Quantization of the topological $σ$-model and the master equation of the BF formalism

Abstract

We quantize the topological $σ$-model. The quantum master equation of the Batalin-Vilkovisky formalism $Δ_ρΨ= 0$ appears as a condition which eliminates the exact states from the BRST invariant states $Ψ$ defined by $Q Ψ= 0$. The phase space of the BV formalism is a supermanifold with a specific symplectic structure, called the fermionic Kähler manifold.