Two-dimensional Yang–Mills theory
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. This situation contrasts with the four-dimensional case, where a rigorous construction of the theory as a measure is currently unknown.
An aspect of the subject of particular interest is the large-N limit, in which the structure group is taken to be the unitary group and then the tends to infinity limit is taken. The large-N limit of two-dimensional Yang–Mills theory has connections to string theory.
