论文标题
探索$ su（n）$ seiberg-witten理论的强耦合区域
Exploring the Strong-Coupling Region of $SU(N)$ Seiberg-Witten Theory
论文作者
论文摘要
我们考虑纯$ \ Mathcal {n} = 2 $量规理论的Seiberg-witten解决方案，其中有四个维度，并带有规格组$ su（n）$。一个简单的精确系列扩展，用于$ 2（n-1）$ seiberg-witten期间$ a_i（u），a_ {di}（u）$上的$ n-1 $ coulomb-coulomb-colomb-branch moduli $ u_n $是在$ \ mathbb {z} _ {z} _ {2n} $ sommem的$ symerm n of colomb and coulomb and coulomb and coulomb and coulomb and coulomb and coulomb n of coul o的coul n of coul of coul的coul n of coul o。在超几何功能方面，$ n = 2 $的早期结果以及$ n = 3 $在Appell功能方面的概括。使用这些和其他分析结果，结合数值计算，我们探索了Kähler电位$ k = \ frac {1} {2π} \ sum_i \ text {im}（\ bar a_i a_i a_ {di}）$的全局结构。有证据表明，$ k $是凸函数，在$ \ mathbb {z} _ {2n} $ - 对称点上具有唯一的最低限度。最后，我们探索了这一点附近边际稳定性的候选壁，以及它们与消失的Kähler潜力的关系。
We consider the Seiberg-Witten solution of pure $\mathcal{N} =2$ gauge theory in four dimensions, with gauge group $SU(N)$. A simple exact series expansion for the dependence of the $2 (N-1)$ Seiberg-Witten periods $a_I(u), a_{DI}(u)$ on the $N-1$ Coulomb-branch moduli $u_n$ is obtained around the $\mathbb{Z}_{2N}$-symmetric point of the Coulomb branch, where all $u_n$ vanish. This generalizes earlier results for $N=2$ in terms of hypergeometric functions, and for $N=3$ in terms of Appell functions. Using these and other analytical results, combined with numerical computations, we explore the global structure of the Kähler potential $K = \frac{1}{2π} \sum_I \text{Im}(\bar a_I a_{DI})$, which is single valued on the Coulomb branch. Evidence is presented that $K$ is a convex function, with a unique minimum at the $\mathbb{Z}_{2N}$-symmetric point. Finally, we explore candidate walls of marginal stability in the vicinity of this point, and their relation to the surface of vanishing Kähler potential.
