scholarly journals Towards a classification of rank r $$ \mathcal{N} $$ = 2 SCFTs. Part II. Special Kahler stratification of the Coulomb branch

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Philip C. Argyres ◽  
Mario Martone
Keyword(s):  
Singular Locus ◽  
Companion Paper ◽  
Coulomb Branch ◽  
Scale Invariant ◽  
Consistency Conditions ◽  
Complex Dimensions ◽  
Rank 2 ◽  
Relationship Of ◽  
Self Consistency

Abstract We study the stratification of the singular locus of four dimensional $$ \mathcal{N} $$ N = 2 Coulomb branches. We present a set of self-consistency conditions on this stratification which can be used to extend the classification of scale-invariant rank 1 Coulomb branch geometries to two complex dimensions, and beyond. The calculational simplicity of the arguments presented here stems from the fact that the main ingredients needed — the rank 1 deformation patterns and the pattern of inclusions of rank 2 strata — are discrete topological data which satisfy strong self-consistency conditions through their relationship to the central charges of the SCFT. This relationship of the stratification data to the central charges is used here, but is derived and explained in a companion paper [1] by one of the authors. We illustrate the use of these conditions by re-analyzing many previously-known examples of rank 2 SCFTs, and also by finding examples of new theories. The power of these conditions stems from the fact that for Coulomb branch stratifications a conjecturally complete list of physically allowed “elementary slices” is known. By contrast, constraining the possible elementary slices of symplectic singularities relevant for Higgs branch stratifications remains an open problem.

scholarly journals Towards the classification of rank-r $$ \mathcal{N} $$ = 2 SCFTs. Part I. Twisted partition function and central charge formulae

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Mario Martone
Keyword(s):  
Partition Function ◽  
Central Charge ◽  
Singular Locus ◽  
Companion Paper ◽  
Coulomb Branch ◽  
Energy Limit ◽  
Superconformal Field Theories ◽  
Rank 2 ◽  
Explicit Formulae

Abstract We derive explicit formulae to compute the a and c central charges of four dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of $$ \mathcal{N} $$ N = 2 SCFTs which culminate with our $$ \mathcal{N} $$ N = 2 UV-IR simple flavor condition. This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d $$ \mathcal{N} $$ N = 2 SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper.This manuscript is dedicated to the memory of Rayshard Brooks, George Floyd, Breonna Taylor and the countless black lives taken by US police forces and still awaiting justice. Our hearts are with our colleagues of color who suffer daily the consequences of this racist world.

scholarly journals Classification of all $\mathcal{N}\geq 3$ moduli space orbifold geometries at rank 2

2020 ◽  
Vol 9 (6) ◽  
Author(s):  
Philip Argyres ◽  
Antoine Bourget ◽  
Mario Martone
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Large Majority ◽  
Field Theories ◽  
Coordinate Ring ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Complex Dimension ◽  
Rank 2

We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional \mathcal{N}\geq 3𝒩≥3 superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to moduli spaces of known theories or discretely gauged version of them. Remarkably, we find 6 geometries which are not realized by any known theory, of which 3 have an \mathcal{N}=2𝒩=2 Coulomb branch slice with a non-freely generated coordinate ring, suggesting the existence of new, exotic \mathcal{N}=3𝒩=3 theories.

Powerfully nilpotent groups of rank 2 or small order

2020 ◽  
Vol 23 (4) ◽  
pp. 641-658
Author(s):  
Gunnar Traustason ◽  
James Williams
Keyword(s):  
Detailed Analysis ◽  
Special Kind ◽  
Nilpotent Groups ◽  
Nilpotency Class ◽  
Central Series ◽  
Rank 2 ◽  
Full Classification

AbstractIn this paper, we continue the study of powerfully nilpotent groups. These are powerful p-groups possessing a central series of a special kind. To each such group, one can attach a powerful nilpotency class that leads naturally to the notion of a powerful coclass and classification in terms of an ancestry tree. In this paper, we will give a full classification of powerfully nilpotent groups of rank 2. The classification will then be used to arrive at a precise formula for the number of powerfully nilpotent groups of rank 2 and order {p^{n}}. We will also give a detailed analysis of the ancestry tree for these groups. The second part of the paper is then devoted to a full classification of powerfully nilpotent groups of order up to {p^{6}}.

scholarly journals Classification of Mukai pairs with dimension $4$ and rank $2$

2019 ◽  
Vol 372 (9) ◽  
pp. 6629-6653
Author(s):  
Akihiro Kanemitsu
Keyword(s):  
Rank 2

scholarly journals Connected Shape-Size Pattern Spectra for Rotation and Scale-Invariant Classification of Gray-Scale Images

2007 ◽  
Vol 29 (2) ◽  
pp. 272-285 ◽  
Author(s):  
Erik R. Urbach ◽  
Jos B.T.M. Roerdink ◽  
Michael H.F. Wilkinson
Keyword(s):  
Gray Scale ◽  
Scale Invariant

scholarly journals Relationship of Hull Mesocarp Color to Seed Germination and Vigor in Large-Seeded Virginia-Type Peanuts

1995 ◽  
Vol 22 (1) ◽  
pp. 22-26 ◽  
Author(s):  
J. F. Spears ◽  
G. A. Sullivan
Keyword(s):  
Accelerated Aging ◽  
Dry Weight ◽  
Seed Moisture Content ◽  
Physiological Maturity ◽  
Seed Maturity ◽  
Seed Moisture ◽  
Arachis Hypogaea L ◽  
Maturity Class ◽  
Relationship Of

Abstract Classification of peanuts (Arachis hypogaea L.) based on pod mesocarp color has become a popular means of estimating maturity of runner peanuts. This study was initiated to determine if the hull mesocarp color is related to seed maturity of virginia-type peanuts and to evaluate changes in quality as seed mature. Cultivars NC 7 and NC 9 peanuts were harvested by hand in 1990, 1991, and 1992. Pods were separated according to mesocarp color. Seed moisture content and dry weight within a maturity class varied with cultivar and production year. Germination of NC 7 seed grown in 1990 and 1992 increased as seed approached maturity. Immature NC 9 seed grown in 1991 and 1992 had substantially lower germination than seed from mature pods. There was no increase in germination during maturation of NC 7 seed harvested in 1991 or NC 9 from 1990. Seed leakage during imbibition, measured by electrical conductivity, decreased as seed matured. The lowest leakage levels occurred when seed had reached physiological maturity. Germination following accelerated aging (AA) increased as seed matured. Maximum AA germination of NC 7 occurred when seed had reached 77, 84, and 100% of their final dry weight in 1990, 1991, and 1992, respectively. NC 9 seed achieved maximum germination following AA after the seed amassed at least 90% of their final dry weight.

GONADAL DYSGENESIS WITH XX-ISOCHROMOSOME CONSTITUTION AND ABNORMAL THYROID PATTERNS

1967 ◽  
Vol 54 (4) ◽  
pp. 609-617 ◽  
Author(s):  
R. G. Milet ◽  
E. R. Plunkett ◽  
D. H. Carr
Keyword(s):  
Autoimmune Disease ◽  
X Chromosome ◽  
Gonadal Dysgenesis ◽  
Ridge Count ◽  
Suppurative Otitis Media ◽  
Lyon Hypothesis ◽  
Relationship Of ◽  
The Relationship ◽  
Thyroid Abnormalities

ABSTRACT The authors report a female patient with XXi constitution for the long arm of the X chromosome associated with thyroid abnormalities, high digital ridge count and chronic suppurative otitis media. This is followed by a discussion of the correlation between genotype and phenotype, comment on the Lyon hypothesis, the relationship of thyroid abnormalities to this condition, autoimmune disease, unbalanced sex chromosomal constitution and the association with a high total digital ridge count. Finally a single hypothesis is proposed for the associated clinical entities that have been found and the suggestion that the classification of this particular type of gonadal dysgenesis be considered as a new syndrome, the »XX-isochromosome syndrome«.

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