scholarly journals 2-Group Symmetries of 6D Little String Theories and T-Duality

2021 ◽  
Author(s):  
Michele Del Zotto ◽  
Kantaro Ohmori
Keyword(s):  
Group Structure ◽  
Discrete Symmetry ◽  
Consistency Check ◽  
Structure Constants ◽  
Group Symmetries ◽  
String Theories

AbstractWe determine the 2-group structure constants for all the six-dimensional little string theories (LSTs) geometrically engineered in F-theory without frozen singularities. We use this result as a consistency check for T-duality: the 2-groups of a pair of T-dual LSTs have to match. When the T-duality involves a discrete symmetry twist, the 2-group used in the matching is modified. We demonstrate the matching of the 2-groups in several examples.

STRUCTURE CONSTANTS OF THE D5, CHIRAL, MINIMAL MODEL

1996 ◽  
Vol 11 (01) ◽  
pp. 111-127 ◽  
Author(s):  
J. MCCABE ◽  
T. SAMI ◽  
T. WYDRO
Keyword(s):  
Ground State ◽  
Minimal Model ◽  
Discrete Symmetry ◽  
Coulomb Gas ◽  
Operator Product ◽  
Conformal Blocks ◽  
Structure Constants ◽  
Product Algebra ◽  
Ade Classification

The operator product algebra of the simplest chiral, minimal model, D5, in the ADE classification, is determined. The construction uses the Coulomb gas technique that was already employed in the nonchiral A series. This technique is supplemented by conformal blocks special to the D series. Explicit results for the structure constants of three-point correlations are given. They demonstrate that the ground state has a discrete symmetry, Z2.

scholarly journals $$\alpha $$-Modulation Spaces for Step Two Stratified Lie Groups

2022 ◽  
Vol 32 (2) ◽  
Author(s):  
Eirik Berge
Keyword(s):  
Frequency Analysis ◽  
Group Structure ◽  
Modulation Spaces ◽  
Metric Geometry ◽  
Rational Structure ◽  
Open Problems ◽  
Stratified Lie Group ◽  
Time Frequency ◽  
Stratified Lie Groups ◽  
Structure Constants

AbstractWe define and investigate $$\alpha $$ α -modulation spaces $$M_{p,q}^{s,\alpha }(G)$$ M p , q s , α ( G ) associated to a step two stratified Lie group G with rational structure constants. This is an extension of the Euclidean $$\alpha $$ α -modulation spaces $$M_{p,q}^{s,\alpha }({\mathbb {R}}^n)$$ M p , q s , α ( R n ) that act as intermediate spaces between the modulation spaces ($$\alpha = 0$$ α = 0 ) in time-frequency analysis and the Besov spaces ($$\alpha = 1$$ α = 1 ) in harmonic analysis. We will illustrate that the group structure and dilation structure on G affect the boundary cases $$\alpha = 0,1$$ α = 0 , 1 where the spaces $$M_{p,q}^{s}(G)$$ M p , q s ( G ) and $${\mathcal {B}}_{p,q}^{s}(G)$$ B p , q s ( G ) have non-standard translation and dilation symmetries. Moreover, we show that the spaces $$M_{p,q}^{s,\alpha }(G)$$ M p , q s , α ( G ) are non-trivial and generally distinct from their Euclidean counterparts. Finally, we examine how the metric geometry of the coverings $${\mathcal {Q}}(G)$$ Q ( G ) underlying the $$\alpha = 0$$ α = 0 case $$M_{p,q}^{s}(G)$$ M p , q s ( G ) allows for the existence of geometric embeddings $$\begin{aligned} F:M_{p,q}^{s}({\mathbb {R}}^k) \longrightarrow {} M_{p,q}^{s}(G), \end{aligned}$$ F : M p , q s ( R k ) ⟶ M p , q s ( G ) , as long as k (that only depends on G) is small enough. Our approach naturally gives rise to several open problems that is further elaborated at the end of the paper.

Theoretical construction of weak topological crystalline insulators

2017 ◽  
Vol 31 (20) ◽  
pp. 1750136
Author(s):  
Qing-Li Zhu ◽  
Liang Hua ◽  
Ji-Mei Shen
Keyword(s):  
Point Group ◽  
Three Dimensional ◽  
Discrete Symmetry ◽  
Topological Phases ◽  
Symmetry Classes ◽  
New Type ◽  
Theoretical Construction ◽  
Topological Crystalline Insulators ◽  
Group Symmetries

Inspired by the discovery of topological crystalline insulators (TCIs) in three-dimensional materials such as Pb[Formula: see text]Sn[Formula: see text]Se(Te), the classification of topological insulators has been extended to other discrete symmetry classes such as crystal point group symmetries. In this paper, we construct and study a simple model of weak TCIs, which will serve as a more viable project in the experimental probe for such new type of topological phases.

scholarly journals Spectral theories and topological strings on del Pezzo geometries

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Sanefumi Moriyama
Keyword(s):  
Topological Strings ◽  
Chemical Potential ◽  
Group Structure ◽  
Partition Functions ◽  
Spectral Operator ◽  
Exceptional Algebras ◽  
Del Pezzo ◽  
Classical Phase Space ◽  
Group Symmetries ◽  
Mirror Map

Abstract Motivated by understanding M2-branes, we propose to reformulate partition functions of M2-branes by quantum curves. Especially, we focus on the backgrounds of del Pezzo geometries, which enjoy Weyl group symmetries of exceptional algebras. We construct quantum curves explicitly and turn to the analysis of classical phase space areas and quantum mirror maps. We find that the group structure helps in clarifying previous subtleties, such as the shift of the chemical potential in the area and the identification of the overall factor of the spectral operator in the mirror map. We list the multiplicities characterizing the quantum mirror maps and find that the decoupling relation known for the BPS indices works for the mirror maps. As a result, with the group structure we can present explicitly the statement for the correspondence between spectral theories and topological strings on del Pezzo geometries.

scholarly journals The group structure of dynamical transformations between quantum reference frames

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 470
Author(s):  
Angel Ballesteros ◽  
Flaminia Giacomini ◽  
Giulia Gubitosi
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Reference Frames ◽  
Group Structure ◽  
Building Blocks ◽  
Quantum Systems ◽  
Galilei Group ◽  
Dynamical Features ◽  
Group Symmetries ◽  
Galilei Algebra

Recently, it was shown that when reference frames are associated to quantum systems, the transformation laws between such quantum reference frames need to be modified to take into account the quantum and dynamical features of the reference frames. This led to a relational description of the phase space variables of the quantum system of which the quantum reference frames are part of. While such transformations were shown to be symmetries of the system's Hamiltonian, the question remained unanswered as to whether they enjoy a group structure, similar to that of the Galilei group relating classical reference frames in quantum mechanics. In this work, we identify the canonical transformations on the phase space of the quantum systems comprising the quantum reference frames, and show that these transformations close a group structure defined by a Lie algebra, which is different from the usual Galilei algebra of quantum mechanics. We further find that the elements of this new algebra are in fact the building blocks of the quantum reference frames transformations previously identified, which we recover. Finally, we show how the transformations between classical reference frames described by the standard Galilei group symmetries can be obtained from the group of transformations between quantum reference frames by taking the zero limit of the parameter that governs the additional noncommutativity introduced by the quantum nature of inertial transformations.

Friedel'S law breakdown and interpretation of stacking fault images in tetrahedral semiconductors

1987 ◽  
Vol 45 ◽  
pp. 318-319
Author(s):  
Rob. W. Glaisher ◽  
A.E.C. Spargo
Keyword(s):  
Relative Phase ◽  
Point Group ◽  
Binary Compound ◽  
Stacking Fault ◽  
Fold Axis ◽  
Atom Pair ◽  
Tetrahedral Semiconductors ◽  
Group Symmetries ◽  
Thin Crystal ◽  
Phase Differences

Images of <11> oriented crystals with diamond structure (i.e. C,Si,Ge) are dominated by white spot contrast which, depending on thickness and defocus, can correspond to either atom-pair columns or tunnel sites. Olsen and Spence have demonstrated a method for identifying the correspondence which involves the assumed structure of a stacking fault and the preservation of point-group symmetries by correctly aligned and stigmated images. For an intrinsic stacking fault, a two-fold axis lies on a row of atoms (not tunnels) and the contrast (black/white) of the atoms is that of the {111} fringe containing the two-fold axis. The breakdown of Friedel's law renders this technique unsuitable for the related, but non-centrosymmetric binary compound sphalerite materials (e.g. GaAs, InP, CdTe). Under dynamical scattering conditions, Bijvoet related reflections (e.g. (111)/(111)) rapidly acquire relative phase differences deviating markedly from thin-crystal (kinematic) values, which alter the apparent location of the symmetry elements needed to identify the defect.

Some effects of unequal distribution of information in a wheel group structure.

1954 ◽  
Vol 49 (4, Pt.1) ◽  
pp. 554-556 ◽  
Author(s):  
J. C. Gilchrist ◽  
Marvin E. Shaw ◽  
L. C. Walker
Keyword(s):  
Group Structure ◽  
Unequal Distribution
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