In this note we apply mathematical results for the volume of certain symmetric spaces to the problem of counting flux vacua in simple IIB Calabi--Yau compactifications. In particular we obtain estimates for the number of flux vacua including the geometric factor related to the Calabi-Yau moduli space, in the large flux limit, for the FHSV model and some closely related models. We see that these geometric factors give rise to contributions to the counting formula that are typically not of order one and might potentially affect the counting qualitatively in some cases. We also note, for simple families of Calabi-Yau moduli spaces, an interesting dependence of the moduli space volumes on the dimension of the flux space, which in turn is governed by the Betti numbers of the Calabi-Yaus.

Miranda C. N. Cheng

Gregory W. Moore

Natalie M. Paquette

Communications in Number Theory and Physics

专注于最广泛意义上的数论在理论物理学中的应用。通过主要发表有关这两个领域之间关系和动态的研究、评论和说明性文章，为数论和理论物理学研究人员之间的交流提供一个论坛。

This journal focuses on the broad applications of number theory in theoretical physics. We primarily publish research, reviews, and expository articles concerning the relationships and dynamics between these two fields, providing a forum for communication among researchers in number theory and theoretical physics.

本期刊专注于数论在理论物理学中的广泛应用。我们主要发表关于这两个领域之间关系和动态的研究、评论和说明性文章，为数论和理论物理学研究人员之间的交流提供一个论坛。

Category	Quartile
数学	3
数学, 数学	3
数学, 应用数学	3
数学, 物理数学物理	3

Flux vacua: a voluminous recount

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Category	Quartile
PHYSICS, MATHEMATICAL	3