Duality Symmetry Research Articles

Critical behavior of the diffusive susceptible-infected-recovered model.

The critical behavior of the nondiffusive susceptible-infected-recovered model on lattices had been well established in virtue of its duality symmetry. By performing simulations and scaling analyses for the diffusive variant on the two-dimensional lattice, we show that diffusion for all agents, while rendering this symmetry destroyed, constitutes a singular perturbation that induces asymptotically distinct dynamical and stationary critical behavior from the nondiffusive model. In particular, the manifested crossover behavior in the effective mean-square radius exponents reveals that slow crossover behavior in general diffusive multispecies reaction systems may be ascribed to the interference of multiple length scales and timescales at early times.

Duality and statistical mirror symmetry in the generalized geometry setting

We describe statistical mirror symmetry, we introduce the notion of quasi-statistical mirror pairs and we give examples for certain quasi-statistical manifolds. As an application, we get families of almost K?hler structures on the tangent bundle manifold of almost complex 4-dimensional solvmanifolds without complex structures. Finally, we prove that statistical mirror symmetry can be understood in terms of generalized geometry.

Structural and magnetic investigations of (1-x) (Bi0.5Na0.5TiO3)0.94-(BaTiO3)0.06 + (x) SrYFe11O19

This paper describes the manufacturing, structural characteristics, and magnetic properties of a ferroelectric (Na0.5 Bi0.5TiO3-BaTiO3; BNBT) and ferromagnetic (SrYFe11O19; SRYFO) composite system. The polycrystalline composite system (1-x) (Bi0.5Na0.5TiO3)0.94-(BaTiO3)0.06 + (x) SrYFe11O19 (x = 0.00, 0.25, 0.50, 0.75 and 1) was synthesized via solid state reaction followed by modified Sol-gel auto-combustion method. Rietveld refinement of the XRD pattern confirms the presence of dual phase symmetry consisting of BNBT (P4bm) and SRYFO (P63/mmc) phases without any external impurity phase. The calculated value of c/a, cell volume, and grain size confirms the lattice distortion. FE-SEM (Field emission scanning electron microscope) was used to study the morphology formation of prepared composites, which revealed that composites are dense ferroelectric grains well distributed in the ferrite matrix, and the grain size of the nanoparticles ranged from 166 to 240 nm. The magnetic characterization was carried out by VSM (Vibrating Sample Magnetometer) with the applied field in the range of −15 kOe to + 15kOe at room temperature. The M−H loop reveals the ferromagnetic nature of composites. The calculated saturation (MS), remnant (Mr), and coercivity (HC) values are increased with ferrite content. The obtained MS/Mr values are found lesser than 0.49, proving the presence of a solitary, non-interacting realm with a single axial anisotropy. These samples can be used to make permanent magnets and perpendicular recording media.

Brownian motor inspired monodirectional continuous spinning triboelectric nanogenerators for extracting energy from irregular gentle water waves

A TENG intrinsically adaptive to chaotic agitations like the Brownian motors is designed based on dual symmetry breakings.

Duality viewpoint of criticality

In this work, we study quantum many-body systems which are self-dual under duality transformation connecting different symmetry protected topological (SPT) phases. We provide a geometric explanation of the criticality of these self-dual models. More precisely, we show a ground state (quasi-)degeneracy under the periodic boundary conditions,i.e., the ingappability of the bulk spectrum. Equivalently, the symmetry group at criticality, including the duality symmetry, has a mixed 't Hooft anomaly. This approach can not only predict the spectrum of the self-dual model with ordinary 0-form symmetry, but also be applied to that with generalized symmetry, such as higher form and subsystem symmetry. As an application, we illustrate our results with several examples in one and two dimensions, which separate two different SPTs.

Switchable edge-line coupler based on parity time-reversal duality symmetry

A compact broadband Edge-Line Coupler (ELC) based on Parity Time-reversal Duality (PTD) symmetry has been conceived, designed, constructed and measured. The coupler connects four PTD bifilar edge lines (BELs), recently introduced by the authors. The PTD-BELs are constituted by a parallel plate waveguide whose walls are formed by a junction between Perfect Electric Conductor (PEC) and Perfect Magnetic Conductor (PMC) boundary conditions. Reversing the axis orthogonal to the plates interchanges the position of PEC and PMC. Such a waveguide supports unimodal transverse electromagnetic (TEM) propagation, extremely confined along the top and bottom junction edges; its propagation is protected against backscattering from any discontinuity that preserves the PTD symmetry. The ELC presented here is constituted by a 4-port junction in which each port is intrinsically matched due to the PTD symmetry, strongly coupled with a second port, strongly decoupled with a third port, and weakly coupled with a fourth port. The ELC is designed by using a mushroom metasurface for the PMC portion of the device; the connection is based on a switch circuit which imposes open and short conditions on the two opposite sides of the structure. Switching simultaneously the open and short circuits reroutes the signal in a different port, while maintaining the same level of coupling with the other ports. A static prototype has been built and its measurements have confirmed the matching performance and the good directionality of the coupler in a broadband frequency range between 24 and 30 GHz.

Universal Non‐Invertible Symmetries

AbstractIt is well‐known that gauging a finite 0‐form symmetry in a quantum field theory leads to a dual symmetry generated by topological Wilson line defects. These are described by the representations of the 0‐form symmetry group which form a 1‐category. We argue that for a d‐dimensional quantum field theory the full set of dual symmetries one obtains is in fact much larger and is described by a ‐category, which is formed out of lower‐dimensional topological quantum field theories with the same 0‐form symmetry. We study in detail a 2‐categorical piece of this ‐category described by 2d topological quantum field theories with 0‐form symmetry. We further show that the objects of this 2‐category are the recently discussed 2d condensation defects constructed from higher‐gauging of Wilson lines. Similarly, dual symmetries obtained by gauging any higher‐form or higher‐group symmetry also form a ‐category formed out of lower‐dimensional topological quantum field theories with that higher‐form or higher‐group symmetry. A particularly interesting case is that of the 2‐category of dual symmetries associated to gauging of finite 2‐group symmetries, as it describes non‐invertible symmetries arising from gauging 0‐form symmetries that act on ‐form symmetries. Such non‐invertible symmetries were studied recently in the literature via other methods, and our results not only agree with previous results, but our approach also provides a much simpler way of computing various properties of these non‐invertible symmetries. We describe how our results can be applied to compute non‐invertible symmetries of various classes of gauge theories with continuous disconnected gauge groups in various spacetime dimensions. We also discuss the 2‐category formed by 2d condensation defects in any arbitrary quantum field theory.

Gravity, duality and conformal symmetry

The ( 4 , 0 ) supermultiplet in six dimensions contains a fourth-rank tensor gauge field with the symmetries of the Riemann tensor and is superconformal, with 32 + 32 supersymmetries. Dimensional reduction on a circle gives the five dimensions N = 8 supergravity multiplet, with the fourth-rank tensor reducing to the graviton. If there is an interacting ( 4 , 0 ) theory, it should reduce to the full N = 8 supergravity theory and so would give a conformal theory of gravity that would reduce to conventional gravity with the usual two-derivative action at low energies. This paper revisits the conjecture that a non-lagrangian interacting ( 4 , 0 ) superconformal theory arises from a strong coupling limit of five-dimensional supergravity (suitably embedded in M -theory) describing M -theory at energies beyond the Planck scale. A key test for this is identified: M -theory toroidally compactified to five dimensions should have certain BPS states carrying a singlet central charge. These 1/2 BPS states are not related to any of the standard BPS states by dualities and do not correspond to non-singular soliton solutions—they appear to correspond to singular solutions related to gravitational instantons. Such states are needed to provide the Kaluza–Klein modes for the compactified six-dimensional theory. If there are no such states, then the conjecture is false, while the presence of such states would be strong indication that the conjecture could be true.

Correction to: Self-energy problem, vacuum polarization, and dual symmetry in Born–Infeld-type U(1) gauge theories

Correction to: Self-energy problem, vacuum polarization, and dual symmetry in Born–Infeld-type U(1) gauge theories

Near-Field Behaviors of Internal Energy Flows of Free-Space Electromagnetic Waves Induced by Electric Point Dipoles

Both orbital and spin energy fluxes constitute the internal flows decomposed from a Poynting vector. For generic electromagnetic waves propagating through source-free media, these energy fluxes are quadratic in field variables so that their properties are not easily predictable. Notwithstanding, their near-field behaviors play important roles in nanoscale photonics. For time-oscillatory fields, we found two hitherto-overlooked distinctions between the two internal flows. The first is an unequal level between them because the vorticity of an orbital energy flux plays a role comparable to a spin energy flux itself. The second is regarding the electric-magnetic dual symmetry in handling the two internal flows, whence the reactive helicity plays a role as important as the electromagnetic helicity. By helicity conservation, an inter-electric-magnetic transport is possible for the spin angular momentum density, while the electric and magnetic constituents of orbital energy fluxes admit only respective intra-electric and intra-magnetic transports. We have tested the validities of all these claims by exemplarily taking the electromagnetic fields induced by an electric point dipole, either a linear or a circular one. We have thus made new contributions not only in deriving explicit forms of the internal energy flows but also in revealing the magnetic activities hidden under the electromagnetic waves induced by electric point dipoles.

Symplectic Grassmannians, dual conformal symmetry and 4-point amplitudes in 6D

We investigate a new algebra-based approach of finding Grassmannian formulas for scattering amplitudes. Our prime motivation is massive amplitudes of 4D mathcal{N} = 4 SYM, and therefore we consider a 6D Grassmannian formula, where we can take advantage of massless kinematics. We next use symmetry arguments, and in particular, 6D dual conformal symmetry generalized to arbitrary dual conformal weights. Assuming a rational ansatz in terms of Plücker coordinates (i.e. minors) for the integrand, this approach leads to a set of algebraic equations. As an example, we explicitly find the solution for 4-point scattering amplitudes up to proportionality constants.

Solutions in Nonlinear Electrodynamics and their double copy regular black holes

We study solutions in non-linear electrodynamics (NED) and establish several general results. We show, that the SO(2) electric-magnetic duality symmetry is restrictive enough to allow for reconstruction of the NED Lagrangian from the spherically-symmetric electrostatic (Coulomb-like) solution — although there are infinitely many different NED theories admitting a given solution, there exists a unique SO(2) invariant one among them under a simple analyticity assumption (that leaves out some interesting physical theories). We introduce a general algorithm for constructing new SO(2) invariant NED theories in the conventional approach, where only a few examples are available. We also show how to derive the Lagrangian of the SO(2) invariant theory admitting a given electrostatic solution. We further show on a simple example that some NED theories may require sources (particles) of finite (non-zero) size. Such a non-zero size source not only regularizes the infinite energy of the point charge but also satisfies the condition of regularity, that the electric field is zero at the origin. The latter condition was identified earlier as necessary and sufficient for the NED solution to generate a regular black hole via so-called double copy construction and is also satisfied by solitons. We propose a large class of solitonic NED solutions that give rise to regular black holes via double copy construction and contain solutions of Maxwell and Born-Infeld as different limits. This class of NED solutions acquires two new properties in the limit where the corresponding regular black hole’s asymptotics becomes Minkowski: it gives rise to regular higher-spin black holes via generalization of double copy — “higher-copy” construction, and for very short distances changes the sign of the force becoming repulsive/attractive for opposite/similar signs of charges.

Precession Caused by Gravitational Waves.

We show that gravitational waves cause freely falling gyroscopes to precess relative to fixed distant stars, extending the stationary Lense-Thirring effect. The precession rate decays as the square of the inverse distance to the source and is proportional to a suitable Noether current for dual asymptotic symmetries at null infinity. Integrating the rate over time yields a net rotation-a "gyroscopic memory"-whose angle reproduces the known spin memory effect but also contains an extra contribution due to the generator of gravitational electric-magnetic duality. The angle's order of magnitude for the first Laser Interferometer Gravitational Wave Observatory signal is estimated to be Φ∼10^{-35} arc sec near Earth, but the effect may be substantially larger for supermassive black hole mergers.

Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly

We study properties of self-duality symmetry in the Cardy-Rabinovici model. The Cardy-Rabinovici model is the 4d U(1) gauge theory with electric and magnetic matters, and it enjoys the SL(2, ℤ) self-duality at low-energies. SL(2, ℤ) self-duality does not realize in a naive way, but we notice that the STp duality transformation becomes the legitimate duality operation by performing the gauging of ℤN 1-form symmetry with including the level-p discrete topological term. Due to such complications in its realization, the fusion rule of duality defects becomes a non-group-like structure, and thus the self-duality symmetry is realized as a non-invertible symmetry. Moreover, for some fixed points of the self-duality, the duality symmetry turns out to have a mixed gravitational anomaly detected on a K3 surface, and we can rule out the trivially gapped phase as a consequence of anomaly matching. We also uncover how the conjectured phase diagram of the Cardy-Rabinovici model satisfies this new anomaly matching condition.

Photonic Z2 Topological Anderson Insulators

That disorder can induce nontrivial topology is a surprising discovery in topological physics. As a typical example, Chern topological Anderson insulators (TAIs) have been realized in photonic systems, where the topological phases exist without symmetry protection. In this Letter, by taking transverse magnetic and transverse electric polarizations as pseudospin degrees of freedom, we theoretically propose a scheme to realize disorder-induced symmetry-protected topological phase transitions in two-dimensional photonic crystals with a combined time-reversal, mirror, and duality symmetry T_{f}=TM_{z}D. In particular, we demonstrate that the disorder-induced symmetry-protected topological phase persists even without pseudospin conservation, thereby realizing a photonic Z_{2} TAI, in contrast to a Z-classified quantum spin Hall (QSH) TAI with decoupled spins. By formulating a new scattering approach, we show that the topology of both the QSH and Z_{2} TAIs can be manifested by the accumulated spin rotations of the reflected waves from the photonic crystals. Using a transmission structure, we also illustrate the trivialization of a disordered QSH phase with an even integer topological index caused by spin coupling.

From pre- to post-big bang: an (almost) self-dual cosmological history

We present a short introduction to a non-standard cosmological scenario motivated by the duality symmetries of string theory, in which the big bang singularity is replaced with a ‘big bounce’ at high but finite curvature. The bouncing epoch is prepared by a long (possibly infinitely extended) phase of cosmic evolution, starting from an initial state asymptotically approaching the string perturbative vacuum. This article is part of the theme issue ‘The future of mathematical cosmology, Volume 2’.

Self-energy problem, vacuum polarization, and dual symmetry in Born–Infeld-type U(1) gauge theories

We extensively explore three different aspects of Born-Infeld (BI) type nonlinear $U(1)$ gauge-invariant modifications of Maxwell's classical electrodynamics (also known as BI-type nonlinear electrodynamics) and bring some new perspectives on these theories. First, within the framework of exponential $U(1)$ gauge theory, it is explicitly proved that although the electric field at the location of the elementary point charges is not finite, but the total electrostatic field energy is finite. Motivated by this observation together with a wealth of evidence, we conjecture that all theories in 4-dimensional spacetime that belong to the BI family result in finite self-energy for elementary charged particles. In higher dimensions, it is found that the weak-field coupling limit of BI-type theories, which is identified as the weak field limit of effective Euler-Heisenberg (EH) theory, does not possess a regularizing ability to make the self-energy of a point charge finite, which implies that the conjecture may not hold for some BI-type theories. However, we explicitly prove that BI, logarithmic and exponential $U(1)$ gauge theories in arbitrary dimensions result in finite self-energy as well. Next, we classically study the problem of vacuum polarization effects and then systematically make a connection between all BI-type theories and QED. It is shown that all the BI-type theories classically predict the vacuum polarization effects, in which the final results are exactly in one-to-one correspondence with QED and the effective EH theory up to the leading order of corrections. Finally, we present a new, simple proof indicating that ...

Reconfigurable Topological States in Arrays of Bianisotropic Particles

Topological photonics promotes a novel approach to resilient light manipulation by exploiting spatio-temporal symmetries of the system and dual symmetry of electromagnetic field. Various prospective device applications pose the need to flexibly control robust field localization associated with topological modes. Here we design a topological array of resonant dielectric meta-atoms with bianisotropic response induced by a spatial symmetry reduction. Mutual orientation of the designed meta-atoms encodes a staggered bianisotropy pattern capable of trapping topological states in a one-dimensional array containing a small number of particles. We show that the topological interface state can be tailored by the rotation of coaxial bianisotropic particles arranged in an equidistant lattice. Our experimental implementation based on ceramic horseshoe-shaped disks demonstrates remarkable reconfigurability of electromagnetic topological states.

Duality, decay rates, and local-field models in macroscopic QED

Any treatment of magnetic interactions between atoms, molecules, and optical media must start at the form of the interaction energy. This forms the base on which predictions about any number of magnetic atom-light properties stands, spontaneous decay rates and forces included. As is well known, the Heaviside-Larmor duality symmetry of Maxwell's equations, where electric and magnetic quantities are exchanged, is broken by the usual form of the magnetic interaction energy. We argue that this symmetry can be restored by including general local-field effects and that local fields should be treated as a necessity for correctly translating between the microscopic world of the dipole and the macroscopic world of the measured fields. This may additionally aid in resolving a long-standing debate over the form of the force on a dipole in a medium. Finally, we compute the magnetic dipole decay rate in a magnetodielectric with local-field effects taken into account and show that macroscopic quantum electrodynamics can be made to be dual symmetric at an operator level, instead of only for expectation values.

Emergence and Breaking of Duality Symmetry in Generalized Fundamental Thermodynamic Relations.

Thermodynamics as limiting behaviors of statistics is generalized to arbitrary systems with probability apriori where the thermodynamic infinite-size limit is replaced by a multiple-measurement limit. A duality symmetry between Massieu's and Gibbs's entropy arises in the limit of infinitely repeated observations, yielding the Gibbs equation and Hill-Gibbs-Duhem equation (HGDE) as a dual pair. If a system has a thermodynamic limit satisfying Callen's postulate, entropy being an Eulerian function, the symmetry is lost: the HGDE reduces to the Gibbs-Duhem equation. This theory provides a de-mechanized foundation for classical and nanothermodynamics and offers a framework for distilling emergence from large data, free from underlying details.