We present a compact formula for the supersymmetric partition function of 2d N= (2, 2), 3d N= 2 and 4d N= 1 gauge theories on ∑_g × T~n with partial topological twist on ∑_g, where E_g is a Riemann surface of arbitrary genus and T~n is a torus with n= 0,1,2, respectively. In 2d we also include certain local operator insertions, and in 3d we include Wilson line operator insertions along S~1. For genus g= 1, the formula computes the Witten index. We present a few simple Abelian and non-Abelian examples, including new tests of non-perturbative dualities. We also show that the large N partition function of ABJM theory on Eg × S~1 reproduces the Bekenstein-Hawking entropy of BPS black holes in AdS_4 whose horizon has ∑_g topology.
展开▼
机译：我们呈现了一个紧凑的公式，用于2d n =（2,2），3d n = 2和4d n = 1尺寸σ_g上的σ_gσ_g×g×t = n的尺寸理论的尺寸序列的公式，其中e_g是a riemann表面的任意属和t〜n是具有n = 0.1,2的圆环。在2D中，我们还包括某些本地操作员插入，并且在3D中，我们包括Wilson Line操作员沿S〜1插入。对于G = 1，该公式计算Witten指数。我们展示了一些简单的雅典和非雅典之例，包括非扰动二元的新测试。我们还表明，ABJM理论的大n个分区功能在例如×S〜1上再现了ADS_4中BPS黑洞的Bekenstein-Hapking熵，其地平线具有Σ_G拓扑。
展开▼
