论文标题
$ i \ times t^2 $，椭圆属和双重界限的超对称指数
Supersymmetric indices on $I \times T^2$, elliptic genera and dualities with boundaries
论文作者
论文摘要
我们研究三维$ \ MATHCAL {N} = 2 $ supersymmetric They在$ i \ i \ times m_2 $上带有2D $ \ MATHCAL {n} =（0,2）$在边界$ \ partial（i \ times m_2）= m_2 \ sqccup m_2 $，$ m_2 $，$ m_2 $，我们在$ i \ i \ times t^2 $上介绍了三维$ \ mathcal {n} = 2 $理论的超对称索引，该夫妇是在两个边界上的2d $ \ mathcal {n} =（0,2）$的椭圆形属的椭圆形属。我们根据超对称本地化评估$ i \ times t^2 $索引，并在$ i \ times m_2 $上研究二元性。我们考虑将$ i \ times t^2 $降低至$ i \ i \ times s^1 $，并获得2d $ \ mathcal {n} =（2,2）$ supersymmetricric in $ i \ i \ times s^1 $的本地化公式。我们说明了基于测量线性Sigma模型的开放字符串witten索引的计算。威尔逊回路在$ i \ times s^1 $上的相关函数在几何阶段与欧拉配对一致，并且在Landau-Ginzburg阶段中GEPNER模型的B型边界状态的缸幅度也一致。
We study three dimensional $\mathcal{N}=2$ supersymmetric theories on $I \times M_2$ with 2d $\mathcal{N}=(0,2)$ boundary conditions at the boundaries $\partial (I \times M_2)=M_2 \sqcup M_2$, where $M_2=\mathbb{C}$ or $ T^2$. We introduce supersymmetric indices of three dimensional $\mathcal{N}=2$ theories on $I \times T^2$ that couple to elliptic genera of 2d $\mathcal{N}=(0,2)$ theories at the two boundaries. We evaluate the $I \times T^2$ indices in terms of supersymmetric localization and study dualities on the $I \times M_2$. We consider the dimensional reduction of $I \times T^2$ to $I \times S^1$ and obtain the localization formula of 2d $\mathcal{N}=(2,2)$ supersymmetric indices on $I \times S^1$. We illustrate computations of open string Witten indices based on gauged linear sigma models. Correlation functions of Wilson loops on $I \times S^1$ agree with Euler pairings in the geometric phase and also agree with cylinder amplitudes for B-type boundary states of Gepner models in the Landau-Ginzburg phase.
