Birationally equivalent Landau-Ginzburg models on cotangent bundles and adjoint orbits

Abstract

We show that the Lie potential on the minimal semisimple adjoint orbit $\mathcal{O}_n$ of $\mathfrak{sl}(n+1,\mathbb{C})$ coincides with toric potential on $T^*\mathbb P^{n}$. We then study the corresponding Landau-Ginzburg models in deformation families and give some examples of how the deformations affect the mirrors.

Figures (6)

• Figure 1: Selfdual $\mathop{\mathrm{LG}}\nolimits_0$ model
• Figure 2: Nontrivial toric duality
• Figure 3: $\mathbb{F}_2$ deforms to $\mathbb{F}_0$
• Figure 4: $T^*\mathbb{P}^1$ deforms to $\mathcal{O}_2$
• Figure 5: $\mathop{\mathrm{LG}}\nolimits_1$ to $\mathop{\mathrm{LG}}\nolimits_2$

Theorems & Definitions (38)

• Definition 2.1
• Definition 2.2
• Definition 2.3
• Example 2.4
• Definition 2.5
• Definition 2.6
• Example 2.7
• Remark 2.8
• Example 2.9
• Definition 3.1