Orientifolding of the ABJ Fermi gas
Orientifolding of the ABJ Fermi gas
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ABJ 费米气体的定向折叠
DOI：
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发表时间：
2016
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通讯作者：
Kazumi Okuyama
中科院分区：
文献类型：
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作者：
Kazumi Okuyama
在费米气体方法中，在费米子坐标的反射下，ABJ理论的宏配分函数可以分解为奇偶部分。在某些情况下，ABJ宏配分函数的偶/奇部分等于N=5on×USpn的数学式{N}=5；\mathm{O}(N)\×\mathrm{U}\mathrm{S}\mathrm{p}\left({n}^{\prime}\right)$$理论，因此很自然地认为宏配分函数的偶/奇投影是ABJ费米气体系统的定向折叠。通过系统的WKB分析，我们确定了这种方向折叠ABJ理论的巨势微扰部分的系数。我们还找到了来自费米子坐标反射扭曲扇区的前几个“半瞬子”修正的确切形式。当k=2，4，8时，我们求出了方向折叠ABJ理论的大配分函数的闭式表达式，并证明了Arxiv：1410.7658中猜想的大配分函数之间的函数关系。
A bstractThe grand partition functions of ABJ theory can be factorized into even and odd parts under the reflection of fermion coordinate in the Fermi gas approach. In some cases, the even/odd part of ABJ grand partition function is equal to that of N=5On×USpn′$$ \mathcal{N}=5\;\mathrm{O}(n)\times \mathrm{U}\mathrm{S}\mathrm{p}\left({n}^{\prime}\right) $$ theory, hence it is natural to think of the even/odd projection of grand partition function as an orientifolding of ABJ Fermi gas system. By a systematic WKB analysis, we determine the coefficients in the perturbative part of grand potential of such orientifold ABJ theory. We also find the exact form of the first few “half-instanton” corrections coming from the twisted sector of the reflection of fermion coordinate. For the Chern-Simons level k = 2,4,8 we find closed form expressions of the grand partition functions of orientifold ABJ theory, and for k = 2, 4 we prove the functional relations among the grand partition functions conjectured in arXiv:1410.7658.