The non-abelian self-dual string. (English) Zbl 1482.81030
Summary: 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.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 70S15 | Yang-Mills and other gauge theories in mechanics of particles and systems |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 18G45 | 2-groups, crossed modules, crossed complexes |
| 22A22 | Topological groupoids (including differentiable and Lie groupoids) |
| 17B45 | Lie algebras of linear algebraic groups |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
| 55R91 | Equivariant fiber spaces and bundles in algebraic topology |
Keywords:
self-dual strings; string group; higher gauge theory; superconformal field theories; strong homotopy Lie algebrasReferences:
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