Loop groups and Yang-Mills theory in dimension two

Loop Equation in Two-dimensional Noncommutative Yang-Mills Theory

The classical analysis of Kazakov and Kostov of the Makeenko-Migdal loop equation in two-dimensional gauge theory leads to usual partial differential equations with respect to the areas of windows formed by the loop. We extend this treatment to the case of U(N) Yang-Mills defined on the noncommutative plane. We deal with all the subtleties which arise in their two-dimensional geometric procedur...

Floer homology groups in Yang–Mills theory

The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory

We present an expression for the leading-color (planar) four-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4 − 2ǫ dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity cuts and infrared divergences. We expand the integrals around ǫ = 0, and obtain analytic expressions for the poles from 1/ǫ8 through 1/ǫ4. We give numerical...

Yang-Mills theory for nonsemisimple groups

For semisimple groups, possibly multiplied by U~1!’s, the number of Yang-Mills gauge fields is equal to the number of generators of the group. In this paper, it is shown that, for nonsemisimple groups, the number of Yang-Mills fields can be larger. These additional Yang-Mills fields are not irrelevant because they appear in the gauge transformations of the original Yang-Mills fields. Such nonse...

Beta-functions in Yang-Mills Theory and Wilson-Loop

The renormalization group equations of the Yang-Mills theory are examined in the non-critical string theory according to the framework of the holography. Under a simple ansatz for the tachyon, we could find several interesting solutions which are classified by the value of the tachyon potential at the vacuum. We show two typical, asymptotic-free solutions which are different in their infrared b...