles. SBLI surface flowfield properties of crossing shocks induced by symmetric Double-Fins (DFs) at fin angles of 8° and 10° at Mach 2 are experimentally investigated; a 10° Single-Fin (SF) is also explored as a comparison. Surface visualization is used to capture distinct flowfield structures such as separation and upstream influence. Steady and unsteady Pressure-Sensitive Paints (PSPs) are used to obtain global surface pressure fields. Characteristics of DF-SBLI surface topology are discussed by comparing the corresponding SF-SBLI. The effect of fin angle on DF-SBLI is characterized, and unsteady dynamics of the pressure field are examined. Spectral Proper Orthogonal Decomposition (SPOD) is performed on unsteady PSP, and traveling surface pressure waves and their frequency-dependent behavior are discussed. Dispersion relation of surface pressure waves is revealed by performing two-dimensional space–time Fourier transform on unsteady PSP, and the results are compared with the phase velocity distributions obtained from SPOD. Accompanying group velocity behavior is examined for distinct SBLI regions wherein wave propagation is found dependent on its frequency. Steady surface pressures along the centerline are compared with previous experimental data. Fin-tip spacing is found to be an essential parameter for scaling of upstream influence length.

Kinks in cuscuton-like models with two scalar fields

This work deals with the presence of localized structures in relativistic systems described by two real scalar fields in two-dimensional spacetime. We consider the usual two-field model with the inclusion of the cuscuton term, which couples the fields regardless the potential. First we follow the steps of previous work to show that the system supports a first-order framework, allowing us to obtain the energy of solutions without knowing their explicit form. The cuscuton term brings versatility into the first-order equations, which gives rise to interesting modifications in the profiles of topological configurations, such as the smooth control over their slope and the internal structure of the energy density.

Solving bound state equation for scalar and hybrid QCD in two-dimensional spacetime

Abstract We investigate the bound-state equations in two-dimensional QCD in the $N_c\to \infty$ limit. We consider two types of hadrons, an exotic ``meson" (which is composed of a bosonic quark and a bosonic anti-quark), and an exotic ``baryon" (composed of a fermionic quark and a bosonic antiquark). Using the operator approach, we derive the corresponding bound-state equations for both types of hadrons from the perspectives of light-front quantization and equal-time quantization and confirm the known results. We also present a novel diagrammatic derivation for the exotic meson bound-state equation in the equal-time quantization.Our bound-state equation for the exotic baryons in the equal-time quantization is new. We also numerically solve various bound-state equations, obtain the hadron spectrum and the bound-state wave functions of the lowest-lying states. We explicitly demonstrate the pattern that as the hadron is boosted to infinite-momentum frame, the forward-moving bound-state wave function approach the light-front wave function. &amp;#xD;Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

Study on regional differences and convergence of the green development quality of the construction industry: evidence from China

The green development quality of the construction industry has vital environmental and economic effects. To explore regional differences and convergence, and further provide a reference for the government. Based on the panel data of construction industry development in 31 provinces from 2006 to 2020, this study measured the green development quality of the construction industry in two-dimensional space-time, focuses on the regional differences, the dynamic evolution trend and the convergence of distribution. The findings supported the fact that the green development quality of construction industry was fluctuating upward trend, the overall difference decreased, and the regional difference showed heterogeneity. The convergence rate in the central region was higher than that in the western region, and there was an obvious “catch-up effect.” The green development quality of the construction industry in the national, central region and western region has absolute β convergence. The green development quality of the construction industry in the national, the eastern region and the central region has conditional β convergence. The influence of control variables shows heterogeneity. Based on the conclusions of this study, policy recommendations are put forward from the aspects of science and technology investment, human capital investment and green construction mode.

Об одной контракции дискретной группы D3

The groups of motions of two-dimensional space-time models&#x0D; from a geometric point of view are groups of motions of&#x0D; two-dimensional homogeneous spaces of a constant curvature.&#x0D; When quantizing these models, discrete subgroups of&#x0D; these groups play an important role. The standard model is&#x0D; based on the gauge groups U(1), SU(2) and SU(3). Discrete&#x0D; subgroups of these groups are now also in the center&#x0D; of attention in the elementary particle physics. In this paper&#x0D; we present contractions of the discrete dihedron group&#x0D; D3 induced by limit transitions in the continuous groupO(2)&#x0D; and O(3). The resulting groups are D4 and infinite groups&#x0D; D∞, generating discrete lattices of two-dimensional spacetime&#x0D; models. We also discuss transitions of discrete symmetry&#x0D; groups of the Platonic solids.

CT or P problem and symmetric gapped fermion solution

An analogous ``strong $CP$ problem'' is identified in a toy model in two-dimensional spacetime: a general $1+1\mathrm{d}$ Abelian U(1) anomaly free chiral fermion and chiral gauge theory with a generic theta instanton term $\frac{\ensuremath{\theta}}{2\ensuremath{\pi}}\ensuremath{\int}F$. The theta term alone violates the charge-conjugation-time-reversal $CT$ and the parity $P$ discrete symmetries. The analogous puzzle here is the $CT$ or $P$ problem in $1+1\mathrm{d}$: Why can the $\overline{\ensuremath{\theta}}$ angle (including the effect of $\ensuremath{\theta}$ and the complex phase of a mass matrix) be zero or small for a natural reason? We show that this $CT$ or $P$ problem can be solved by a symmetric mass generation mechanism (SMG, namely generating a mass or energy gap while preserving an anomaly free symmetry). This $1+1\mathrm{d}$ toy model mimics several features of the $3+1\mathrm{d}$ Standard Model: chiral matter content, confinement, and Anderson-Higgs mass by Yukawa-Higgs term. One solution replaces some chiral fermion's Higgs-induced mean-field mass with SMG-induced non-mean-field mass. Another solution enriches this toy model by introducing several new physics beyond the Standard Model: a parity-reflection $PR$ discrete symmetry maps between the chiral and mirror fermions as fermion doubling localized on two domain walls at high energy, and SMG dynamically generates mass to the mirror fermion while still preserving the anomaly free chiral symmetry at an intermediate energy scale, much before the Higgs mechanism generates mass to the chiral fermion at lower energy. Without loss of generality, an arguably simplest $1+1\mathrm{d}$ U(1) symmetric anomaly free chiral fermion/gauge theory (e.g., Weyl fermions with ${3}_{L}\text{\ensuremath{-}}{4}_{L}\text{\ensuremath{-}}{5}_{R}\text{\ensuremath{-}}{0}_{R}$ U(1) charges) is demonstrated in detail. As an analogy to the superfluid-insulator or order-disorder quantum phase transition, in contrast to the conventional Peccei-Quinn solution sitting in the (quasi-long-range-order)-superfluid ordered phase, our solution is in the SMG insulator disordered phase.

A family of non-modular covariant AQFTs

Based on the construction provided in our paper “Covariant homogeneous nets of standard subspaces”, Comm Math Phys 386:305–358, (2021), we construct non-modular covariant one-particle nets on the two-dimensional de Sitter spacetime and on the three-dimensional Minkowski space.

Gravitational radiation in higher order non-local gravity

In this paper, we examine gravitational radiation in higher order non-local gravity described by the non-local gravitational Lagrangian density [Formula: see text]. This non-local theory of gravitation always exhibits the tensor transverse gravitational radiation for [Formula: see text], corresponding to the angular frequency [Formula: see text], composed of two standard [Formula: see text] and [Formula: see text] polarization modes, massless and of helicity 2. Furthermore, it shows, under suitable constraint and [Formula: see text], an additional massive transverse scalar gravitational radiation with helicity 0. It is composed of [Formula: see text] modes associated to [Formula: see text] angular frequencies [Formula: see text], each of which is of breathing polarization [Formula: see text] to lowest order in [Formula: see text], a parameter that takes into account the difference in speed between the slightly massive wave and the massless one. Thanks to NP formalism, we find that the [Formula: see text] class of non-local gravitational waves is [Formula: see text], according to Petrov classification, where the presence or absence of all modes are observer independent. Also, the scalar radiation is forbidden for [Formula: see text] and [Formula: see text] cases, when some conditions are satisfied. Finally, in [Formula: see text] gravity where [Formula: see text], a possible degenerate case with a continuous infinity of transverse massive scalar breathing modes appears under a particular constraint, which reproduces in two-dimensional spacetime the Polyakov–effective action.

Generalized geodesic deviation in de Sitter spacetime

The geodesic deviation equation (GDE) describes the tendency of objects to accelerate towards or away from each other due to spacetime curvature. The GDE assumes that nearby geodesics have a small rate of separation, which is formally treated as the same order in smallness as the separation itself. This assumption is discussed in various papers but is not articulated in any standard textbooks on general relativity. Relaxing this assumption leads to the generalized geodesic deviation equation (GGDE). We elucidate the distinction between the GDE and the GGDE by explicitly computing the relative acceleration between timelike geodesics in two-dimensional de Sitter spacetime. We do this by considering a fiducial geodesic and a secondary geodesic (both timelike) that cross with nonzero speed. These geodesics are spanned by a spacelike geodesic, whose tangent evaluated at the fiducial geodesic defines the separation. The second derivative of the separation describes the relative acceleration between the fiducial and secondary geodesics. Near the crossing point, where the separation between the timelike geodesics is small but their rates of separation can be large, we show that the GGDE holds but the GDE fails to apply.

Bulk reconstruction in moduli space holography

It was recently suggested that certain UV-completable supersymmetric actions can be characterized by the solutions to an auxiliary non-linear sigma-model with special asymptotic boundary conditions. The space-time of this sigma-model is the scalar field space of these effective theories while the target space is a coset space. We study this sigma-model without any reference to a potentially underlying geometric description. Using a holographic approach reminiscent of the bulk reconstruction in the AdS/CFT correspondence, we then derive its near-boundary solutions for a two-dimensional space-time. Specifying a set of Sl(2, ℝ) boundary data we show that the near-boundary solutions are uniquely fixed after imposing a single bulk-boundary matching condition. The reconstruction exploits an elaborate set of recursion relations introduced by Cattani, Kaplan, and Schmid in the proof of the Sl(2)-orbit theorem. We explicitly solve these recursion relations for three sets of simple boundary data and show that they model asymptotic periods of a Calabi-Yau threefold near the conifold point, the large complex structure point, and the Tyurin degeneration.

Synthesis of near-diffraction-free orbital-angular-momentum space-time wave packets having a controllable group velocity using a frequency comb.

Novel forms of light beams carrying orbital angular momentum (OAM) have recently gained interest, especially due to some of their intriguing propagation features. Here, we experimentally demonstrate the generation of near-diffraction-free two-dimensional (2D) space-time (ST) OAM wave packets (ℓ = +1, +2, or +3) with variable group velocities in free space by coherently combining multiple frequency comb lines, each carrying a unique Bessel mode. Introducing a controllable specific correlation between temporal frequencies and spatial frequencies of these Bessel modes, we experimentally generate and detect near-diffraction-free OAM wave packets with high mode purities (>86%). Moreover, the group velocity can be controlled from 0.9933c to 1.0069c (c is the speed of light in vacuum). These ST OAM wave packets might find applications in imaging, nonlinear optics, and optical communications. In addition, our approach might also provide some insights for generating other interesting ST beams.

Holomorphic solutions of soliton equations

We present a holomorphic version of the inverse scattering method for soliton equations of parabolic type in two-dimensional space-time. It enables one to construct examples of solutions holomorphic in both variables and study the properties of all such solutions. We show that every local holomorphic solution of any of these equations admits an analytic continuation to a globally meromorphic function of the spatial variable. We also discuss the role of the Riemann problem in the theory of integrable systems, solubility conditions for the Cauchy problem, the property of trivial monodromy for all solutions of the auxiliary linear system, and the Painlevé property for soliton equations.

Holography of time machines

We use holography to examine the response of interacting quantum fields to the appearance of closed timelike curves in a dynamically evolving background that initially does not contain them. For this purpose, we study a family of two-dimensional spacetimes that model very broad classes of wormhole time machines. The behavior of strongly coupled conformal theories in these spacetimes is then holographically described by three-dimensional AdS bulk geometries that we explicitly construct. The dual bulk spacetime is free from any divergences, but splits into two disconnected components, without and with CTCs, which are joined only through the boundary; then, passages across the chronology horizon are impossible for any field excitations. In dual terms, the strong self-interaction of the CFT decouples the pathological part from the rest of the spacetime. We also find that entangling the CFTs in two separate time machines connects them through a traversable bulk wormhole. Nevertheless, any entanglement-assisted chronology violations will be prevented by quantum bulk corrections, i.e., subleading 1/N effects, again without needing any gravitational backreaction of the CFT. We are led to speculate that chronology may be protected without involving Planck scale physics.