Batalin-Vilkovisky cohomology and supergravity


The Batalin-Vilkovisky formalism is a theory of gauge symmetry in derived geometry which takes Nöther’s formalism for classical field theories off-shell (that is, away from the locus where the Euler-Lagrange equations are satisfied). This property of the formalism can be viewed as a prerequisite to quantization. In this talk, we introduce the BV formalism, and then construct cohomology classes in negative degrees in a toy model with supergravity (related to the Dirac operator), which have not been observed in previous examples.