scholarly journals Topological defects and SUSY RG flow

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
I. Brunner ◽  
I. Mayer ◽  
C. Schmidt-Colinet
Keyword(s):  
Topological Defects ◽  
Matrix Factorizations ◽  
Minimal Models

AbstractWe study the effect of bulk perturbations of N=(2) superconformal minimal models on topological defects. In particular, symmetries and more general topological defects which survive the flow to the IR are identified. Our method is to consider the topological subsector and make use of the Landau-Ginzburg formulation to describe RG flows and topological defects in terms of matrix factorizations.

scholarly journals Defects and perturbation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm
Keyword(s):  
Entanglement Entropy ◽  
Topological Defects ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

scholarly journals Numerical Study of Membrane Configurations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Luka Mesarec ◽  
Miha Fošnarič ◽  
Samo Penič ◽  
Veronika Kralj Iglič ◽  
Samo Kralj ◽  
...  
Keyword(s):  
Numerical Study ◽  
Thin Sheet ◽  
Topological Defects ◽  
Spontaneous Curvature ◽  
Minimal Models ◽  
Nematic Ordering ◽  
Curvature Energy ◽  
Spherical Topology ◽  
Numerical Minimization ◽  
Orientational Ordering

We studied biological membranes of spherical topology within the framework of the spontaneous curvature model. Both Monte Carlo simulations and the numerical minimization of the curvature energy were used to obtain the shapes of the vesicles. The shapes of the vesicles and their energy were calculated for different values of the reduced volume. The vesicles which exhibit in-plane ordering were also studied. Minimal models have been developed in order to study the orientational ordering in colloids coated with a thin sheet of nematic liquid crystal (nematic shells). The topological defects are always present on the surfaces with the topology of a sphere. The location of the topological defects depends strongly on the curvature of the surface. We studied the nematic ordering and the formation of topological defects on vesicles obtained by the minimization of the spontaneous curvature energy.

scholarly journals Fusion of interfaces in Landau-Ginzburg models: a functorial approach

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Nicolas Behr ◽  
Stefan Fredenhagen
Keyword(s):  
Topological Defects ◽  
Polynomial Rings ◽  
Two Dimensional ◽  
Minimal Models ◽  
Actual Computation ◽  
Category Of Modules ◽  
Chiral Superfields ◽  
Functorial Approach

Abstract We investigate the fusion of B-type interfaces in two-dimensional supersymmetric Landau-Ginzburg models. In particular, we propose to describe the fusion of an interface in terms of a fusion functor that acts on the category of modules of the underlying polynomial rings of chiral superfields. This uplift of a functor on the category of matrix factorisations simplifies the actual computation of interface fusion. Besides a brief discussion of minimal models, we illustrate the power of this approach in the SU(3)/U(2) Kazama-Suzuki model where we find fusion functors for a set of elementary topological defects from which all rational B-type topological defects can be generated.

A Pseudo Five-Fold Symmetrical Ligand Drives Geometric Frustration in Porous Metal-Organic and Hydrogen Bonded Frameworks

2020 ◽  
Author(s):  
Frederik Haase ◽  
Gavin Craig ◽  
Mickaele Bonneau ◽  
kunihisa sugimoto ◽  
Shuhei Furukawa
Keyword(s):  
Topological Defects ◽  
Porous Metal ◽  
Building Blocks ◽  
Structural Features ◽  
Equilibrium Structure ◽  
Sorption Behavior ◽  
Building Unit ◽  
Geometric Frustration ◽  
Secondary Building Units ◽  
Hydrogen Bonded

Reticular framework materials thrive on designability, but unexpected reaction outcomes are crucial in exploring new structures and functionalities. By combining “incompatible” building blocks, we employed geometric frustration in reticular materials leading to emergent structural features. The combination of a pseudo C<sub>5</sub> symmetrical organic building unit based on a pyrrole core, with a C<sub>4</sub> symmetrical copper paddlewheel synthon led to three distinct frameworks by tuning the synthetic conditions. The frameworks show structural features typical for geometric frustration: self-limiting assembly, internally stressed equilibrium structures and topological defects in the equilibrium structure, which manifested in the formation of a hydrogen bonded framework, distorted and broken secondary building units and dangling functional groups, respectively. The influence of geometric frustration on the CO<sub>2</sub> sorption behavior and the discovery of a new secondary building unit shows geometric frustration can serve as a strategy to obtain highly complex porous frameworks.

A Pseudo Five-Fold Symmetrical Ligand Drives Geometric Frustration in Porous Metal-Organic and Hydrogen Bonded Frameworks

2020 ◽  
Author(s):  
Frederik Haase ◽  
Gavin Craig ◽  
Mickaele Bonneau ◽  
kunihisa sugimoto ◽  
Shuhei Furukawa
Keyword(s):  
Topological Defects ◽  
Porous Metal ◽  
Building Blocks ◽  
Structural Features ◽  
Equilibrium Structure ◽  
Sorption Behavior ◽  
Building Unit ◽  
Geometric Frustration ◽  
Secondary Building Units ◽  
Hydrogen Bonded

Reticular framework materials thrive on designability, but unexpected reaction outcomes are crucial in exploring new structures and functionalities. By combining “incompatible” building blocks, we employed geometric frustration in reticular materials leading to emergent structural features. The combination of a pseudo C<sub>5</sub> symmetrical organic building unit based on a pyrrole core, with a C<sub>4</sub> symmetrical copper paddlewheel synthon led to three distinct frameworks by tuning the synthetic conditions. The frameworks show structural features typical for geometric frustration: self-limiting assembly, internally stressed equilibrium structures and topological defects in the equilibrium structure, which manifested in the formation of a hydrogen bonded framework, distorted and broken secondary building units and dangling functional groups, respectively. The influence of geometric frustration on the CO<sub>2</sub> sorption behavior and the discovery of a new secondary building unit shows geometric frustration can serve as a strategy to obtain highly complex porous frameworks.

scholarly journals Parafermionization, bosonization, and critical parafermionic theories

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yuan Yao ◽  
Akira Furusaki
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Degrees Of Freedom ◽  
Lattice Models ◽  
Partition Functions ◽  
Minimal Models ◽  
Fermionic Model ◽  
Conformal Field ◽  
Critical Theories ◽  
Wigner Transformation

AbstractWe formulate a ℤk-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising duality atk= 2. The ℤk-parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their criticality cannot be described by any existing conformal field theory. The modular transformations of these parafermionic low-energy critical theories as general consistency conditions are found to be unconventional in that their partition functions on a torus transform differently from any conformal field theory whenk >2. Explicit forms of partition functions are obtained by the developed parafermionization for a large class of critical ℤk-parafermionic chains, whose operator contents are intrinsically distinct from any bosonic or fermionic model in terms of conformal spins and statistics. We also use the parafermionization to exhaust all the ℤk-parafermionic minimal models, complementing earlier works on fermionic cases.

scholarly journals Properties of twisted topological defects in 2D nematic liquid crystals

Soft Matter ◽  
2021 ◽  
Author(s):  
Daniel Pearce ◽  
Karsten Kruse
Keyword(s):  
Liquid Crystals ◽  
Nematic Liquid Crystals ◽  
Topological Defects ◽  
Two Dimensional

Topological defects are one of the most conspicuous features of liquid crystals. In two dimensional nematics, they have been shown to behave effectively as particles with both, charge and orientation,...

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