标题： 四维/三维约化中的$\mathcal{N}=1$对偶性的双重尺度变换 显示英文标题

标题： A double scaling for the 4d/3d reduction of $\mathcal{N}=1$ dualities

摘要： 本文我们重新考察了4维$S^1$归约的$\mathcal{N}=1$规范理论，考虑了圆周半径和由紧致化中全局对称性产生的实质量上的双重尺度。 我们讨论了这种双重尺度对具有 \$ABCD\$ 型规范代数的超对称 \$SQCD\$ 的影响。 然后我们展示如何将我们的方法转化为从4维超共形指标到3维扭球面配分函数的归约。 这使我们能够直接从四维积分恒等式推导出预期的三维对偶性关系。 这对于正交 \$SQCD\$ 的研究尤为重要，在没有双重尺度的情况下，由于圈上有效理论库仑分支中的平坦方向引起的发散，无法从4维指标推导。 此外，对于偶数维正交情形，我们得到了一个已经出现在文献中的具有二次基本磁单极超势的3维对偶性，在这里它从4维得到了解释。 显示英文摘要

摘要： In this paper we revisit the $S^1$ reduction of 4d $\mathcal{N}=1$ gauge theories, considering a double scaling on the radius of the circle and on the real masses arising from the global symmetries in the compactification. We discuss the implication of this double scaling for SQCD with gauge algebra of ABCD type. We then show how our prescription translates in the reduction of the 4d superconformal index to the 3d squashed three sphere partition function. This allows us to derive the expected integral identities for the 3d dualities directly from the four dimensional ones. This is relevant for the study of orthogonal SQCD, where the derivation from the 4d index is not possible in absence of the double scaling, because of a divergence due to a flat direction in the Coulomb branch of the effective theory on the circle. Furthermore, we obtain, for the even orthogonal case, a 3d duality with a quadratic fundamental monopole superpotential already discussed in the literature, that receives in this way an explanation from 4d.