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In the last decade methods and techniques based on supersymmetry have provided deep insights in quantum chromodynamics and other nonsupersymmetric gauge theories at strong coupling. This book summarizes major advances in critical solitons in supersymmetric theories, and their implications for understanding basic dynamical regularities of nonsupersymmetric theories. After an extended introduction on the theory of critical solitons, including a historical introduction, the authors focus on three topics: non-Abelian strings and confined monopoles; reducing the level of supersymmetry; and domain walls as D brane prototypes. They also provide a thorough review of issues at the cutting edge, such as non-Abelian flux tubes. The book presents an extensive summary of the current literature so researchers in this field can understand the background and related issues.

We consider non-Abelian BPS-saturated flux tubes (strings) in N = 2 supersymmetric QCD deformed by superpotential terms of a special type breaking N = 2 supersymmetry down to N = 1 . Previously it was believed that worldsheet supersymmetry is "accidentally" enhanced due to the facts that N = (1, 1) SUSY is automatically elevated up to N = (2, 2) on CP (N − 1) and, at the same time, there are no N = (0, 2) generalizations of the bosonic CP (N − 1) model. Edalati and Tong noted that the target space is in fact CP (N − 1) × C rather than CP (N − 1). This allowed them to suggest a "heterotic" N = (0, 2) sigma model, with the CP (N − 1) target space for bosonic fields and an extra right-handed fermion which couples to the fermion fields of the N = (2, 2) CP (N −1) model. We derive the heterotic N = (0, 2) worldsheet model directly from the bulk theory. The relation between the bulk and worldsheet deformation parameters we obtain does not coincide with that suggested by Edalati and Tong at large values of the deformation parameter. For polynomial deformation superpotentials in the bulk we find nonpolynomial response in the worldsheet model. We find a geometric representation for the heterotic model. Supersymmetry is proven to be spontaneously broken for small deformations (at the quantum level). This confirms Tong's conjecture. A proof valid for large deformations will be presented in the subsequent publication.

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