arXiv subjects

Yangrui Hu

Publications and source records attributed to Yangrui Hu.

28 records · Page 2Linked to original sources

arXiv2021

The 300 "Correlators" Suggests 4D, $\cal N$ = 1 SUSY Is a Solution to a Set of Sudoku Puzzles

A conjecture is made that the weight space for 4D, $\cal N$-extended supersymmetrical representations is embedded within the permutahedra associated with permutation groups ${\mathbb{S}}{}_{d}$. Adinkras and Coxeter Groups associated with minimal representations of 4D, $\cal N$ = 1 supersymmetry provide evidence supporting this conjecture. It is shown the appearance of the mathematics of 4D, $\cal N$ = 1 minimal off-shell supersymmetry representations is equivalent to solving a four color problem on the truncated octahedron. This observation suggest an entirely new way to approach the off-shell SUSY auxiliary field problem based on IT algorithms probing the properties of ${\mathbb{S}}{}_{d}$.

hep-th↗

arXiv2021

Weyl Covariance, and Proposals for Superconformal Prepotentials in 10D Superspaces

Proposals are made to describe the Weyl scaling transformation laws of supercovariant derivatives $\nabla{}_{\underline A}$, the torsion supertensors $T{}_{{\underline A} \, {\underline B}}{}^{\underline C}$, and curvature supertensors $R{}_{{\underline A} \, {\underline B}}{}_{\, \underline c} {}^{\underline d}$ in 10D superspaces. Starting from the proposal that an unconstrained supergravity prepotential for the 11D, $\mathcal{N}$ = 1 theory is described by a scalar superfield, considerations for supergravity prepotentials in the 10D theories are enumerated. We derive infinitesimal 10D superspace Weyl transformation laws and discover ten possible 10D, $\mathcal{N}$ = 1 superfield supergravity prepotentials. The first identification of all off-shell ten dimensional supergeometrical Weyl field strength tensors, constructed from respective torsions, is presented.

hep-th↗

arXiv2020

Properties of HYMNs in Examples of Four-Color, Five-Color, and Six-Color Adinkras

The mathematical concept of a "Banchoff index" associated with discrete Morse functions for oriented triangular meshes has been shown to correspond to the height assignments of nodes in adinkras. In recent work there has been introduced the concept of "Banchoff matrices" leading to HYMNs - height yielding matrix numbers. HYMNs map the shape of an adinkra to a set of eigenvalues derived from Banchoff matrices. In the context of some examples of four-color, minimal five-color, and minimal six-color adinkras, properties of the HYMNs are explored.

hep-th↗

arXiv2020

Advening to Adynkrafields: Young Tableaux to Component Fields of the 10D, N = 1 Scalar Superfield

Starting from higher dimensional adinkras constructed with nodes referenced by Dynkin Labels, we define "adynkras." These suggest a computationally direct way to describe the component fields contained within supermultiplets in all superspaces. We explicitly discuss the cases of ten dimensional superspaces. We show this is possible by replacing conventional $θ$-expansions by expansions over Young Tableaux and component fields by Dynkin Labels. Without the need to introduce $σ$-matrices, this permits rapid passages from Adynkras $\to$ Young Tableaux $\to$ Component Field Index Structures for both bosonic and fermionic fields while increasing computational efficiency compared to the starting point that uses superfields. In order to reach our goal, this work introduces a new graphical method, "tying rules," that provides an alternative to Littlewood's 1950 mathematical results which proved branching rules result from using a specific Schur function series. The ultimate point of this line of reasoning is the introduction of mathematical expansions based on Young Tableaux and that are algorithmically superior to superfields. The expansions are given the name of "adynkrafields" as they combine the concepts of adinkras and Dynkin Labels.

hep-th↗

arXiv2020

Adinkra Foundation of Component Decomposition and the Scan for Superconformal Multiplets in 11D, N = 1 Superspace

For the first time in the physics literature, the Lorentz representations of all 2,147,483,648 bosonic degrees of freedom and 2,147,483,648 fermionic degrees of freedom in an unconstrained eleven dimensional scalar superfield are presented. Comparisons of the conceptual bases for this advance in terms of component field, superfield, and adinkra arguments, respectively, are made. These highlight the computational efficiency of the adinkra-based approach over the others. It is noted at level sixteen in the 11D, N = 1 scalar superfield, the {65} representation of SO(1,10), the conformal graviton, is present. Thus, Adinkra-based arguments suggest the surprising possibility that the 11D, N = 1 scalar superfield alone might describe a Poincare supergravity prepotential in analogy to one of the off-shell versions of 4D, N = 1 superfield supergravity.

hep-th↗

arXiv2020

Superfield Component Decompositions and the Scan for Prepotential Supermultiplets in 10D Superspaces

The first complete and explicit SO(1,9) Lorentz descriptions of all component fields contained in $\mathcal{N} = 1$, $\mathcal{N} = 2$A, and $\mathcal{N} = 2$B unconstrained scalar 10D superfields are presented. These are made possible by the discovery of the relation of the superfield component expansion as a consequence of the branching rules of irreducible representations in one ordinary Lie algebra into one of its Lie subalgebras. Adinkra graphs for ten dimensional superspaces are defined for the first time, whose nodes depict spin bundle representations of SO(1,9). An analog of Breitenlohner's approach is implemented to scan for superfields that contain graviton(s) and gravitino(s), which are the candidates for the prepotential superfields of 10D off-shell supergravity theories and separately abelian Yang-Mills theories are similarly treated. Version three contains additional content, both historical and conceptual, which broaden the reach of the scan in the 10D Yang-Mills case.

hep-th↗

arXiv2019

On Linearized Nordström Supergravity in Eleven and Ten Dimensional Superspaces

As the full off-shell theories of supergravity in the important dimensions of eleven and ten dimensions are currently unknown, we introduce a superfield formalism as a foundation and experimental laboratory to explore the possibility that the scalar versions of the higher dimensional supergravitation theory can be constructed.

hep-th↗

arXiv2019

Adinkra Height Yielding Matrix Numbers: Eigenvalue Equivalence Classes for Minimal Four-Color Adinkras

An adinkra is a graph-theoretic representation of spacetime supersymmetry. Minimal four-color valise adinkras have been extensively studied due to their relations to minimal 4D, $\cal N$ = 1 supermultiplets. Valise adinkras, although an important subclass, do not encode all the information present when a 4D supermultiplet is reduced to 1D. Eigenvalue equivalence classes for valise adinkra matrices exist, known as $χ_{\rm o}$ equivalence classes, where valise adinkras within the same $χ_{\rm o}$ equivalence class are isomorphic in the sense that adinkras within a $χ_{\rm o}$-equivalence class can be transformed into each other via field redefinitions of the nodes. We extend this to non-valise adinkras, via Python code, providing a complete eigenvalue classification of "node-lifting" for all 36,864 valise adinkras associated with the Coxeter group $BC{}_4$. We term the eigenvalues associated with these node-lifted adinkras Height Yielding Matrix Numbers (HYMNs) and introduce HYMN equivalence classes. These findings have been summarized in a $Mathematica$ notebook that can found at the HEPTHools Data Repository (https://hepthools.github.io/Data/) on GitHub.

hep-th↗

arXiv2019

On Linearized Nordstr\" om Supergravity in Eleven and Ten Dimensional Superspaces (2)

We present aspects of the component description of linearized Nordstr\" om Supergravity in eleven and ten dimensions. The presentation includes low order component fields in the supermultiplet, the supersymmetry variations of the scalar graviton and gravitino trace, their supercovariantized field strengths, and the supersymmetry commutator algebra of these theories.

hep-th↗

arXiv2016

Statistical imprints of CMB B-type polarization leakage in an incomplete sky survey analysis

One of the main goals of modern cosmology is to search for primordial gravitational waves by looking on their imprints in the B-type polarization in the cosmic microwave background radiation. However, this signal is contaminated by various sources, including cosmic weak lensing, foreground radiations, instrumental noises, as well as the E-to-B leakage caused by the partial sky surveys, which should be well understood to avoid the misinterpretation of the observed data. In this paper, we adopt the E/B decomposition method suggested by Smith in 2006, and study the imprints of E-to-B leakage residuals in the constructed B-type polarization maps, $\mathcal{B}(\hat{n})$, by employing various statistical tools. We find that the effects of E-to-B leakage are negligible for the $\mathcal{B}$-mode power spectrum, as well as the skewness and kurtosis analyses of $\mathcal{B}$-maps. However, if employing the morphological statistical tools, including Minkowski functionals and/or Betti numbers, we find the effect of leakage can be detected at very high confidence level, which shows that in the morphological analysis, the leakage can play a significant role as a contaminant for measuring the primordial B-mode signal and must be taken into account for a correct explanation of the data.

astro-ph.CO↗