Let $u \colon \Sigma^2 \to M^{2n}$ be a holomorphic disk (so $\Sigma = \{z \in \mathbb{C} \colon |z| \leq 1\}$) in a compact Calabi-Yau manifold $M$ of real dimension $2n$ with boundary on a Lagrangian submanifold $L^n \subset M^{2n}$. Note that the normal bundle $N\Sigma \to \Sigma$ is a complex vector bundle of complex rank $n-1$. At points of $\partial \Sigma$, let's orthogonally decompose $TL|_{\partial \Sigma} = T(\partial \Sigma)|_{\partial \Sigma} \oplus F$, so that $F \subset N\Sigma|_{\partial \Sigma}$ is a totally real subbundle of real rank $n-1$.

I am interested in the boundary Maslov index $\mu(N\Sigma, F) \in \mathbb{Z}$. My question is: Among all possible pairs $(u, L)$ of holomorphic curves with Lagrangian boundary, can $\mu(N\Sigma, F)$ attain every possible integer value, or are there restrictions (coming from, say, the Calabi-Yau assumption on $M$)?

I am not a symplectic geometer, so I don't know what to expect. In particular, I don't know whether there are standard examples of holomorphic curves with Lagrangian boundary for which $\mu(N\Sigma, F)$ is easily computable.