Gauge theories and non-commutative geometry

Abstract

It is shown that a $d$-dimensional classical SU(N) Yang-Mills theory can be formulated in a $d+2$-dimensional space, with the extra two dimensions forming a surface with non-commutative geometry. In this paper we present an explicit proof for the case of the torus and the sphere.

12 pages

References in corpus (9)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Moyal Nahm Equations
• Uncertainty relation and non-dispersive states in Finite Quantum Mechanics
• Fast Quantum Maps
• W_\infty and w_\infty Gauge Theories and Contraction
• Strings and matrix models on genus g Riemann Surfaces
• Gauge theories formulated on surfaces with non-commutative geometry

Cited by in corpus (6)

• Time-Space Noncommutativity in Gravitational Quantum Well scenario
• Non-perturbative Double Copy in Flatland
• Galilean symmetry in noncommutative Gravitational Quantum Well
• $W_{\infty }$ Algebras, Hawking Radiation and Information Retention by Stringy Black Holes
• Scalar and vector gauges unification in de Sitter ambient space formalism
• Non trivial spacetime effects in a supersymmetric model