费米气体的三维$\mathcal{N}=4$ OPE系数
3d $\mathcal{N}=4$ OPE Coefficients from Fermi Gas
摘要：
具有秩$N$的3dPDMATHABMM规范理论的配分函数可以使用矩阵模型的超对称局域化来计算，该模型通常可以被公式化为具有非平凡单粒子哈密顿量的理想费米气体。我们展示了如何保护运营商的OPE系数对应于在这种形式主义的平均$n$体运营商的费米气体，它可以计算到所有订单在$1/N$使用WKB展开。我们使用这种形式主义来计算OPE系数的$U(N)_k\times U(N)_{-k}$ ABJM理论以及$U(N)$理论与一个伴随和$N_f$基本超多重态，这两个都有弱耦合的M-理论在大$N$和有限$k$或$N_f$制度。对于ABJM，我们再现了已知的结果，而对于$N_f$理论，我们计算了应力张量两点函数的系数$c_T$在有限$N_f$上与$1/N$相关的所有阶数。
英文摘要：
The partition function of a 3d $\mathcal{N}=4$ gauge theory with rank $N$ can be computed using supersymmetric localization in terms of a matrix model, which often can be formulated as an ideal Fermi gas with a non-trivial one-particle Hamiltonian. We show how OPE coefficients of protected operators correspond in this formalism to averages of $n$-body operators in the Fermi gas, which can be computed to all orders in $1/N$ using the WKB expansion. We use this formalism to compute OPE coefficients in the $U(N)_k\times U(N)_{-k}$ ABJM theory as well as the $U(N)$ theory with one adjoint and $N_f$ fundamental hypermultiplets, both of which have weakly coupled M-theory duals in the large $N$ and finite $k$ or $N_f$ regimes. For ABJM we reproduce known results, while for the $N_f$ theory we compute the all orders in $1/N$ dependence at finite $N_f$ for the coefficient $c_T$ of the stress tensor two-point function.
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