IIB型弦理论中的全息系综
Holographic Ensembles in Type IIB
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中文总结 AI 辅助
该研究探讨IIB型弦理论中全息系综的选择机制，通过计算体配分函数的单圈近似，证明其可匹配Schur指标对应的正则或巨正则边界配分函数。
中文摘要 AI 辅助
我们研究IIB型弦理论在Schur扭曲AdS₅×S⁵背景下的全息系综及其对应的边界配分函数：𝒩=4超对称杨-米尔斯理论（SYM）的Schur指标。在超引力极限下，两种自然的系综分别是S⁵上固定通量的系综，对应边界理论具有固定秩；或是其共轭选择，即AdS₅边界上固定势的系综，对应边界上具有固定化学势的巨正则系综。由于IIB型超引力中五形式的自对偶性质，系综的选择并非体标准作用量中体现，而是通过额外拓扑项的耦合体现。我们计算了单圈近似下的体配分函数，包括卡鲁扎-克莱因行列式和系综变更求和的测度，结果表明，根据该拓扑项的符号，体配分函数可匹配正则系综或巨正则系综下的微扰边界配分函数。
英文摘要
We study holographic ensembles in type IIB string theory on the Schur twisted AdS$_5 \times S^5$ background, and its corresponding boundary partition function: the Schur index of $\mathcal{N}=4$ SYM. In the supergravity limit the two natural ensembles are either at fixed flux on $S^5$, corresponding to a boundary theory at fixed rank, or its conjugate choice of fixed potential on the boundary of AdS$_5$, corresponding on the boundary to a grand canonical ensemble of theories at fixed chemical potential. Due to the self-dual nature of the five-form in type IIB supergravity the choice of ensembles is not seen in the standard bulk action, but rather by the coupling of an additional topological term. We compute the bulk partition function to one loop, including the Kaluza-Klein determinant and the measure of the ensemble-changing sum, and show that depending on the sign of this topological term it matches the perturbative boundary partition function in either the canonical or the grand canonical ensemble.
