符号、曲面算子与$S$ -对偶
Symbol, Surface operators and $S$-duality
摘要：
本文研究了规范群为$SO(n)$和$Sp(2n)$的超对称Yang-Mills理论中的刚性面算符。使用这两个理论之间的映射$X_S$和$Y_S$，Wyllard明确提出了$S$ -对偶映射应如何作用于曲面算子的某些子类。进一步研究了映射$X_S$和$Y_S$，并利用一种简便的技巧简化了刚性曲面算子符号不变量的构造.通过一致性检验，我们恢复和扩展了Wyllard提出的$S$ -对偶映射.我们发现了与$S$ -对偶相关的刚性曲面算子的新子类。我们试图解释$S$ -对偶映射的例外。我们还讨论了$B_n/C_n$理论中使用的技术到$D_n$理论的扩展。
英文摘要：
We study rigid surface operators in the $N=4$ supersymmetric Yang-Mills theories with gauge groups $SO(n)$ and $Sp(2n)$. Using maps $X_S$ and $Y_S$ between these two theories, Wyllard made explicit proposals for how the $S$-duality map should act on certain subclasses of surface operators. We study the maps $X_S$ and $Y_S$ further and simplify the construction of symbol invariant of rigid surface operators by a convenient trick. By consistency checks, we recover and extend the $S$-duality maps proposed by Wyllard. We find new subclasses of rigid surface operators related by $S$-duality. We try to explain the exceptions of $S$-duality maps. We also discuss the extension of the techniques used in the $B_n/C_n$ theories to the $D_n$ theories.
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