论文标题
五维量规理论，具有负耦合的球
Five-dimensional gauge theories on spheres with negative couplings
论文作者
论文摘要
我们认为在$ s^5 $上的超对称规格理论，其大型$ n $限制的负轴耦合。使用本地化，我们计算分区的功能，并表明纯$ {\ Mathrm {su}}（n）$量学理论降至$ {\ m atrm {su}}}（n/2）_ {+n/2）_ {+n/2} \ time {\ mathrm {su}}（2）$ Chern-simons量规理论，因为逆't Hooft耦合被以$ n $偶数为$ n $。 $ {\ mathrm {su}}（n/2）_ {\ pm n/2} $的Yang-mills耦合是正的且无限的，而在$ {\ mathrm {surm {su}}}}（2）$上的yang-millms _ {\ pm n/2} $是零的。我们还表明，奇数$ n $ case的行为有所不同。然后，我们研究$ {\ mathrm {su}}（n/2）_ {n/2} $ pure chern-simons理论。尽管仅在数值上找到特征值密度，但我们表明其宽度等于倒数球半径的$ 1 $，这使我们能够在打开Yang-Mills项时找到对自由能的领先校正。然后，我们考虑具有反对称超对称性的$ {\ mathrm {usp}}（2n）$理论，$ n_f <8 $基本超级甲基元素并进行了类似的分析。在此过程中，我们表明，对分区功能的一单位贡献贡献在大$ n $限制中的$ {\ mathrm {su}}}（n）$理论的负耦合时仍被指数抑制。
We consider supersymmetric gauge theories on $S^5$ with a negative Yang-Mills coupling in their large $N$ limits. Using localization we compute the partition functions and show that the pure ${\mathrm{SU}}(N)$ gauge theory descends to an ${\mathrm{SU}}(N/2)_{+N/2}\times {\mathrm{SU}}(N/2)_{-N/2}\times {\mathrm{SU}}(2)$ Chern-Simons gauge theory as the inverse 't Hooft coupling is taken to negative infinity for $N$ even. The Yang-Mills coupling of the ${\mathrm{SU}}(N/2)_{\pm N/2}$ is positive and infinite, while that on the ${\mathrm{SU}}(2)$ goes to zero. We also show that the odd $N$ case has somewhat different behavior. We then study the ${\mathrm{SU}}(N/2)_{N/2}$ pure Chern-Simons theory. While the eigenvalue density is only found numerically, we show that its width equals $1$ in units of the inverse sphere radius, which allows us to find the leading correction to the free energy when turning on the Yang-Mills term. We then consider ${\mathrm{USp}}(2N)$ theories with an antisymmetric hypermultiplet and $N_f<8$ fundamental hypermultiplets and carry out a similar analysis. Along the way we show that the one-instanton contribution to the partition function remains exponentially suppressed at negative coupling for the ${\mathrm{SU}}(N)$ theories in the large $N$ limit.
