Symmetries of topological field theories in the BV-framework
F. Gieres, J.M. Grimstrup, H. Nieder, T. Pisar, M. Schweda
TL;DR
This paper analyzes the symmetries of topological field theories within the BV formalism, providing an algebraic framework for understanding off-shell symmetries in Schwarz- and Witten-type models.
Contribution
It offers a comprehensive algebraic approach to symmetries in topological field theories, including non-closure off-shell, within the BV framework.
Findings
Detailed classification of symmetries in Schwarz-type theories
Algebraic construction of topological models of both Schwarz- and Witten-type
Insights into the role of symmetries in perturbative finiteness
Abstract
Topological field theories of Schwarz-type generally admit symmetries whose algebra does not close off-shell, e.g. the basic symmetries of BF models or vector supersymmetry of the gauge-fixed action for Chern-Simons theory (this symmetry being at the origin of the perturbative finiteness of the theory). We present a detailed discussion of all these symmetries within the algebraic approach to the Batalin-Vilkovisky formalism. Moreover, we discuss the general algebraic construction of topological models of both Schwarz- and Witten-type.
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