arXiv 2102.076962021-02hep-th

PDMATHAAB超共形$SU(N)\times SU(N)$中圆威尔逊圈的$1/N$展开

$1/N$ expansion of circular Wilson loop in $\mathcal N=2$ superconformal $SU(N)\times SU(N)$ quiver

Matteo Beccaria, Arkady A. Tseytlin

备注：: 29 pages, several pdf figures. v3: minor corrections and note added on recent exact results in arXiv:2207.11475
DOI：: 10.1007/JHEP04(2021)265

摘要：

通过对$\mathcal N=2$超共形$SU(N) \times SU(N)$理论的局部化处理，得到了BPS圆形$SU(N)$威尔逊圈$\langle\mathcal W\rangle$的期望值的非高斯双矩阵模型表示.研究了$\langle\mathcal W\rangle$的大$N$展开式在弱耦合和强耦合下的次前导$1/N^2$项.我们集中在对称的情况下，等规范耦合，这是等价的$\mathbb Z_{2}$轨道的$SU(2N)$ $\mathcal N=4$ SYM理论。这个轨道规范理论应该是${\rm AdS}_5\times (S^{5}/\mathbb Z_{2})$中IIB型超弦的对偶。我们提出了一个弦理论的论点，表明在轨道理论的$\langle\mathcal W\rangle$中的$1/N^2$项应该具有与$\mathcal N=4$ SYM情况相同的强耦合渐近性$ λ^{3/2}$。我们支持这一预测的规范理论侧的局域化矩阵模型的数值研究。我们还发现了4球上威尔逊圈期望值中的$1/N^2$项与轨道规范理论自由能的导数之间的关系。

英文摘要：

Localization approach to $\mathcal N=2$ superconformal $SU(N) \times SU(N)$ quiver theory leads to a non-Gaussian two-matrix model representation for the expectation value of BPS circular $SU(N)$ Wilson loop $\langle\mathcal W\rangle$. We study the subleading $1/N^2$ term in the large $N$ expansion of $\langle\mathcal W\rangle$ at weak and strong coupling. We concentrate on the case of the symmetric quiver with equal gauge couplings which is equivalent to the $\mathbb Z_{2}$ orbifold of the $SU(2N)$ $\mathcal N=4$ SYM theory. This orbifold gauge theory should be dual to type IIB superstring in ${\rm AdS}_5\times (S^{5}/\mathbb Z_{2})$. We present a string theory argument suggesting that the $1/N^2$ term in $\langle\mathcal W\rangle$ in the orbifold theory should have the same strong-coupling asymptotics $ λ^{3/2}$ as in the $\mathcal N=4$ SYM case. We support this prediction by a numerical study of the localization matrix model on the gauge theory side. We also find a relation between the $1/N^2$ term in the Wilson loop expectation value and the derivative of the free energy of the orbifold gauge theory on 4-sphere.

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