publication . Preprint . 2019

Higher-Rank Non-Abelian Tensor Field Theory: Higher-Moment or Subdimensional Polynomial Global Symmetry, Algebraic Variety, Noether's Theorem, and Gauge

Wang, Juven; Xu, Kai; Yau, Shing-Tung;
Open Access English
  • Published: 29 Oct 2019
Abstract
With a view toward a theory of fracton and embeddon in condensed matter, we introduce a higher-moment polynomial degree-(m-1) global symmetry, acting on complex scalar/vector/tensor fields. We relate this higher-moment global symmetry of $n$-dimensional space, to a lower degree (either ordinary or higher-moment, e.g., degree-(m-1-$\ell$)) subdimensional or subsystem global symmetry on layers of $(n-\ell)$-submanifolds. These submanifolds are algebraic affine varieties (i.e., solutions of polynomials). The structure of layers of submanifolds as subvarieties can be studied via mathematical tools of embedding, foliation and algebraic geometry. We also generalize No...
Subjects
free text keywords: High Energy Physics - Theory, Condensed Matter - Strongly Correlated Electrons, Mathematical Physics
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