Instanton effects in ABJM theory from Fermi gas approach
Instanton effects in ABJM theory from Fermi gas approach
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DOI：
10.1007/jhep01(2013)158
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发表时间：
2012-11
影响因子：
5.4
通讯作者：
Yasuyuki Hatsuda;Sanefumi Moriyama;Kazumi Okuyama
中科院分区：
文献类型：
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作者：
Yasuyuki Hatsuda;Sanefumi Moriyama;Kazumi Okuyama
我们使用费米气体形式主义研究了ABJM配分函数的瞬子效应。我们分别计算了在Chern-Simons水平k= 1，2，3，4，6到N= 44，20，18，16，14下配分函数的精确值，并从这些精确结果中提取了非微扰修正.拟合得到的非微扰修正的预期形式从费米气体，我们确定未知参数。在分离了起源于巨配分函数的周期性的巨势的振荡行为和由拓扑弦理论计算的世界面瞬子贡献之后，我们成功地提出了主导D2-瞬子修正的解析表达式。与微扰结果一样，配分函数的瞬子修正也用Airy函数表示。
We study the instanton effects of the ABJM partition function using the Fermi gas formalism. We compute the exact values of the partition function at the Chern-Simons levels k= 1, 2, 3, 4, 6 up to N= 44, 20, 18, 16, 14 respectively, and extract non-perturbative corrections from these exact results. Fitting the resulting non-perturbative corrections by their expected forms from the Fermi gas, we determine unknown parameters in them. After separating the oscillating behavior of the grand potential, which originates in the periodicity of the grand partition function, and the worldsheet instanton contribution, which is computed from the topological string theory, we succeed in proposing an analytical expression for the leading D2-instanton correction. Just as the perturbative result, the instanton corrections to the partition function are expressed in terms of the Airy function.