Seiberg-Witten maps and noncommutative Yang-Mills theories for arbitrary gauge groups

DOI10.1088/1126-6708/2002/08/023zbMath1226.81120arXivhep-th/0206003OpenAlexW2060828997MaRDI QIDQ648881

Glenn Barnich, Maxim Grigoriev, Friedemann Brandt

Publication date: 29 November 2011

Published in: Journal of High Energy Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/0206003

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Quantization in field theory; cohomological methods (81T70) Noncommutative geometry methods in quantum field theory (81T75)

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Seiberg-Witten maps for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>gauge invariance and deformations of gravity ⋮ Gauge theories on quantum spaces ⋮ Local BRST cohomology and Seiberg-Witten maps in noncommutative Yang-Mills theory ⋮ Four-dimensional gravity on a covariant noncommutative space ⋮ Higher-Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions ⋮ Gauge theoretic approach to (ordinary) gravity and its fuzzy extensions in three and four dimensions

Cites Work

• Enveloping algebra-valued gauge transformations for non-abelian gauge groups on non-commutative spaces
• Comments on gauge equivalence in noncommutative geometry
• String theory and noncommutative geometry
• A path integral representation of the map between commutative and noncommutative gauge fields
• Restrictions on gauge groups in noncommutative gauge theory
• Noncommutative \(\text{SO}(n)\) and \(\text{Sp}(n)\) gauge theories.
• Noncommutative gauge theory for Poisson manifolds
• Construction of non-Abelian gauge theories on noncommutative spaces