Scalar potential bounds on one-parameter Calabi-Yau threefolds with fluxes
Abstract
We study the refined de Sitter conjecture (RdSC), the Trans-Planckian Censorship Conjecture (TCC) and the species scale Λs in the multifield flux potential of type IIB string theory compactified on one-parameter Calabi--Yau threefolds. The scalar potential depends on the axio-dilaton and on the single complex-structure modulus, and is no-scale along the Kähler directions. Restricting to h2,1=1 allows us to work with the exact periods obtained from the Picard--Fuchs equations rather than with their large-complex-structure expansion, and therefore to probe the conifold region. For the mirror quintic, (h2,1,h1,1)=(1,101), we scan 200 flux configurations and find unstable extrema in 96% of the cases, with c'=0.18. Once the Kähler runaway is taken into account, the no-scale structure fixes the logarithmic slope of the potential at every critical point to the universal value √6, so that the first RdSC condition is satisfied throughout. Statistically, the complex structure is the heavier sector and the axio-dilaton dominates the unstable directions. For the TCC we obtain analytic results valid for the whole class of one-parameter models: the slope approaches the universal value $2$ at large complex structure, diverges at the conifold, and equals exactly √2 in the axio-dilaton directions, where the leading potential takes a single SL(2)-covariant form, as the multifield evolutions confirm numerically. The TCC further translates into a lower bound on the compactification volume, v>v0∼ eN, controlled by the number of e-folds. Finally, the field displacements along our trajectories are compatible with the species-scale field-range bound, and restoring the volume dependence of Λs shows that V≲3Λs2 is implied by the TCC volume bound, which is thus the genuine constraint on these models.
Related
- Chern bounds and tangent geometry of polarized Calabi-Yau threefolds
- The Tate Conjecture for Ordinary Calabi-Yau Threefolds
- Integral Bott--Chern cohomology of Generalized Calabi--Eckmann threefolds
- Degeneration of Calabi-Yau threefolds with Galois action induced by modular form of weight 3
- Stability conditions on Calabi-Yau threefolds of type K
BibTeX
@misc{bizet2026scalar,
title = {{Scalar potential bounds on one-parameter Calabi-Yau threefolds with fluxes}},
author = {Nana Geraldine Cabo Bizet and José de J. Pérez Lona},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04858},
eprint = {2610.04858},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04858},
}
RIS
TY - UNPB
TI - Scalar potential bounds on one-parameter Calabi-Yau threefolds with fluxes
AU - Nana Geraldine Cabo Bizet
AU - José de J. Pérez Lona
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.04858
UR - https://arxiv.org/abs/2610.04858
AB - We study the refined de Sitter conjecture (RdSC), the Trans-Planckian Censorship Conjecture (TCC) and the species scale Λ_s in the multifield flux potential of type IIB string theory compactified on one-parameter Calabi--Yau threefolds. The scalar potential depends on the axio-dilaton and on the single complex-structure modulus, and is no-scale along the Kähler directions. Restricting to h^2,1=1 allows us to work with the exact periods obtained from the Picard--Fuchs equations rather than with their large-complex-structure expansion, and therefore to probe the conifold region. For the mirror quintic, (h^2,1,h^1,1)=(1,101), we scan 200 flux configurations and find unstable extrema in 96% of the cases, with c'=0.18. Once the Kähler runaway is taken into account, the no-scale structure fixes the logarithmic slope of the potential at every critical point to the universal value √6, so that the first RdSC condition is satisfied throughout. Statistically, the complex structure is the heavier sector and the axio-dilaton dominates the unstable directions. For the TCC we obtain analytic results valid for the whole class of one-parameter models: the slope approaches the universal value $2$ at large complex structure, diverges at the conifold, and equals exactly √2 in the axio-dilaton directions, where the leading potential takes a single SL(2)-covariant form, as the multifield evolutions confirm numerically. The TCC further translates into a lower bound on the compactification volume, v>v_0∼ e^N, controlled by the number of e-folds. Finally, the field displacements along our trajectories are compatible with the species-scale field-range bound, and restoring the volume dependence of Λ_s shows that V≲3Λ_s^2 is implied by the TCC volume bound, which is thus the genuine constraint on these models.
ER -