Pictures from super Chern-Simons theory

C.A. Cremonini (Dipartimento di Scienze e Alta Tecnologia (DiSAT), Università degli Studi dell’Insubria, via Valleggio 11, Como, 22100, Italy; INFN, Sezione di Milano, via G. Celoria 16, Milano, 20133, Italy) ; P.A. Grassi (Dipartimento di Scienze e Innovazione Tecnologica (DiSIT), Universit`a del Piemonte Orientale, viale T. Michel, 11, Alessandria, 15121, Italy; INFN, Sezione di Torino, via P. Giuria 1, Torino, 10125, Italy; Arnold-Regge Center, via P. Giuria 1, Torino, 10125, Italy)

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.

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Published on:
09 March 2020
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2020 (2020)
Issue 3
Pages 1-61
DOI:
https://doi.org/10.1007/JHEP03(2020)043
arXiv:
1907.07152
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: