Root Structures of Infinite Gauge Groups and Supersymmetric Field Theories

21st International Conference on Integrable Systems and Quantum Symmetries

Catto, Sultan^1,2 ; Gürcan, Yasemin^3 ; Khalfan, Amish^4 ; Kurt, Levent^5

Physics Department, Graduate School, City University of New York, New York, NY 10016-4309, United States^1

Theoretical Physics Group, Rockefeller University, 1230 York Avenue, NY 10021-6399, New York, NY 10021-6399, United States^2

Physics Department, Manhattanville College, Brownson 129, Purchase, NY 10577, United States^3

Physics Department, Yeshiva University, New York, NY 10033, United States^4

Department of Science, Borough of Manhattan Community College, City University of New York, 199 Chambers Street, New York, NY 10007, United States^5

关键词: Algebraic method;    Algebraic properties;    Critical dimension;    Fundamental theory;    Hidden symmetry;    Infinite groups;    Jordan algebra;    Position vector;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/474/1/012013/pdf
DOI  :  10.1088/1742-6596/474/1/012013

来源: IOP

【 摘 要 】

We show the relationship between critical dimensions of supersymmetric fundamental theories and dimensions of certain Jordan algebras. In our approach position vectors in spacetime or in superspace are endowed with algebraic properties that are present only in those critical dimensions. A uniform construction of super Poincare´ groups in these dimensions will be shown. Some applications of these algebraic methods to hidden symmetries present in the covariant and interacting string Lagrangians and to superparticle will be discussed. Algebraic methods we develop will be shown to generate the root structure of some infinite groups that play the role of gauge groups in a second quantized theory of strings.