scholarly journals Symmetries and anomalies of (1+1)d theories: 2-groups and symmetry fractionalization

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Matthew Yu
Keyword(s):  
Spectral Sequence ◽  
Global Symmetries ◽  
Group Symmetry ◽  
Low Dimension ◽  
The One ◽  
Group Symmetries

Abstract We investigate the interactions of discrete zero-form and one-form global symmetries in (1+1)d theories. Focus is put on the interactions that the symmetries can have on each other, which in this low dimension result in 2-group symmetries or symmetry fractionalization. A large part of the discussion will be to understand a major feature in (1+1)d: the multiple sectors into which a theory decomposes. We perform gauging of the one-form symmetry, and remark on the effects this has on our theories, especially in the case when there is a global 2-group symmetry. We also implement the spectral sequence to calculate anomalies for the 2-group theories and symmetry fractionalized theory in the bosonic and fermionic cases. Lastly, we discuss topological manipulations on the operators which implement the symmetries, and draw insights on the (1+1)d effects of such manipulations by coupling to a bulk (2+1)d theory.

RAINBOW STATISTICS

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4623-4641 ◽  
Author(s):  
MICHELE ARZANO ◽  
DARIO BENEDETTI
Keyword(s):  
Quantum Group ◽  
Hilbert Spaces ◽  
Group Symmetry ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Additional Structure ◽  
Local Quantum ◽  
Group Symmetries ◽  
Noncommutative Quantum

Noncommutative quantum field theories and their global quantum group symmetries provide an intriguing attempt to go beyond the realm of standard local quantum field theory. A common feature of these models is that the quantum group symmetry of their Hilbert spaces induces additional structure in the multiparticle states which reflects a nontrivial momentum-dependent statistics. We investigate the properties of this "rainbow statistics" in the particular context of κ-quantum fields and discuss the analogies/differences with models with twisted statistics.

scholarly journals catena-Poly[barium(II)-μ2-(dimethyl sulfoxide)-κ2 O:O-bis(μ2-2,4,6-trinitrophenolato-κ4 O 2,O 1:O 1,O 6)]

IUCrData ◽  
2020 ◽  
Vol 5 (11) ◽  
Author(s):  
Bikshandarkoil R. Srinivasan ◽  
Neha U. Parsekar ◽  
Kedar U. Narvekar
Keyword(s):  
Coordination Polymer ◽  
Oxygen Atom ◽  
Dimethyl Sulfoxide ◽  
Point Group ◽  
Binding Mode ◽  
Group Symmetry ◽  
Site Symmetry ◽  
Cation Site ◽  
A Chain ◽  
The One

The asymmetric unit of the title barium coordination polymer, [Ba(C6H2N3O7)2(C2H6OS)] n , consists of a barium cation (site symmetry m) and a dimethyl sulfoxide (DMSO) ligand (point group symmetry m) and a 2,4,6-trinitrophenolate anion located in general positions. The S atom and the methyl group of DMSO are disordered over two sets of sites. The DMSO ligand bridges a pair of BaII atoms resulting in a chain extending parallel to the a axis. The unique 2,4,6-trinitrophenolate anion also bridges a pair of BaII ions via the phenolic oxygen atom, with each BaII being additionally bonded to an oxygen atom of an adjacent nitro group. The μ 2-monoatomic bridging binding mode of both types of ligands results in the formation of an infinite chain of face-sharing {BaO10} polyhedra flanked by the remaining parts of the 2,4,6-trinitrophenolato and DMSO ligands. In the one-dimensional coordination polymer, parallel chains are interlinked with the aid of C—H...O hydrogen bonds.

Vibrational spectra of metal-nitro complexes. II. Substituted halo complexes of platinum(IV)

1973 ◽  
Vol 26 (7) ◽  
pp. 1413 ◽  
Author(s):  
MJ Nolan ◽  
DW James
Keyword(s):  
Raman Spectra ◽  
Point Group ◽  
Factor Group ◽  
Group Symmetry ◽  
Infrared And Raman Spectra ◽  
Point Group Symmetry ◽  
Nitro Complexes ◽  
Site Group ◽  
Group Symmetries ◽  
Complex Ion

The infrared and Raman spectra of compounds forming the series given by [Pt(NO2)6-nCln]2- (n = 0-5) together with some of the analogous bromo and iodo compounds have been obtained. Most compounds were studied in the solid state, but the Raman spectra of solutions of some of the compounds were also obtained. The spectra were interpreted initially by considering the likely point group symmetry of the complex ion. Where details of the crystal structures were known, the site group and factor group symmetries were also considered.

scholarly journals 2-Group global symmetries and anomalies in six-dimensional quantum field theories

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Clay Córdova ◽  
Thomas T. Dumitrescu ◽  
Kenneth Intriligator
Keyword(s):  
Global Symmetries ◽  
Group Symmetry ◽  
Field Theories ◽  
Global Symmetry ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Six Dimensions ◽  
String Theories

Abstract We examine six-dimensional quantum field theories through the lens of higher-form global symmetries. Every Yang-Mills gauge theory in six dimensions, with field strength f(2), naturally gives rise to a continuous 1-form global symmetry associated with the 2-form instanton current J(2)∼ ∗Tr (f(2) ∧ f(2)). We show that suitable mixed anomalies involving the gauge field f(2) and ordinary 0-form global symmetries, such as flavor or Poincaré symmetries, lead to continuous 2-group global symmetries, which allow two flavor currents or two stress tensors to fuse into the 2-form current J(2). We discuss several features of 2-group symmetry in six dimensions, many of which parallel the four-dimensional case. The majority of six-dimensional supersymmetric conformal field theories (SCFTs) and little string theories have infrared phases with non-abelian gauge fields. We show that the mixed anomalies leading to 2-group symmetries can be present in little string theories, but that they are necessarily absent in SCFTs. This allows us to establish a previously conjectured algorithm for computing the ’t Hooft anomalies of most SCFTs from the spectrum of weakly-coupled massless particles on the tensor branch of these theories. We then apply this understanding to prove that the a-type Weyl anomaly of all SCFTs with a tensor branch must be positive, a > 0.

scholarly journals Spherical polar Fourier assembly of protein complexes with arbitrary point group symmetry

2016 ◽  
Vol 49 (1) ◽  
pp. 158-167 ◽  
Author(s):  
David W. Ritchie ◽  
Sergei Grudinin
Keyword(s):  
Protein Complexes ◽  
Complex Structure ◽  
Point Group ◽  
Arbitrary Point ◽  
Group Symmetry ◽  
Test Cases ◽  
Point Group Symmetry ◽  
Group Symmetries ◽  
The Given ◽  
Ab Inito

A novel fast Fourier transform-basedab initodocking algorithm calledSAMis presented, for building perfectly symmetrical models of protein complexes with arbitrary point group symmetry. The basic approach uses a novel and very fast one-dimensional symmetry-constrained spherical polar Fourier search to assemble cyclicCnsystems from a given protein monomer. Structures with higher-order (Dn,T,OandI) point group symmetries may be built using a subsequent symmetry-constrained Fourier domain search to assemble trimeric sub-units. The results reported here show that theSAMalgorithm can correctly assemble monomers of up to around 500 residues to produce a near-native complex structure with the given point group symmetry in 17 out of 18 test cases. TheSAMprogram may be downloaded for academic use at http://sam.loria.fr/.

scholarly journals Multipliers and unicentral Leibniz algebras

2021 ◽  
pp. 2350008
Author(s):  
Erik Mainellis
Keyword(s):  
Spectral Sequence ◽  
Cohomology Group ◽  
Leibniz Algebras ◽  
Low Dimension ◽  
Definition Of ◽  
Exact Sequences

In this paper, we prove Leibniz analogues of results found in Peggy Batten’s 1993 dissertation. We first construct a Hochschild–Serre-type spectral sequence of low dimension, which is used to characterize the multiplier in terms of the second cohomology group with coefficients in the field. The sequence is then extended by a term and a Ganea sequence is constructed for Leibniz algebras. The maps involved with these exact sequences, as well as a characterization of the multiplier, are used to establish criteria for when a central ideal is contained in a certain set seen in the definition of unicentral Leibniz algebras. These criteria are then specialized, and we obtain conditions for when the center of the cover maps onto the center of the algebra.

scholarly journals The phase transitions of 4-aminopyridine-based indolocarbazoles: twinning, local- and pseudo-symmetry

2019 ◽  
Vol 75 (1) ◽  
pp. 97-106 ◽  
Author(s):  
Thomas Kader ◽  
Berthold Stöger ◽  
Johannes Fröhlich ◽  
Paul Kautny
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
High Temperature ◽  
Low Temperature ◽  
Group Symmetry ◽  
Temperature Phase ◽  
Space Group ◽  
Local Symmetries ◽  
Group Symmetries ◽  
Low Temperature Phase

The phase transitions and polymorphism of three 4-aminopyridine-based indolocarbazole analogues are analyzed with respect to symmetry relationships and twinning. Seven polymorphs were structurally characterized using single-crystal diffraction. 5NICz (the indolo[3,2,1-jk]carbazole derivative with the C atom in the 5-position replaced by N) crystallizes as a P21/a high-temperature (270 K) polymorph and as a Pca21 low-temperature (150 K) polymorph. Even though their space-group symmetry is not related by a group–subgroup relationship, the local symmetries of both belong to the same order–disorder (OD) groupoid family. Both are polytypes of a maximum degree of order and are twinned by point operations of the other polytype. 2NICz (C atom in the 2-position replaced by N) likewise crystallizes in a high-temperature (Pcca, 280 K) polymorph and a low-temperature (P21/c, 150 K) polymorph. Here, the space-group symmetries are related by a group–subgroup relationship. The low-temperature phase is twinned by the point operations lost on cooling. The crystal structure of bulk 2,5NICz (N-substitution at the 2- and 5-positions) was unrelated to 2NICz and 5NICz and no phase transition was observed. Isolated single crystals of a different polymorph of 2,5NICz, isotypic with 2NICz, were isolated. However, the analogous phase transition in this case takes place at distinctly higher temperatures (> 300 K).

Singularities in Differential-Algebraic Boundary-Value Problems Governing the Excitation Response of Beam Structures

2014 ◽  
Vol 10 (1) ◽  
Author(s):  
Mehdi Saghafi ◽  
Harry Dankowicz
Keyword(s):  
Finite Element ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Convergence Rates ◽  
Boundary Value ◽  
Differential Algebraic Equations ◽  
Group Symmetry ◽  
Algebraic Equations ◽  
Beam Structures ◽  
Group Symmetries

The objective of this paper2 is to identify and, where possible, resolve singularities that may arise in the discretization of spatiotemporal boundary-value problems governing the steady-state behavior of nonlinear beam structures. Of particular interest is the formulation of nondegenerate continuation problems of a geometrically-nonlinear model of a slender beam, subject to a uniform harmonic excitation, which may be analyzed numerically in order to explore the parameter-dependence of the excitation response. In the instances of degeneracy investigated here, the source is either found (i) directly in a differential-algebraic system of equations obtained from a finite-element-based spatial discretization of the governing partial differential boundary-value problem(s) together with constraints on the trial functions or (ii) in the further collocation-based discretization of the time-periodic boundary-value problem. It is shown that several candidate spatial finite-element discretizations of a mixed weak formulation of the governing boundary-value problem either result in (i) spatial group symmetries corresponding to equivariant vector fields and one-parameter families of periodic orbits along the group symmetry orbit or (ii) temporal group symmetries corresponding to ghost solutions and indeterminacy in a subset of the field variables. The paper demonstrates several methods for breaking the spatial equivariance, including projection onto a symmetry-reduced state space or the introduction of an artificial continuation parameter. Similarly, the temporal indeterminacy is resolved by an asymmetric discretization of the governing differential-algebraic equations. Finally, in the absence of theoretical bounds, computation is used to estimate convergence rates of the different discretization schemes, in the case of numerical calibration experiments performed on equilibrium and periodic responses for a linear beam, as well as for the full nonlinear models.

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