where Φ Φ denotes collection of all the fields, p.b.c. stands for periodic boundary conditions, the so-called gauge fermion, Ψ Ψ = ∫ ∫ t ′ t d τ τ ( ı ı x ˙ ˙ − − d ¯ ¯ ) ( τ τ ) , with ı ı x ˙ ˙ = i χ χ ¯ ¯ j x ˙ ˙ j and d ¯ ¯ = − − i χ χ ¯ ¯ j δ δ j k ( ∂ ∂ k U + Θ Θ i B k ) , and the BRST symmetry defined via its action on arbitrary functional A ( Φ Φ ) as ( Q , A ( Φ Φ ) ) = ∫ ∫ t ′ t d τ τ ( χ χ i ( τ τ ) δ δ / δ δ x i ( τ τ ) + B i ( τ τ ) δ δ / δ δ χ χ ¯ ¯ i ( τ τ ) ) A ( Φ Φ ) . In the BRST formalism, the Q-exact pieces like, ( Q , Ψ Ψ ) , serve as gauge fixing tools. Therefore, the path integral expression for W can be interpreted as a model whose action contains nothing else but the gauge fixing term. This is a definitive feature of Witten-type topological field theories and in this particular case of BRST procedure approach to SDEs, the BRST symmetry can be also recognized as the topological supersymmetry.