Homotopy Algebras of Differential (Super)forms in Three and Four Dimensions

Abstract

We consider various $A_{\infty }$-algebras of differential (super)forms, which are related to gauge theories and demonstrate explicitly how certain reformulations of gauge theories lead to the transfer of the corresponding $A_{\infty }$-structures. In $N=2$ 3D space we construct the homotopic counterpart of the de Rham complex, which is related to the superfield formulation of the $N=2$ Chern-Simons theory.

v2: 22 pages, minor revision

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• Loop Amplitudes and Quantum Homotopy Algebras
• $L_{\infty }$-Algebras, the BV Formalism, and Classical Fields
• BV equivalence with boundary
• On deformations of $A_{\infty }$-algebras
• The teleparallel complex
• BV Quantization
• Ambitwistor Yang-Mills Theory Revisited