Freckled Instantons in Two and Four Dimensions

TL;DR

This paper explores how adding degrees of freedom to field theories with instantons introduces new topological defects called freckles, affecting models in two and four dimensions, including supersymmetric gauge theories.

Contribution

It introduces the concept of freckles as new topological defects arising from regularization, and studies their effects in various two- and four-dimensional models, including compactified supersymmetric theories.

Findings

Freckles have characteristic sizes depending on the scale of extra degrees of freedom.

New phenomena emerge in compactified four-dimensional supersymmetric gauge theories.

The study provides insights into the regularization of instantons and associated topological defects.

Abstract

Field theory with instantons can be partially regularized by adding degrees of freedom at some scale. These extra degrees of freedom lead to the appearence of the new topological defects. These defects which we call freckles have some characteristic size depending on the scale at which the extra degrees of freedom revive. The examples of two dimensional sigma model, four dimensional gauge theory are studied. The compactification of the four dimensional supersymmetric gauge theory down to two dimensions is also considered and the new phenomena are found.