We consider two-dimensional $\mathcal{N}=(2,2)$ Yang-Mills theory with gauge group $\mathrm{SU}(N)$ in Euclidean signature compactified on a torus with thermal fermion boundary conditions imposed on one cycle. We perform nonperturbative lattice analyses of this theory for large $12\le N\le 20$. Although no holographic dual of this theory is yet known, we conduct numerical investigations to check for features similar to the two-dimensional $\mathcal{N}=(8,8)$ Yang–Mills theory, which has a well-defined gravity dual. We perform lattice field theory calculations to determine the phase diagram, observing a spatial deconfinement transition similar to the maximally supersymmetric case. However, the transition does not continue to low temperature, implying the absence of a topology-changing transition between black hole geometries in any holographic dual for this four-supercharge theory.

中文翻译：

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二维N=(2, 2)超Yang-Mills理论的非微扰相图


我们考虑二维 $\mathcal{N}=(2,2)$ 具有规范群的杨-米尔斯理论 $\mathrm{SU}(N)$ 在一个循环上施加热费米子边界条件的环面上的欧几里得签名被致密化。我们对该理论进行了大范围的非微扰晶格分析 $12\le N\le 20$ 。尽管尚不知道该理论的全息对偶，但我们进行了数值研究以检查类似于二维的特征 $\mathcal{N}=(8,8)$ 杨-米尔斯理论，具有明确定义的引力对偶。我们进行晶格场理论计算以确定相图，观察类似于最大超对称情况的空间解除限制转变。然而，这种转变不会持续到低温，这意味着在这种四增压理论的任何全息对偶中，黑洞几何形状之间不存在拓扑变化的转变。