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.

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 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,...

scholarly journals Prime ideals in two-dimensional polynomial rings

1989 ◽  
Vol 107 (3) ◽  
pp. 577-577 ◽  
Author(s):  
William Heinzer ◽  
Sylvia Wiegand
Keyword(s):  
Polynomial Rings ◽  
Prime Ideals ◽  
Two Dimensional

scholarly journals Prime ideals in birational extensions of two-dimensional polynomial rings

2005 ◽  
Vol 201 (1-3) ◽  
pp. 142-153 ◽  
Author(s):  
A. Serpil Saydam ◽  
Sylvia Wiegand
Keyword(s):  
Polynomial Rings ◽  
Prime Ideals ◽  
Two Dimensional

scholarly journals On 2d CFTs that interpolate between minimal models

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Sylvain Ribault
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Exactly Solvable ◽  
Structure Constants

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.

scholarly journals Tunable two-dimensional polarization grating using a self-organized micropixelated liquid crystal structure

RSC Advances ◽  
2018 ◽  
Vol 8 (72) ◽  
pp. 41472-41479 ◽  
Author(s):  
Reo Amano ◽  
Péter Salamon ◽  
Shunsuke Yokokawa ◽  
Fumiaki Kobayashi ◽  
Yuji Sasaki ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
Topological Defects ◽  
Self Organization ◽  
Two Dimensional ◽  
Self Organized ◽  
Optical Grating ◽  
Liquid Crystal Structure ◽  
Polarization Grating

A micro-pixelated pattern of a nematic liquid crystal formed by self-organization of topological defects is shown to work as a tunable two-dimensional optical grating.

scholarly journals VORTEX NUCLEATION IN ROTATING BOSE–EINSTEIN CONDENSATE: THE ROLE OF THE BOUNDARY CONDITION FOR THE ORDER PARAMETER

2006 ◽  
Vol 20 (15) ◽  
pp. 2147-2158
Author(s):  
W. V. POGOSOV ◽  
K. MACHIDA
Keyword(s):  
Boundary Condition ◽  
Order Parameter ◽  
Topological Defects ◽  
Einstein Condensate ◽  
Two Dimensional ◽  
Surface Modes ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Vortex Nucleation

We study the problem of vortex nucleation in rotating two-dimensional Bose–Einstein condensate confined in a harmonic trap. We show that, within the Gross–Pitaevskii theory with the boundary condition of vanishing of the order parameter at infinity, topological defects nucleation occurs via the creation of vortex-antivortex pairs far from the cloud center, where the modulus of the order parameter is small. Then vortices move toward the center of the cloud and antivortices move in the opposite direction but never disappear. We also discuss the role of surface modes.

Homomorphisms of two-dimensional linear groups over Laurent polynomial rings and Gaussian domains

1991 ◽  
Vol 109 (2) ◽  
pp. 287-297 ◽  
Author(s):  
Yu Chen
Keyword(s):  
Commutative Ring ◽  
Linear Group ◽  
Unit Group ◽  
Commutative Rings ◽  
Laurent Polynomial ◽  
Polynomial Rings ◽  
Linear Groups ◽  
Two Dimensional ◽  
Euclidean Domain ◽  
Invertible Matrices

Let GL2(R) be the general linear group of 2 × 2 invertible matrices in M2(R) over a commutative ring R with 1 and SL2(R) be the special linear group consisting of 2 × 2 matrices over R with determinant 1. In this paper we determine the homomorphisms from GL2 and SL2, as well as their projective groups, over Laurent polynomial rings to those groups over Gaussian domains, i.e. unique factorization domains (cf. Theorems 1, 2, 3 below). We also consider more generally the homomorphisms of non-projective groups over commutative rings containing a field which are generated by their units (cf. Theorems 4 and 5). So far the homomorphisms of two-dimensional linear groups over commutative rings have only been studied in some specific cases. Landin and Reiner[7] obtained the automorphisms of GL2(R), where R is a Euclidean domain generated by its units. When R is a type of generalized Euclidean domain with a degree function and with units of R and 0 forming a field, Cohn[3] described the automorphisms of GL2(R). Later, Cohn[4] applied his methods to the case of certain rings of quadratic integers. Dull[6] has considered the automorphisms of GL2(R) and SL2(R), along with their projective groups, provided that R is a GE-ring and 2 is a unit in R. McDonald [9] examined the automorphisms of GL2(R) when R has a large unit group. The most recent work of which we are aware is that of Li and Ren[8] where the automorphisms of E2(R) and GE2(R) were determined for any commutative ring R in which 2, 3 and 5 are units.

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