scholarly journals Interpolations between Jordanian twists, the Poincaré–Weyl algebra and dispersion relations

2020 ◽  
Vol 35 (08) ◽  
pp. 2050034
Author(s):  
Daniel Meljanac ◽  
Stjepan Meljanac ◽  
Zoran Škoda ◽  
Rina Štrajn
Keyword(s):  
Star Product ◽  
Dispersion Relations ◽  
Parameter Family ◽  
Noncommutative Space ◽  
Similarity Transformations ◽  
Similarity Maps ◽  
Symmetry Generators ◽  
Physical Phenomena ◽  
Two Parameter ◽  
Real Forms

We consider a two-parameter family of Drinfeld twists generated from a simple Jordanian twist further twisted by 1-cochains. Twists from this family interpolate between two simple Jordanian twists. Relations between them are constructed and discussed. It is proved that there exists a one-parameter family of twists identical to a simple Jordanian twist. The twisted coalgebra, star product and coordinate realizations of the [Formula: see text]-Minkowski noncommutative space–time are presented. Real forms of Jordanian deformations are also discussed. The method of similarity transformations is applied to the Poincaré–Weyl Hopf algebra and two types of one-parameter families of dispersion relations are constructed. Mathematically equivalent deformations, that are related to nonlinear changes of symmetry generators and linked with similarity maps, may lead to differences in the description of physical phenomena.

scholarly journals The holographic conformal manifold of 3d $$ \mathcal{N} $$ = 2 S-fold SCFTs

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nikolay Bobev ◽  
Friðrik Freyr Gautason ◽  
Jesse van Muiden
Keyword(s):  
String Theory ◽  
Three Dimensional ◽  
Parameter Family ◽  
Global Symmetry ◽  
Maximal Supergravity ◽  
All Solutions ◽  
Operator Spectrum ◽  
Type Iib String Theory ◽  
Two Parameter

Abstract We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS4 J-fold solutions preserving $$ \mathcal{N} $$ N = 2 supersymmetry. All solutions preserve $$ \mathfrak{u} $$ u (1) × $$ \mathfrak{u} $$ u (1) global symmetry and in special limits we recover the previously known $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{u} $$ u (1) invariant $$ \mathcal{N} $$ N = 2 and $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{su} $$ su (2) invariant $$ \mathcal{N} $$ N = 4 J-fold solutions. This family of AdS4 backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional S-fold SCFTs obtained from the $$ \mathcal{N} $$ N = 4 T [U(N)] theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS4 solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.

Dynamics of a two-parameter family of maps of the interval

1986 ◽  
Vol 10 (5) ◽  
pp. 415-423 ◽  
Author(s):  
J.R. Pounder ◽  
Thomas D. Rogers
Keyword(s):  
Parameter Family ◽  
Two Parameter

CONTINUITY OF ENTROPY FOR A TWO-PARAMETER FAMILY OF BIMODAL MAPS

1995 ◽  
pp. 101-116
Author(s):  
LOUIS BLOCK ◽  
ROZA GALEEVA ◽  
JAMES KEESLING
Keyword(s):  
Parameter Family ◽  
Two Parameter

scholarly journals Moffatt-type flows in a trihedral cone

2013 ◽  
Vol 725 ◽  
pp. 446-461 ◽  
Author(s):  
Julian F. Scott
Keyword(s):  
Linear Combination ◽  
Particle Motion ◽  
Particle Trajectory ◽  
Three Dimensional ◽  
Parameter Family ◽  
The Other ◽  
Transient Phase ◽  
Primary Flow ◽  
Special Cases ◽  
Two Parameter

AbstractThe three-dimensional analogue of Moffatt eddies is derived for a corner formed by the intersection of three orthogonal planes. The complex exponents of the first few modes are determined and the flows resulting from the primary modes (those which decay least rapidly as the apex is approached and, hence, should dominate the near-apex flow) examined in detail. There are two independent primary modes, one symmetric, the other antisymmetric, with respect to reflection in one of the symmetry planes of the cone. Any linear combination of these modes yields a possible primary flow. Thus, there is not one, but a two-parameter family of such flows. The particle-trajectory equations are integrated numerically to determine the streamlines of primary flows. Three special cases in which the flow is antisymmetric under reflection lead to closed streamlines. However, for all other cases, the streamlines are not closed and quasi-periodic limiting trajectories are approached when the trajectory equations are integrated either forwards or backwards in time. A generic streamline follows the backward-time trajectory in from infinity, undergoes a transient phase in which particle motion is no longer quasi-periodic, before being thrown back out to infinity along the forward-time trajectory.

scholarly journals A two-parameter family of an extension of Beatty sequences

2008 ◽  
Vol 308 (20) ◽  
pp. 4578-4588 ◽  
Author(s):  
Shiri Artstein-Avidan ◽  
Aviezri S. Fraenkel ◽  
Vera T. Sós
Keyword(s):  
Parameter Family ◽  
Beatty Sequences ◽  
Two Parameter
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