TY - JOUR

T1 - Flux vacua

T2 - a voluminous recount

AU - Cheng, Miranda C.N.

AU - Moore, Gregory W.

AU - Paquette, Natalie M.

N1 - Funding Information:
#640159 and NWO vidi grant (number 016.Vidi.189.182). The work of N.M.P is supported by a Sherman Fairchild Postdoctoral Fellowship. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DESC0011632. We thank the Isaac Newton Institute for hospitality during the conception of this project. Part of this work was performed at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611. N.M.P also thanks Perimeter Institute for hospitality while this work was being completed. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Research and Innovation.
Funding Information:
We thank T. Grimm, S. Kachru, D. Morrison and W. Taylor for useful conversations. The work of M.C. is supported by ERC starting grant H2020
Publisher Copyright:
© 2022, Communications in Number Theory and Physics. All Rights Reserved.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

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U2 - 10.4310/CNTP.2022.v16.n4.a4

DO - 10.4310/CNTP.2022.v16.n4.a4

M3 - Article

AN - SCOPUS:85140732343

SN - 1931-4523

VL - 16

SP - 761

EP - 800

JO - Communications in Number Theory and Physics

JF - Communications in Number Theory and Physics

IS - 4

ER -