论文标题
巨型引力，Harish-Chandra积分和BPS状态在符号和正交$ \ Mathcal {n} $ = 4 sym中
Giant Gravitons, Harish-Chandra integrals, and BPS states in symplectic and orthogonal $\mathcal{N}$= 4 SYM
论文作者
论文摘要
我们发现，通过计算一类BPS Cooherent状态的规范，我们发现具有$ \ Mathcal {n} = 4 $ SYMERION的HALF BPS相关器的生成函数，具有量规组$ sp（2n）$，$ SO（2n）$，$ SO（2n）$（2n）$（2n+1）$，以及$ SO（2n）$。这些连贯的国家是由涉及Harish-Chandra积分的运营商建造的。此类操作员在大部分反de-sitter空间中将其解释为局部巨型重力。这将\ cite {Berenstein：2022srd}的分析扩展到$ sp（2n）$，$ so（2n+1）$，以及$ SO（2n）$ gauge理论。我们表明，我们可以将普通的Schur函数用作这些理论中没有交叉盖的状态部门的基础。这与这些理论的构建是$ su（2n）$理论的方向预测。我们记下了这些相干状态扩展中出现的对称函数和符号舒尔函数之间的某些关系。我们还评论了与舒伯特演算和格罗莫夫·沃特不变的一些联系，这表明Harish-Chandra积分可能扩展到了此类问题。
We find generating functions for half BPS correlators in $\mathcal{N}=4$ SYM theories with gauge groups $Sp(2N)$, $SO(2N+1)$, and $SO(2N)$ by computing the norms of a class of BPS coherent states. These coherent states are built from operators involving Harish-Chandra integrals. Such operators have an interpretation as localized giant gravitons in the bulk of anti-de-Sitter space. This extends the analysis of \cite{Berenstein:2022srd} to $Sp(2N)$, $SO(2N+1)$, and $SO(2N)$ gauge theories. We show that we may use ordinary Schur functions as a basis for the sector of states with no cross-caps in these theories. This is consistent with the construction of these theories as orientifold projections of an $SU(2N)$ theory. We make note of some relations between the symmetric functions that appear in the expansion of these coherent states and symplectic Schur functions. We also comment on some connections to Schubert calculus and Gromov-Witten invariants, which suggest that the Harish-Chandra integral may be extended to such problems.
