Alberto S. Cattaneo, Shuhan Jiang
We derive equivariant localization formulas of Atiyah--Bott and cohomological field theory types in the Batalin-Vilkovisky formalism and discuss their applications in Poisson geometry and quantum field theory.
This paper contains 9 sections, 5 theorems, 67 equations.
Theorem 3.1
Let $P \in \mathcal{V}_{\mathrm{U}(1)}(M)$. If $\Delta_{\mathfrak{u}(1)} P = 0$ and $M_X$ is of codimension $2m$, then where $\nabla$ is the Levi-Civita connection of $g$ and $N_X$ is the normal bundle of $M_X$. In particular, if $n=2m$, i.e., if $M_X$ is discrete, then where $\lambda_1(p), \dots, \lambda_m(p)$ are the weights of the induced $\mathrm{U}(1)$-action on $T_pM$.
