Assuming automatic transversality, we can rewrite the Solomon functional (20) as a moduli space integral in terms of the notations introduced in section 3.5. Let $u:\Sigma\to X$ be a holomorphic polygon, with first order deformation vector fields $v_{1},\ldots v_{n-1}$, so we can define a holomorphic function $F$ via (33). In clockwise order on $\partial\Sigma$, we encounter the degree one intersections on $L$, an intersection $p\in CF^{0}(L,L_{0})$, the degree one self intersections on $L_{0}$, and an intersection $q\in CF^{0}(L_{0},L)$. As before, we fix the additive constant by $F(q)=0$.

In the following calculation, we will use the complex orientation on $\Sigma$, and the counterclockwise orientation on $\partial\Sigma$. The Solomon functional contains a term $-\int_{\mathcal{C}}\lambda\wedge\text{Im}(e^{-i\hat{\theta}}\Omega).$ Now $-\int_{\mathcal{C}}\lambda\wedge\Omega$ can be expressed as an integral of the following $(n-1)$-form over the $(n-1)$-dimensional moduli spaces $\mathcal{M}$ of holomorphic curves:

$$\int_{\Sigma}\lambda\wedge\Omega(\cdot,v_{1},\ldots v_{n-1})=\int_{\Sigma}\lambda\wedge dF.$$

Notice that since $u:\Sigma\to X$ is a holomorphic curve and $\Omega$ is an $(n,0)$-form, adjusting $v_{i}$ by a vector field tangent to $\Sigma$ does not change this integrand, and all $v_{i}$ must hit $\Omega$ instead of the 1-form $\lambda$. After integration by part,

$$\int_{\Sigma}\lambda\wedge dF=\int_{\Sigma}Fd\lambda-\int_{\partial\Sigma}F\lambda=\int_{\Sigma}F\omega-\int_{\partial\Sigma}F\lambda.$$

The Solomon functional contains another two terms $\int_{L}f_{L}\text{Im}(e^{-i\hat{\theta}}\Omega)$ and $-\int_{L_{0}}f_{L_{0}}\text{Im}(e^{-i\hat{\theta}}\Omega)$. Now $\int_{L}f_{L}\Omega$ can be expressed as an integral of the following $(n-1)$-form over the moduli spaces $\mathcal{M}$:

$$-\int_{\partial\Sigma\cap L}f_{L}\Omega(\cdot,v_{1},\ldots v_{n-1})=-\int_{\partial\Sigma\cap L}f_{L}dF.$$

The abused notation $\partial\Sigma\cap L$ means the part of $\partial\Sigma$ mapping to $L$ instead of $L_{0}$. Similarly $-\int_{L_{0}}f_{L_{0}}\Omega$ is the moduli space integral of the $(n-1)$-form

$$-\int_{\partial\Sigma\cap L_{0}}f_{L_{0}}\Omega(\cdot,v_{1},\ldots v_{n-1})=-\int_{\partial\Sigma\cap L_{0}}f_{L_{0}}dF.$$

The extra minus sign comes from the fact that $\partial\mathcal{C}$ sweeps out the cycle $-L_{0}$ instead of $L_{0}$.

Combining all the three contributions, the Solomon functional is the moduli space integral with integrand

$$\mathcal{I}=\text{Im}\int_{\Sigma}e^{-i\hat{\theta}}F\omega-\text{Im}\int_{\partial\Sigma\cap L}e^{-i\hat{\theta}}d(f_{L}F)-\text{Im}\int_{\partial\Sigma\cap L_{0}}e^{-i\hat{\theta}}d(f_{L_{0}}F).$$

The last two terms involve total derivatives, so can be integrated along boundary segments between the corner points, to yield

$$\begin{split}&-\text{Im}\int_{\partial\Sigma\cap L}e^{-i\hat{\theta}}d(f_{L}F)-\text{Im}\int_{\partial\Sigma\cap L_{0}}e^{-i\hat{\theta}}d(f_{L_{0}}F)\\ &=\text{Im}\sum_{\text{all corners}}e^{-i\hat{\theta}}Ff|^{+}_{-},\end{split}$$

(38)

where $f|^{+}_{-}$ stands for the difference of the potentials $f_{L_{+}}-f_{L-}$ at a Lagrangian intersection point, such that $\partial\Sigma$ moves from $L_{+}$ to $L_{-}$ in the clockwise direction. In the more general framework of Floer theory with Novikov coefficients, $f|^{+}_{-}$ have the interpretation as the Novikov exponents of these intersection points. The bounding cochain elements have $f|^{+}_{-}\geq 0$, while $p\in CF^{0}(L,L_{0}),q\in CF^{0}(L_{0},L)$ may have negative Novikov exponents.