Showing papers on "Symmetry (geometry) published in 2021"

Overcoming Symmetry Mismatch in Vaccine Nanoassembly through Spontaneous Amidation.

Abstract: Matching of symmetry at interfaces is a fundamental obstacle in molecular assembly. Virus-like particles (VLPs) are important vaccine platforms against pathogenic threats, including Covid-19. However, symmetry mismatch can prohibit vaccine nanoassembly. We established an approach for coupling VLPs to diverse antigen symmetries. SpyCatcher003 enabled efficient VLP conjugation and extreme thermal resilience. Many people had pre-existing antibodies to SpyTag:SpyCatcher but less to the 003 variants. We coupled the computer-designed VLP not only to monomers (SARS-CoV-2) but also to cyclic dimers (Newcastle disease, Lyme disease), trimers (influenza hemagglutinins), and tetramers (influenza neuraminidases). Even an antigen with dihedral symmetry could be displayed. For the global challenge of influenza, SpyTag-mediated display of trimer and tetramer antigens strongly induced neutralizing antibodies. SpyCatcher003 conjugation enables nanodisplay of diverse symmetries towards generation of potent vaccines.

Z 2 -enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups

Abstract: The authors develop a framework to diagnose topological superconductivity based on irreducible representations and Pfaffian invariants.

PRS-Net: Planar Reflective Symmetry Detection Net for 3D Models

Abstract: In geometry processing, symmetry is a universal type of high-level structural information of 3D models and benefits many geometry processing tasks including shape segmentation, alignment, matching, and completion. Thus it is an important problem to analyze various symmetry forms of 3D shapes. Planar reflective symmetry is the most fundamental one. Traditional methods based on spatial sampling can be time-consuming and may not be able to identify all the symmetry planes. In this article, we present a novel learning framework to automatically discover global planar reflective symmetry of a 3D shape. Our framework trains an unsupervised 3D convolutional neural network to extract global model features and then outputs possible global symmetry parameters, where input shapes are represented using voxels. We introduce a dedicated symmetry distance loss along with a regularization loss to avoid generating duplicated symmetry planes. Our network can also identify generalized cylinders by predicting their rotation axes. We further provide a method to remove invalid and duplicated planes and axes. We demonstrate that our method is able to produce reliable and accurate results. Our neural network based method is hundreds of times faster than the state-of-the-art methods, which are based on sampling. Our method is also robust even with noisy or incomplete input surfaces.

Hidden Symmetry of Vanishing Love Numbers.

Abstract: We show that perturbations of massless fields in a black hole background enjoy a hidden $SL(2,\mathbb{R})\ifmmode\times\else\texttimes\fi{}U(1)$ (``Love'') symmetry in the properly defined near zone approximation. Love symmetry mixes low- and high-frequency modes. Still, this approximate symmetry allows us to derive exact results about static tidal responses. Generators of the Love symmetry are globally well defined for any value of black hole spin. Generic regular solutions of the near zone equation for linearized perturbations form infinite-dimensional $SL(2,\mathbb{R})$ representations. In some special cases, these are highest weight representations. This situation corresponds to vanishing Love numbers. Other known facts about static Love numbers also acquire an elegant explanation in terms of the $SL(2,\mathbb{R})$ representation theory.

Symmetries of the black hole interior and singularity regularization

Abstract: We reveal an $\mathfrak{iso}(2,1)$ Poincare algebra of conserved charges associated with the dynamics of the interior of black holes The action of these Noether charges integrates to a symmetry of the gravitational system under the Poincare group ISO$(2,1)$, which allows to describe the evolution of the geometry inside the black hole in terms of geodesics and horocycles of AdS${}_2$ At the Lagrangian level, this symmetry corresponds to Mobius transformations of the proper time together with translations Remarkably, this is a physical symmetry changing the state of the system, which also naturally forms a subgroup of the much larger $\textrm{BMS}_{3}=\textrm{Diff}(S^1)\ltimes\textrm{Vect}(S^1)$ group, where $S^1$ is the compactified time axis It is intriguing to discover this structure for the black hole interior, and this hints at a fundamental role of BMS symmetry for black hole physics The existence of this symmetry provides a powerful criterion to discriminate between different regularization and quantization schemes Following loop quantum cosmology, we identify a regularized set of variables and Hamiltonian for the black hole interior, which allows to resolve the singularity in a black-to-white hole transition while preserving the Poincare symmetry on phase space This unravels new aspects of symmetry for black holes, and opens the way towards a rigorous group quantization of the interior

Topological field theories and symmetry protected topological phases with fusion category symmetries

Abstract: Fusion category symmetries are finite symmetries in 1+1 dimensions described by unitary fusion categories. We classify 1+1d time-reversal invariant bosonic symmetry protected topological (SPT) phases with fusion category symmetry by using topological field theories. We first formulate two-dimensional unoriented topological field theories whose symmetry splits into time-reversal symmetry and fusion category symmetry. We then solve them to show that SPT phases are classified by equivalence classes of quintuples (Z, M, i, s, ϕ) where (Z, M, i) is a fiber functor, s is a sign, and ϕ is the action of orientation- reversing symmetry that is compatible with the fiber functor (Z, M, i). We apply this classification to SPT phases with Kramers-Wannier-like self-duality.

Kagome superconductors AV$_3$Sb$_5$ (A=K, Rb, Cs)

Abstract: The quasi two-dimensional (quasi-2D) kagome materials AV$_3$Sb$_5$ (A=K, Rb, Cs) were found to be a prime example of kagome superconductors, a new quantum platform to investigate the interplay between electron correlation effects, topology and geometric frustration. In this review, we report recent progress on the experimental and theoretical studies of AV$_3$Sb$_5$ and provide a broad picture of this fast-developing field in order to stimulate an expanded search for unconventional kagome superconductors. We review the electronic properties of AV$_3$Sb$_5$, the experimental measurements of the charge density wave state, evidence of time-reversal symmetry breaking, and other potential hidden symmetry breaking in these materials. A variety of theoretical proposals and models that address the nature of the time-reversal symmetry breaking are discussed. Finally, we review the superconducting properties of AV$_3$Sb$_5$, especially the potential pairing symmetries and the interplay between superconductivity and the charge density wave state.

The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs

Abstract: 2-group symmetries arise when 1-form symmetries and 0-form symmetries of a theory mix with each other under group multiplication. We discover the existence of 2-group symmetries in 5d N=1 abelian gauge theories arising on the (non-extended) Coulomb branch of 5d superconformal field theories (SCFTs), leading us to argue that the UV 5d SCFT itself admits a 2-group symmetry. Furthermore, our analysis determines the global forms of the 0-form flavor symmetry groups of 5d SCFTs, irrespective of whether or not the 5d SCFT admits a 1-form symmetry. As a concrete application of our method, we analyze 2-group symmetries of all 5d SCFTs, which reduce in the IR, after performing mass deformations, to 5d N=1 non-abelian gauge theories with simple, simply connected gauge groups. For rank-1 Seiberg theories, we check that our predictions for the flavor symmetry groups match with the superconformal and ray indices available in the literature. We also comment on the mixed 't Hooft anomaly between 1-form and 0-form symmetries arising in 5d N=1 non-abelian gauge theories and its relation to the 2-groups, discussing various scenarios for the UV SCFT completions of these gauge theories. In particular, we provide one possible scenario that consists of an anomaly cancellation mechanism by an additional (topological) sector.

D-instantons in Type IIA string theory on Calabi-Yau threefolds

Abstract: Type IIA string theory compactified on a Calabi-Yau threefold has a hypermultiplet moduli space whose metric is known to receive non-perturbative corrections from Euclidean D2-branes wrapped on 3-cycles. These corrections have been computed earlier by making use of mirror symmetry, S-duality and twistorial description of quaternionic geometries. In this paper we compute the leading corrections in each homology class using a direct world-sheet approach without relying on any duality symmetry or supersymmetry. Our results are in perfect agreement with the earlier predictions.

Global Form of Flavor Symmetry Groups in 4d N=2 Theories of Class S

Abstract: We provide a systematic method to deduce the global form of flavor symmetry groups in 4d N=2 theories obtained by compactifying 6d N=(2,0) superconformal field theories (SCFTs) on a Riemann surface carrying regular punctures and possibly outer-automorphism twist lines. Apriori, this method only determines the group associated to the manifest part of the flavor symmetry algebra, but often this information is enough to determine the group associated to the full enhanced flavor symmetry algebra. Such cases include some interesting and well-studied 4d N=2 SCFTs like the Minahan-Nemeschansky theories. The symmetry groups obtained via this method match with the symmetry groups obtained using a Lagrangian description if such a description arises in some duality frame. Moreover, we check that the proposed symmetry groups are consistent with the superconformal indices available in the literature. As another application, our method finds distinct global forms of flavor symmetry group for pairs of interacting 4d N=2 SCFTs (recently pointed out in the literature) whose Coulomb branch dimensions, flavor algebras and levels coincide (along with other invariants), but nonetheless are distinct SCFTs.

Symmetric Parallax Attention for Stereo Image Super-Resolution

Abstract: Although recent years have witnessed the great advances in stereo image super-resolution (SR), the beneficial information provided by binocular systems has not been fully used. Since stereo images are highly symmetric under epipolar constraint, in this paper, we improve the performance of stereo image SR by exploiting symmetry cues in stereo image pairs. Specifically, we propose a symmetric bi-directional parallax attention module (biPAM) and an inline occlusion handling scheme to effectively interact cross-view information. Then, we design a Siamese network equipped with a biPAM to super-resolve both sides of views in a highly symmetric manner. Finally, we design several illuminance-robust losses to enhance stereo consistency. Experiments on four public datasets demonstrate the superior performance of our method. Source code is available at https://github.com/YingqianWang/iPASSR.

2-Group Symmetries and their Classification in 6d

Abstract: We uncover 2-group symmetries in 6d superconformal field theories. These symmetries arise when the discrete 1-form symmetry and continuous flavor symmetry group of a theory mix with each other. We classify all 6d superconformal field theories with such 2-group symmetries. The approach taken in 6d is applicable more generally, with minor modifications to include dimension specific operators (such as instantons in 5d and monopoles in 3d), and we provide a discussion of the dimension-independent aspects of the analysis. We include an ancillary mathematica code for computing 2-group symmetries, once the dimension specific input is provided. We also discuss a mixed 't Hooft anomaly between discrete 0-form and 1-form symmetries in 6d.

1-form symmetries of 4d N=2 class S theories

Abstract: We determine the 1-form symmetry group for any 4d N = 2 class S theory constructed by compactifying a 6d N=(2,0) SCFT on a Riemann surface with arbitrary regular untwisted and twisted punctures. The 6d theory has a group of mutually non-local dimension-2 surface operators, modulo screening. Compactifying these surface operators leads to a group of mutually non-local line operators in 4d, modulo screening and flavor charges. Complete specification of a 4d theory arising from such a compactification requires a choice of a maximal subgroup of mutually local line operators, and the 1-form symmetry group of the chosen 4d theory is identified as the Pontryagin dual of this maximal subgroup. We also comment on how to generalize our results to compactifications involving irregular punctures. Finally, to complement the analysis from 6d, we derive the 1-form symmetry from a Type IIB realization of class S theories.

Topological classification and diagnosis in magnetically ordered electronic materials

Abstract: We show that compositions of time-reversal and spatial symmetries, also known as the magnetic-space-group symmetries, protect topological invariants as well as surface states that are distinct from those of all preceding topological states. We obtain, by explicit and exhaustive construction, the topological classification of electronic band insulators that are magnetically ordered for each one of the 1421 magnetic space groups in three dimensions. We have also computed the symmetry-based indicators for each nontrivial class, and, by doing so, establish the complete mapping from symmetry representations to topological invariants.

Algebra of Symmetry Operators for Klein-Gordon-Fock Equation

Abstract: All external electromagnetic fields in which the Klein-Gordon-Fock equation admits the first-order symmetry operators are found, provided that in the space-time V4 a group of motion G3 acts simply transitively on a non-null subspace of transitivity V3. It is shown that in the case of a Riemannian space Vn, in which the group Gr acts simply transitively, the algebra of symmetry operators of the n-dimensional Klein-Gordon-Fock equation in an external admissible electromagnetic field coincides with the algebra of operators of the group Gr.

Finding symmetry breaking order parameters with Euclidean neural networks

Abstract: The authors explore using neural networks to elucidate symmetry questions by using Euclidean neural networks to learn the symmetry-breaking input necessary to turn a square into a rectangle.

Acoustic Möbius insulators from projective symmetry

Abstract: Symmetry plays a critical role in classifying phases of matter. This is exemplified by how crystalline symmetries enrich the topological classification of materials and enable unconventional phenomena in topologically nontrivial ones. After an extensive study over the past decade, the list of topological crystalline insulators and semimetals seems to be exhaustive and concluded. However, in the presence of gauge symmetry, common but not limited to artificial crystals, the algebraic structure of crystalline symmetries needs to be projectively represented, giving rise to unprecedented topological physics. Here we demonstrate this novel idea by exploiting a projective translation symmetry and constructing a variety of Mobius-twisted topological phases. Experimentally, we realize two Mobius insulators in acoustic crystals for the first time: a two-dimensional one of first-order band topology and a three-dimensional one of higher-order band topology. We observe unambiguously the peculiar Mobius edge and hinge states via real-space visualization of their localiztions, momentum-space spectroscopy of their 4{\pi} periodicity, and phase-space winding of their projective translation eigenvalues. Not only does our work open a new avenue for artificial systems under the interplay between gauge and crystalline symmetries, but it also initializes a new framework for topological physics from projective symmetry.

Machine-learning hidden symmetries.

Abstract: We present an automated method for finding hidden symmetries, defined as symmetries that become manifest only in a new coordinate system that must be discovered. Its core idea is to quantify asymmetry as violation of certain partial differential equations, and to numerically minimize such violation over the space of all invertible transformations, parametrized as invertible neural networks. For example, our method rediscovers the famous Gullstrand-Painleve metric that manifests hidden translational symmetry in the Schwarzschild metric of non-rotating black holes, as well as Hamiltonicity, modularity and other simplifying traits not traditionally viewed as symmetries.

NeRD: Neural 3D Reflection Symmetry Detector

Abstract: Recent advances have shown that symmetry, a structural prior that most objects exhibit, can support a variety of single-view 3D understanding tasks. However, detecting 3D symmetry from an image remains a challenging task. Previous works either assume the symmetry is given or detect the symmetry with a heuristic-based method. In this paper, we present NeRD, a Neural 3D Reflection Symmetry Detector, which combines the strength of learning-based recognition and geometry-based reconstruction to accurately recover the normal direction of objects’ mirror planes. Specifically, we enumerate the symmetry planes with a coarse-to-fine strategy and find the best ones by building 3D cost volumes to examine the intra-image pixel correspondence from the symmetry. Our experiments show that the symmetry planes detected with our method are significantly more accurate than the planes from direct CNN regression on both synthetic and real datasets. More importantly, we also demonstrate that the detected symmetry can be used to improve the performance of downstream tasks such as pose estimation and depth map regression by a wide margin over existing methods. The code of this paper has been made public at https://github.com/zhou13/nerd.

Flat bands by latent symmetry

Abstract: The geometry of a lattice may cause energy eigenstates to localize compactly by destructive interference, resulting in flat energy bands. This effect is often induced by symmetry. A ``latent'' symmetry, inspired from graph theory, is a hidden permutation symmetry revealed upon reduction of the original system onto a subsystem; here, an effective two-site dimer. Combined with collective symmetries between possible pathways connecting the dimer sites to special site subsets in the lattice unit cell, latent symmetry provides a novel systematic way to explore and construct flat bands.

Symmetry indicator in non-Hermitian systems

Abstract: Recently, topological phases in non-Hermitian systems have attracted much attention because non-Hermiticity sometimes gives rise to unique phases with no Hermitian counterparts. Non-Hermitian Bloch Hamiltonians can always be mapped to doubled Hermitianized Hamiltonians with chiral symmetry, which enables us to utilize the existing framework for Hermitian systems to classify non-Hermitian topological phases. While this strategy succeeded in the topological classification of non-Hermitian Bloch Hamiltonians in the presence of internal symmetries, the generalization of symmetry indicators---a way to efficiently diagnose topological phases---to non-Hermitian systems is still elusive. In this work, we study a theory of symmetry indicators for non-Hermitian systems. We define space group symmetries of non-Hermitian Bloch Hamiltonians as the ones of the doubled Hermitianized Hamiltonians. Consequently, symmetry indicator groups for chiral symmetric Hermitian systems are equivalent to those for non-Hermitian systems. Based on this equivalence, we list symmetry indicator groups for non-Hermitian systems in the presence of space group symmetries. We also discuss the physical implications of symmetry indicators for some symmetry classes. Furthermore, explicit formulas of symmetry indicators for spinful electronic systems are included in appendices.

Numerical evidence for a Haagerup conformal field theory

Abstract: We numerically study an anyon chain based on the Haagerup fusion category, and find evidence that it leads in the long-distance limit to a conformal field theory whose central charge is $\sim 2$. Fusion categories generalize the concept of finite group symmetries to non-invertible symmetry operations, and the Haagerup fusion category is the simplest one which comes neither from finite groups nor affine Lie algebras. As such, ours is the first example of conformal field theories which have truly exotic generalized symmetries.

Different shapes of spin textures as a journey through the Brillouin zone

Abstract: Crystallographic point group symmetry (CPGS) such as polar and nonpolar crystal classes have long been known to classify compounds that have spin-orbit-induced spin splitting. While taking a journey through the Brillouin zone (BZ) from one $k$-point to another for a fixed CPGS, it is expected that the wave vector point group symmetry (WPGS) can change, and consequently, a qualitative change in the texture of the spin polarization can occur [the expectation value of spin operator ${\stackrel{P\vec}{S}}_{n{k}_{0}}$ in Bloch state $u(n,k)$ and the wave vector ${k}_{0}$]. However, the nature of the spin texture (ST) change is generally unsuspected. In this paper, we determine a full classification of the linear-in-$k$ ST patterns based on the polarity and chirality reflected in the WPGS at ${k}_{0}$. The spin-polarization vector ${\stackrel{P\vec}{S}}_{n{k}_{0}}$ controlling the ST is bound to be parallel to the rotation axis and perpendicular to the mirror planes, and hence, symmetry operation types in WPGSs impose symmetry restriction to the ST. For instance, the ST is always parallel to the wave vector $k$ in nonpolar chiral WPGSs since they contain only rotational symmetries. Some consequences of the ST classification based on the symmetry operations in the WPGS include the observation of ST patterns that are unexpected according to the symmetry of the crystal. For example, it is usually established that spin-momentum locking effect (spin vector always perpendicular to the wave vector) requires the crystal inversion symmetry breaking by an asymmetric electric potential. However, we find that polar WPGS can have this effect even in compounds without electric dipoles or external electric fields. We use the determined relation between WPGS and ST as a design principle to select compounds with multiple STs near band edges at different $k$ valleys. Based on high-throughput calculations for 1481 compounds, we find 37 previously fabricated materials with different STs near band edges. The ST classification as well as the predicted compounds with multiple STs can be a platform for potential application for spin-valleytronics and the control of the ST by accessing different valleys.

Flavor symmetry of 5d SCFTs. Part I. General setup

Abstract: A large class of 5d superconformal field theories (SCFTs) can be constructed by integrating out BPS particles from 6d SCFTs compactified on a circle. We describe a general method for extracting the flavor symmetry of any 5d SCFT lying in this class. For this purpose, we utilize the geometric engineering of 5d $$ \mathcal{N} $$ = 1 theories in M-theory, where the flavor symmetry is encoded in a collection of non-compact surfaces.

A Novel Symmetry of Colored HOMFLY Polynomials Coming from sl (N |M ) Superalgebras

Abstract: We present a novel symmetry of the colored HOMFLY polynomial. It relates pairs of polynomials colored by different representations at specific values of N and generalizes the previously known “tug-the-hook” symmetry of the colored Alexander polynomial (Mishnyakov et al. in Annales Henri Poincare, 2021. https://doi.org/10.1007/s00023-020-00980-8 , arXiv:2001.10596 ). As we show, the symmetry has a superalgebra origin, which we discuss qualitatively. Our main focus are the constraints that such a property imposes on the general group-theoretical structure, namely the $$\mathfrak {sl}(N)$$ weight system, arising in the perturbative expansion of the invariant. Finally, we demonstrate its tight relation to the eigenvalue conjecture.

Topological field theories and symmetry protected topological phases with fusion category symmetries

Abstract: Fusion category symmetries are finite symmetries in 1+1 dimensions described by unitary fusion categories We classify 1+1d time-reversal invariant bosonic symmetry protected topological (SPT) phases with fusion category symmetry by using topological field theories We first formulate two-dimensional unoriented topological field theories whose symmetry splits into time-reversal symmetry and fusion category symmetry We then solve them to show that SPT phases are classified by equivalence classes of quintuples $(Z, M, i, s, \phi)$ where $(Z, M, i)$ is a fiber functor, $s$ is a sign, and $\phi$ is the action of orientation-reversing symmetry that is compatible with the fiber functor $(Z, M, i)$ We apply this classification to SPT phases with Kramers-Wannier-like self-duality