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arXiv 1603.01290hep-th
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用Calabi-Yau流形的拓扑数据读出非几何标量势

Reading off the non-geometric scalar potentials via topological data of the Calabi Yau manifolds

Pramod Shukla

备注：
version 3: 46 pages; slight rewording in the title, improved overall presentation with lengthy eqns. shifted to two newly added appendices B and D, one more appendix A listing the symbols and notations added; to appear in PRD
发表信息：
Phys. Rev. D 94, 086003 (2016)
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摘要：

在研究IIB型非几何通量紧致化的4D有效势的背景下，本文有两个目标。首先，我们提出了一个由通量超势产生的树级非几何标量势的模不变辛重排，该超势包括非几何通量$(Q, P)$的S-对偶对，标准NS-NS和RR三形式通量$(F_3, H_3)$以及几何通量（$ω$）。这“辛公式”是有效的任意数量的凯勒模量，和复杂的结构模量是隐含编码在一组辛矩阵。在第二部分中，我们进一步明确地重写所有的辛成分的saxionic和axionic组件的复杂结构模。这同样导致了通用标量势的紧凑形式被明确地写在所有实模/轴子方面。此外，标势的最终形式只需要紧化（CY）三重及其镜像的某些拓扑数据（如Hodge数和三重交数）的知识.最后，我们证明了同样的等价于说，对于一个给定的具体例子，标量势的各个部分可以直接从我们的一般建议中读出，而不需要从凯勒势和超势开始。

英文摘要：

In the context of studying the 4D effective potentials of type IIB non-geometric flux compactifications, this article has a twofold goal. First, we present a modular invariant symplectic rearrangement of the tree level non-geometric scalar potential arising from a flux superpotential which includes the S-dual pairs of non-geometric fluxes $(Q, P)$, the standard NS-NS and RR three-form fluxes $(F_3, H_3)$ and the geometric flux ($ω$). This `symplectic formulation' is valid for arbitrary numbers of Kähler moduli, and the complex structure moduli which are implicitly encoded in a set of symplectic matrices. In the second part, we further explicitly rewrite all the symplectic ingredients in terms of saxionic and axionic components of the complex structure moduli. The same leads to a compact form of the generic scalar potential being explicitly written out in terms of all the real moduli/axions. Moreover, the final form of the scalar potential needs only the knowledge of some topological data (such as hodge numbers and the triple intersection numbers) of the compactifying (CY) threefolds and their respective mirrors. Finally, we demonstrate how the same is equivalent to say that, for a given concrete example, various pieces of the scalar potential can be directly read off from our generic proposal, without the need of starting from the Kähler- and super-potentials.

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