AI 中文总结
本文研究带通量的IIA型弦论在Spin(7)流形上的二维紧致化，推导相关超引力，发现未扭曲形状模式可经典稳定，且大欧拉示性数的Spin(7)流形可抑制α'修正。
AI 中文摘要
我们启动对II型弦论在具有通量和源的里奇平坦空间上紧致化到二维的系统研究，推导此类紧致化的普适约束，随后发展带体通量的Spin(7)完整空间上的IIA型紧致化，其 tadpole 由OF1-平面对消。我们针对环面Spin(7)轨形推导所得的二维$\boldsymbol{\textit{N}=(1,1)}$超引力，并将度规和普适部分几何扩展到一般紧致Spin(7)流形。在候选超对称闵可夫斯基真空中，所有未扭曲形状模式均出现在通量标量势中，原则上可经典稳定；但在一个显式环面轨形例子中，通量量子化结合 tadpole 边界可能完全阻碍仅存在于未扭曲部分的候选真空。弦单位下的弦框架体积受限于$\boldsymbol{7\boldsymbol{\textit{\text{χ}}}/192}$，因此抑制$\boldsymbol{\textit{α}'}$修正需要具有大欧拉示性数的Spin(7)流形。
英文摘要
We initiate a systematic study of compactifications of type II string theory to two dimensions on Ricci-flat spaces with fluxes and sources. We derive universal constraints on such compactifications, and then develop type IIA compactifications on $\mathrm{Spin}(7)$-holonomy spaces with bulk fluxes whose tadpole is cancelled by $\mathrm{OF1}$-planes. We derive the resulting two-dimensional $\mathcal N=(1,1)$ supergravity for a toroidal $\mathrm{Spin}(7)$ orbifold, and we extend the metric and universal sectors geometrically to general compact $\mathrm{Spin}(7)$ manifolds. In candidate supersymmetric Minkowski vacua, all untwisted shape modes appear in the flux scalar potential and can in principle be classically stabilised. However, in an explicit toroidal orbifold example flux quantisation together with the tadpole bound may obstruct the existence of candidate vacua supported entirely within the untwisted sector. The string-frame volume in string units is bounded by $7χ/192$, so suppressing $α'$ corrections requires $\mathrm{Spin}(7)$ manifolds with large Euler characteristic.
Comments47 pages
