Pictures from super Chern-Simons theory

A bstract We study super-Chern-Simons theory on a generic supermanifold. After a self-contained review of integration on supermanifolds, the complexes of forms (superforms, pseudoforms and integral forms) and the extended Cartan calculus are discussed. We then introduce Picture Changing Operators an...

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Bibliographic Details
Published in:The journal of high energy physics 2020-03, Vol.2020 (3), p.1-61, Article 43
Main Authors: Cremonini, C.A., Grassi, P.A.
Format: Article
Language:English
Subjects:
Algebra
Calculus
Chern-Simons Theories
Classical and Quantum Gravitation
Differential and Algebraic Geometry
Elementary Particles
Equations of motion
Field theory
Field theory (physics)
High energy physics
Hilbert space
Mathematical analysis
Operators (mathematics)
Physics
Physics and Astronomy
Pictures
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Quantum theory
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Superspaces
Theory of relativity
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Summary:A bstract We study super-Chern-Simons theory on a generic supermanifold. After a self-contained review of integration on supermanifolds, the complexes of forms (superforms, pseudoforms and integral forms) and the extended Cartan calculus are discussed. We then introduce Picture Changing Operators and their mathematical properties. We show that the free equations of motion reduce to the usual Chern-Simons equations proving on-shell equivalence between the formulations at different pictures of the same theory. Finally, we discuss the interaction terms. They require a suitable definition in order to take into account the picture number. This leads to the construction of a series of non-associative products which yield an A ∞ algebra structure, sharing several similarities with the super string field theory action by Erler, Konopka and Sachs.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP03(2020)043