Homotopy algebras of differential (super)forms in three and four dimensions



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 addition, for \(N=2\) 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.


Supersymmetric field theories Homotopical algebra Supergeometry 

Mathematics Subject Classification

18G55 81T60 83E30 



We are grateful to K. Costello, M. Markl, M. Movshev and J. Stasheff for illuminating discussions. We are indebted to the valuable comments of the referee. We would like to express our gratitude to the wonderful environment of Simons Summer Workshops where this work was partially done. A.M.Z. is grateful to A.N. Fedorova for careful reading of the manuscript.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.C.N. Yang Institute for Theoretical PhysicsStony Brook UniversityStony BrookUSA
  2. 2.Department of MathematicsLouisiana State UniversityBaton RougeUSA
  3. 3.IPME RASSt. PetersburgRussia

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