Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories

Abstract

In the last decade it became clear that methods and techniques based on supersymmetry provide deep insights in quantum chromodynamics and other supersymmetric and non-supersymmetric gauge theories at strong coupling. In this review we summarize major advances in the critical (Bogomol'nyi-Prasad-Sommerfeld-saturated, BPS for short) solitons in supersymmetric theories and their implications for understanding basic dynamical regularities of non-supersymmetric theories. After a brief introduction in the theory of critical solitons (including a historical introduction) we focus on three topics: (i) non-Abelian strings in N=2 and confined monopoles; (ii) reducing the level of supersymmetry; and (iii) domain walls as D brane prototypes.

239 pages, 27 figures. A part of this review will be published in Rev. Mod. Phys. Comments and suggestions welcome

References in corpus (5)

• All Exact Solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield Equation
• Construction of Non-Abelian Walls and Their Complete Moduli Space
• Non-Abelian Walls in Supersymmetric Gauge Theories
• Webs of Walls
• Global Structure of Moduli Space for BPS Walls

Cited by in corpus (27)

• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• On the moduli space of semilocal strings and lumps
• Constructing Non-Abelian Vortices with Arbitrary Gauge Groups
• Integrability of Vortex Equations on Riemann Surfaces
• Domain Walls with Non-Abelian Clouds
• Intersecting Solitons, Amoeba and Tropical Geometry
• Non-Abelian Vortices on Riemann Surfaces: an Integrable Case
• Non-Abelian Vortices in SO(N) and USp(N) Gauge Theories
• Fractional Vortices and Lumps
• Magnetic strings in Lattice QCD as Nonabelian Vortices
• Non-Abelian Chern-Simons vortices with generic gauge groups
• The Dynamics of Chern-Simons Vortices
• Dynamics of Strings between Walls
• Static Interactions of non-Abelian Vortices
• Manifestations of magnetic vortices in equation of state of Yang-Mills plasma
• On the Stability of Non-Abelian Semi-local Vortices
• Quantum corrections to the noncommutative kink
• Monopoles and Modifications of Bundles over Elliptic Curves
• Dyonic Non-Abelian Vortices
• Nonabelian strings in a dense matter
• Non-Abelian Vortices on the Torus
• One-loop results for kink and domain wall profiles at zero and finite temperature
• Quantum SUSY Algebra of $Q$-lumps in the Massive Grassmannian Sigma Model
• Revisiting Critical Vortices in Three-Dimensional SQED
• String Dynamics, Spontaneous Breaking of Supersymmetry and Dual Scalar Field Theory
• Effective Lagrangian of Domain Wall Networks
• Theoretical Developments in SUSY