论文标题
3D $ \ MATHCAL {N} = 4 $ FEMI GAS的OPE系数
3d $\mathcal{N}=4$ OPE Coefficients from Fermi Gas
论文作者
论文摘要
3D $ \ MATHCAL {n} = 4 $ gauge理论的分区函数可以使用矩阵模型来计算级别的$ n $，而矩阵模型通常可以作为理想的费米气体配方，具有非平凡的单颗粒汉密尔顿。我们展示了受保护操作员的OPE系数在这种形式主义中与费米气体中$ n $ body运算符的平均值相对应，可以使用WKB扩展将其计算为$ 1/n $的所有订单。我们使用这种形式主义来计算$ u（n）_k \ times u（times u（n）_ { - k} $ abjm理论以及带有一个伴随的$ u（n）$理论的$ n_f $ n_f $ cottalmental hypermultiplets，这两个$ n $ n $ n $ n $ n $ n $ $ n nite $ n $ k $ n nite $ n $或finite $ n $ k $ n $ n $ n $ n $ k $ n $ k $或finite，对于ABJM，我们复制已知结果，而对于$ n_f $理论，我们计算出$ 1/n $依赖的所有订单，以有限的$ n_f $，用于压力张量的系数$ c_t $两点功能。
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.
