论文标题
s偶性和Q-MAP空间的通用异构体
S-duality and the universal isometries of q-map spaces
论文作者
论文摘要
树级Q-MAP分配给Dimension $ N-1 \ GEQ 0 $的投影特殊真实（PSR）歧管，QuaternionicKähler（QK）dimension $ 4N+4 $。众所周知，由此产生的QK歧管允许$（3N+5）$ - 尺寸的异构体（即独立于PSR歧管的选择）。另一方面，在IIB型字符串理论的Calabi-Yau压缩的背景下，经典的超级模量模量空间公制是树级Q-Map空间的一个实例，从物理学文献中知道，这样一个度量标准的$ \ \ \ \ \ \ \ m m mathrm {slrm {slrm {slbb}（2，\ mathbb {r}） $ \ mathrm {sl}（2，\ mathbb {z}）$ s-duality对称对称性。我们提供了一个纯粹的数学证明，任何树级Q-MAP空间都承认了$ \ mathrm {sl}（2，\ mathbb {r}）$ iSometries $ action $ action y iSometries，将以前的偶像构态组扩大到$（3N+6）$ -6）$ dimensional $ g $ $ g $。作为本分析的一部分，我们描述了$（3N+5）$ - 尺寸子组如何与$ \ mathrm {sl}（2，\ mathbb {r}）$ - action相互作用，并找到一个$ g $的$ g $的一个正常子组。通过对单峰组的晶格进行商，我们可以在带有有限体积的纤维的投影特殊的真实歧管上获得QuaternionicKähler歧管纤维，并计算该体积作为底座的函数。我们此外，还提供了有关物理学文献的数学处理，涉及树级Q-MAP空间的扭曲器空间以及$（3N+6）$ - 尺寸的通用异构体与扭曲器空间的圆锥形升力。
The tree-level q-map assigns to a projective special real (PSR) manifold of dimension $n-1\geq 0$, a quaternionic Kähler (QK) manifold of dimension $4n+4$. It is known that the resulting QK manifold admits a $(3n+5)$-dimensional universal group of isometries (i.e. independently of the choice of PSR manifold). On the other hand, in the context of Calabi-Yau compactifications of type IIB string theory, the classical hypermultiplet moduli space metric is an instance of a tree-level q-map space, and it is known from the physics literature that such a metric has an $\mathrm{SL}(2,\mathbb{R})$ group of isometries related to the $\mathrm{SL}(2,\mathbb{Z})$ S-duality symmetry of the full 10d theory. We present a purely mathematical proof that any tree-level q-map space admits such an $\mathrm{SL}(2,\mathbb{R})$ action by isometries, enlarging the previous universal group of isometries to a $(3n+6)$-dimensional group $G$. As part of this analysis, we describe how the $(3n+5)$-dimensional subgroup interacts with the $\mathrm{SL}(2,\mathbb{R})$-action, and find a codimension one normal subgroup of $G$ that is unimodular. By taking a quotient with respect to a lattice in the unimodular group, we obtain a quaternionic Kähler manifold fibering over a projective special real manifold with fibers of finite volume, and compute the volume as a function of the base. We furthermore provide a mathematical treatment of results from the physics literature concerning the twistor space of the tree-level q-map space and the holomorphic lift of the $(3n+6)$-dimensional group of universal isometries to the twistor space.
