Six-Dimensional (1,0) Superconformal Models and Higher Gauge Theory

Abstract

We analyze the gauge structure of a recently proposed superconformal field theory in six dimensions. We find that this structure amounts to a weak Courant-Dorfman algebra, which, in turn, can be interpreted as a strong homotopy Lie algebra. This suggests that the superconformal field theory is closely related to higher gauge theory, describing the parallel transport of extended objects. Indeed we find that, under certain restrictions, the field content and gauge transformations reduce to those of higher gauge theory. We also present a number of interesting examples of admissible gauge structures such as the structure Lie 2-algebra of an abelian gerbe, differential crossed modules, the 3-algebras of M2-brane models and string Lie 2-algebras.

31+1 pages, presentation slightly improved, version published in JMP

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• Towards an M5-Brane Model I: A 6d Superconformal Field Theory
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• Semistrict Higher Gauge Theory
• Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions
• Leibniz Gauge Theories and Infinity Structures
• Towards an M5-Brane Model II: Metric String Structures
• Lie 2-algebra models
• The ABJM Model is a Higher Gauge Theory
• Chern-Simons Actions and Their Gaugings in 4D, N=1 Superspace
• The Non-Abelian Self-Dual String and the (2,0)-Theory
• Infinity-enhancing of Leibniz algebras
• Generalized Yang-Mills Theory and Gravity
• Leibniz-Yang-Mills Gauge Theories and the 2-Higgs Mechanism
• Aspects of Effective Theory for Multiple M5-Branes Compactified On Circle
• Superforms in Simple Six-dimensional Superspace
• Non-Abelian tensor hierarchy in (1,0) D=6 superspace
• Self-dual String and Higher Instanton Solutions
• Algebraic formulation of higher gauge theory
• Higher Gauge Theory
• All Chern-Simons Invariants of 4D, N = 1 Gauged Superform Hierarchies
• Massless chiral fields in six dimensions
• A class of hermitian generalized Jordan triple systems and Chern-Simons gauge theory
• $E_2{L}_{\infty }$-algebras, Generalized Geometry, and Tensor Hierarchies