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Yang–Mills theory is a quantum field theory for nuclear binding devised by Chen Ning Yang and Robert Mills in 1953, as well as a generic term for the class of similar theories. The Yang–Mills theory is a gauge theory based on a special unitary group SU( n ) , or more generally any compact Lie group .
N = 4 super Yang–Mills can be derived from a simpler 10-dimensional theory, and yet supergravity and M-theory exist in 11 dimensions. The connection is that if the gauge group U( N ) of SYM becomes infinite as N → ∞ {\displaystyle N\rightarrow \infty } it becomes equivalent to an 11-dimensional theory known as matrix theory .
Through the process of dimensional reduction, the Yang–Mills equations may be used to derive other important equations in differential geometry and gauge theory. Dimensional reduction is the process of taking the Yang–Mills equations over a four-manifold, typically R 4 {\displaystyle \mathbb {R} ^{4}} , and imposing that the solutions be ...
In theoretical physics, more specifically in quantum field theory and supersymmetry, supersymmetric Yang–Mills, also known as super Yang–Mills and abbreviated to SYM, is a supersymmetric generalization of Yang–Mills theory, which is a gauge theory that plays an important part in the mathematical formulation of forces in particle physics.
This means that if such a QFT is well-defined at all scales, as it has to be to satisfy the axioms of axiomatic quantum field theory, it would have to be trivial (i.e. a free field theory). Quantum Yang–Mills theory with a non-abelian gauge group and no quarks is an exception, because asymptotic freedom characterizes this theory, meaning that ...
For instance, this is the case of gauge symmetries in classical field theory. [2] Yang–Mills gauge theory and gauge gravitation theory exemplify classical field theories with gauge symmetries. [3] Gauge symmetries possess the following two peculiarities.
In mathematical physics, two-dimensional Yang–Mills theory is the special case of Yang–Mills theory in which the dimension of spacetime is taken to be two. This special case allows for a rigorously defined Yang–Mills measure, meaning that the (Euclidean) path integral can be interpreted as a measure on the set of connections modulo gauge transformations.
Yang–Mills connections are solutions of the Yang–Mills equations following from them being local extrema of the curvature, hence critical points of the Yang–Mills action functional, which are determined by a vanishing first derivative of a variation. (Weakly) stable Yang–Mills connections furthermore have a positive or even strictly ...