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Magic square from Yang-Mills squared.

L Borsten1, M J Duff1, L J Hughes1

  • 1Theoretical Physics, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom.

Physical Review Letters
|April 22, 2014
PubMed
Summary
This summary is machine-generated.

This study unifies D=3 super-Yang-Mills theories using four division algebras. This framework generates a magic square describing D=3 supergravity with various supersymmetry levels.

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Area of Science:

  • Theoretical Physics
  • Mathematical Physics
  • String Theory

Background:

  • Super-Yang-Mills theory is a fundamental concept in quantum field theory.
  • Division algebras (reals, complexes, quaternions, octonions) play a role in advanced physics.
  • Understanding different supersymmetry (N) levels is crucial for theoretical consistency.

Purpose of the Study:

  • To provide a unified description of D=3 super-Yang-Mills theory.
  • To explore the connection between division algebras and supersymmetry.
  • To construct a comprehensive description of D=3 supergravity.

Main Methods:

  • Utilizing the four division algebras: reals (R), complexes (C), quaternions (H), and octonions (O).
  • Tensoring left and right super-Yang-Mills multiplets with varying N values (1, 2, 4, 8).
  • Developing a 'magic square' formalism for supergravity.

Main Results:

  • A unified description of D=3 super-Yang-Mills theory across N=1, 2, 4, 8 supersymmetries is achieved.
  • A novel 'magic square' is presented, detailing D=3 supergravity.
  • The resulting supergravity theories exhibit a wide range of supersymmetry levels (N=2 to 16).

Conclusions:

  • Division algebras offer a powerful framework for unifying super-Yang-Mills and supergravity theories.
  • The 'magic square' construction provides a systematic way to generate diverse supergravity models.
  • This work deepens the understanding of the interplay between algebra and supersymmetry in D=3.