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Covariant Interacting Fractons

Erica Bertolini, Hyungrok Kim

Abstract

We show that there exists a natural analogue of the Yang-Mills equations using the Frölicher-Nijenhuis bracket between vector-valued differential forms. The gauge field is a rank-two tensor, and when one constrains it to be symmetric, then the system exhibits fractonic behaviours. In the linearised limit, the constrained equations of motion reduce to those of the covariant fracton model [Bertolini-Maggiore 2022].

Covariant Interacting Fractons

Abstract

We show that there exists a natural analogue of the Yang-Mills equations using the Frölicher-Nijenhuis bracket between vector-valued differential forms. The gauge field is a rank-two tensor, and when one constrains it to be symmetric, then the system exhibits fractonic behaviours. In the linearised limit, the constrained equations of motion reduce to those of the covariant fracton model [Bertolini-Maggiore 2022].
Paper Structure (11 sections, 35 equations)

This paper contains 11 sections, 35 equations.

Table of Contents

  1. Introduction and summary
  2. Acknowledgements
  3. Mathematical background
  4. Frölicher--Nijenhuis bracket
  5. Twisting
  6. Motivation and idea
  7. A review of Yang--Mills theory
  8. Nonabelianising the covariant fracton model: the idea
  9. Covariant interacting fractonic gauge theory
  10. Non-symmetric theory
  11. Symmetric theory