12 problems

Let the compactified Coulomb branch of the rank two theory be an elliptic fibered surface, with singular fibers whose monodromies are represented by Dehn twists. The total mapping…

Consider the $\mathcal{N}=2^*$ $Sp(2n)$ gauge theory whose fiber at infinity is given by the periodic-map data $(n,g^{'}=0,\frac{1}{2n}+\frac{1}{2}+\frac{1}{2}+\frac{2n-1}{2n})$ an…

For the singular fiber in the displayed $SU(n)$ gauge-theory geometry, let $\delta_x$ be its topological Euler number and $d_x$ its holomorphic invariant. Local-invariant equality…

Consider a four-dimensional theory described by a genus-$g$ fiberation with one special singular fiber $F_\infty$ at $z=\infty$, only $A_1$ singularities in the bulk, and, in the h…

The Seiberg–Witten geometry associated with a classical gauge theory is the geometric data underlying its low-energy description, while non-perturbative Schwinger–Dyson equations c…

Finite-instanton conjecture. Only the $\widetilde{\mathfrak{q}}$ and $\widetilde{\mathfrak{q}}^2$ terms in the Schwinger–Dyson equation survive this limit.

First-instanton survival conjecture. This pattern continues at every instanton order, and only the first instanton contribution $k=1$ survives the flat-space limit.

Adjoint-matter Seiberg–Witten conjecture. Taking the flat-space limit $\epsilon_1,\epsilon_2\rightarrow 0$, the Schwinger–Dyson equation describes the Seiberg–Witten geometry of fi…

First-instanton survival conjecture. This pattern continues at every instanton order, and only the first instanton contribution $k=1$ survives the flat-space limit.

Higher-instanton cancellation conjecture. The cancellation observed at the tested orders is a generic feature of all higher-instanton contributions.

Finite-term conjecture. When $T^{5d}$ is a pure $G$-theory, all but a finite number of terms disappear in the flat-space limit.

Finite Laurent-series conjecture. $T$ is a finite Laurent series in $e^M$; equivalently, the number $i$ of parameters $\{e_i^{\epsilon_1,\epsilon_2}\}$ is finite.