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--- blog:2024-12-06 [2024/12/09 07:08] – pzhou
+++ blog:2024-12-06 [2024/12/09 07:37] (current) – pzhou
@@ Line 8: / Line 8: @@
 . we know Hori-Vafa mirror for $\C^n$. It is $Y=(\C^*)_A^n, W_Y=\sum_i y_i$ where $y_i$ are coordinates on $Y$.
-. we know the mirror for $\C^n / T$ for some subtorus $T \In (\C^*)_B^n$, whose mirror is $\pi_A: Y \to T^\vee_\C$. Then we do the log unfolding for $\pi_A$.
+. we know the mirror for $\C^n / T$ for some (complex) subtorus $T \In (\C^*)_B^n$, whose mirror is $\pi_A: Y \to T^\vee$. Then we do the log unfolding for $\pi_A$, that defines a map
+$$ \tilde \pi_A: \wt Y \to Lie(T^\vee) $$
+We have the pullback super-potential $\wt W_Y$ on $\wt Y$ from $Y$.
+. Somehow, we have an extra factor $Lie(T^\vee)^\vee = Lie(T)$, where the 'sigma' field and 'gamma' contour lives. Doing an integral along $\sigma \in \gamma$ with exponential factor $\exp(i \sigma(\wt \pi - t))$ forces $\wt pi = t$.
+. However, we don't want to just do integral. We want to have A-model objects.