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Non-commutative gauge symmetry from strong homotopy algebras

Vladislav Kupriyanov, Fernando Oliveira, Alexey Sharapov, Dmitri Vassilevich

Abstract

We explicitly construct an L$_\infty$ algebra that defines U$_{\star}(1)$ gauge transformations on a space with an arbitrary non-commutative and even non-associative star product. Matter fields are naturally incorporated in this scheme as L$_\infty$ modules. Some possibilities for including P$_\infty$ algebras are also discussed.

Non-commutative gauge symmetry from strong homotopy algebras

Abstract

We explicitly construct an L algebra that defines U gauge transformations on a space with an arbitrary non-commutative and even non-associative star product. Matter fields are naturally incorporated in this scheme as L modules. Some possibilities for including P algebras are also discussed.
Paper Structure (10 sections, 89 equations)

This paper contains 10 sections, 89 equations.

Table of Contents

  1. Introduction
  2. Setup and main definitions
  3. Construction of the L$_\infty$ algebra
  4. The first step
  5. All order solution
  6. Example
  7. Matter fields as an L$_\infty$ module
  8. A$_\infty$ and P$_\infty$ algebras
  9. Conclusion
  10. Acknowledgements.

Theorems & Definitions (3)

  • Definition 4.1
  • Definition 5.1
  • Definition 5.2