II型弦论导出的尺度分离AdS$_2$通量真空

中文摘要 AI 辅助

受能否将紧化的内部尺度与外部曲率尺度参数化解耦、以及能否通过全息方法探测这类真空的问题驱动，我们构建了首个具有参数化尺度分离的AdS$_2$通量真空。我们在弥散的时空填充O1/O5-平面或O4/O8-平面，以及NSNS和RR通量存在的情况下，将II型弦论紧化在G₂结构轨形乘一个圆上。我们推导了二维dilaton-引力有效理论，并展示了多族真空：在IIB型中，无界的F₅和H₇通量提供参数化控制；在IIA型中，无界的F₄、F₈和H₇通量提供参数化控制。对于大量子通量，弦耦合参数化变弱，所有内部整体半径在弦单位下参数化变大，卡鲁扎-克莱因尺度与AdS₂曲率尺度分离。我们分析了十维Killing旋量方程，识别出二维中保持𝒩=(1,1)超对称的参数化分支。我们解释了几何上尺度分离的AdS₂真空如何与近期关于具有扩展超对称理论中尺度分离的无-go定理兼容。最后，我们讨论了各类T-对偶，导出了IIB型和IIA型在G₂结构空间乘圆、SU(3)结构空间乘二维环面上的其他紧化。

英文摘要

Motivated by the question of whether the internal scales of a compactification can be parametrically decoupled from the external curvature scale, and by the possibility of probing such vacua holographically, we construct the first AdS$_2$ flux vacua with parametric scale separation. We compactify type II string theory on a $G_2$ structure orbifold times a circle in the presence of smeared spacetime-filling O1/O5-planes or O4/O8-planes, together with NSNS and RR fluxes. We derive the two-dimensional dilaton-gravity effective theory and exhibit families of vacua in which unbounded $F_5$ and $H_7$ fluxes provide parametric control in type IIB, while unbounded $F_4$, $F_8$, and $H_7$ fluxes provide parametric control in type IIA. For large flux quanta, the string coupling becomes parametrically weak, all internal bulk radii become parametrically large in string units, and the Kaluza--Klein scale separates from the $\mathrm{AdS}_2$ curvature scale. We analyze the ten-dimensional Killing-spinor equations and identify parametric branches preserving $\mathcal N=(1,1)$ supersymmetry in two dimensions. We explain how our geometrically scale-separated AdS$_2$ vacua are compatible with a recent no-go theorem for scale separation in theories with extended supersymmetry. Finally, we discuss various T-dualities leading to other type IIB and type IIA compactifications on $G_2$ structure spaces times a circle and $SU(3)$ structure spaces times a two-torus.

发表机构

• Lehigh University（利哈伊大学）

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44 pages