The Non-Abelian Self-Dual String and the (2,0)-Theory

Abstract

We argue that the relevant higher gauge group for the non-abelian generalization of the self-dual string equation is the string 2-group. We then derive the corresponding equations of motion and discuss their properties. The underlying geometric picture is a string structure, i.e. a categorified principal bundle with connection whose structure 2-group is the string 2-group. We readily write down the explicit elementary solution to our equations, which is the categorified analogue of the 't Hooft-Polyakov monopole. Our solution passes all the relevant consistency checks; in particular, it is globally defined on ${\mathbb{R}}^4$ and approaches the abelian self-dual string of charge one at infinity. We note that our equations also arise as the BPS equations in a recently proposed six-dimensional superconformal field theory and we show that with our choice of higher gauge structure, the action of this theory can be reduced to four-dimensional supersymmetric Yang-Mills theory.

v3: 1+42 pages, presentation improved, typos fixed, published version

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• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Higher-Dimensional Algebra V: 2-Groups
• M2 to D2
• Higher Gauge Theory: 2-Connections on 2-Bundles
• Higher Yang-Mills Theory
• Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries
• General Yang-Mills type gauge theories for p-form gauge fields: From physics-based ideas to a mathematical framework OR From Bianchi identities to twisted Courant algebroids
• Semistrict Higher Gauge Theory
• Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions
• M-brane Models from Non-Abelian Gerbes
• Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations
• Generalizing Geometry - Algebroids and Sigma Models
• L_infinity algebras as 1-jets of simplicial manifolds (and a bit beyond)
• Instantonic string solitons on M5 branes

Cited by in corpus (10)

• (2,0) Lagrangian Structures
• Towards an M5-Brane Model II: Metric String Structures
• Smooth 2-Group Extensions and Symmetries of Bundle Gerbes
• Adjusted Parallel Transport for Higher Gauge Theories
• Towards an M5-Brane Model III: Self-Duality from Additional Trivial Fields
• Higher Gauge Theory
• Massless chiral fields in six dimensions
• M5-brane prongs, string soliton bound states and wall-crossing
• Explicit Non-Abelian Gerbes with Connections
• $E_2{L}_{\infty }$-algebras, Generalized Geometry, and Tensor Hierarchies