Flux vacua of the mirror octic

We study M-Theory solutions with G-flux on the Fermat sextic Calabi-Yau fourfold, focussing on the relationship between the number of stabilized complex structure moduli and the tadpole contribution of the flux. We use two alternative approaches to define the fluxes: algebraic cycles and (appropriately quantized) Griffiths residues. In both cases, we collect evidence for the non-existence of solutions which stabilize all moduli and stay within the tadpole bound.

Section: Jhep06(2024)046mentioning

confidence: 99%

More on G-flux and general hodge cycles on the Fermat sextic

Braun,

Fortin,

Garcia

et al. 2024

“…In the context of string Landscape, there have been many studies on the statistics that count flux vacua to discuss the naturalness. Considering only the Ramond-Ramond (R-R) and Neveu Schwarz-Neveu Schwarz (NS-NS) fluxes, 3 the number of "physical" vacua with a certain bound on fluxes is shown to be finite by the density method which treats fluxes as continuous variables and is reliable in large flux region [19], and many concrete examples with no approximation can be found in [20][21][22][23][24] for instance. Furthermore, the number of SUSY vacua is proved to be finite with the D3 brane charge of fluxes bounded [25].…”

Section: Introductionmentioning

confidence: 99%

Flux Landscape with enhanced symmetry not on SL(2, ℤ) elliptic points

Ishiguro,

Kai,

Kobayashi

et al. 2024

We study structures of solutions for SUSY Minkowski F-term equations on two toroidal orientifolds with h2,1 = 1. Following our previous study [1], with fixed upper bounds of a flux D3-brane charge Nflux, we obtain a whole Landscape and a distribution of degeneracies of physically-distinct solutions for each case. In contrast to our previous study, we consider a non-factorizable toroidal orientifold and its Landscape on which SL(2, ℤ) is violated into a certain congruence subgroup, as it had been known in past studies. We find that it is not the entire duality group that a complex-structure modulus U enjoys but its outer semi-direct product with a “scaling” outer automorphism group. The fundamental region is enlarged to include the |U| < 1 region. In addition, we find that high degeneracy is observed at an elliptic point, not of SL(2, Z) but of the outer automorphism group. Furthermore, ℤ2-enhanced symmetry is realized on the elliptic point. The outer automorphism group is exceptional in the sense that it is consistent with a symplectic basis transformation of background three-cycles, as opposed to the outer automorphism group of SL(2, ℤ). We also compare this result with Landscape of another factorizable toroidal orientifold.

Finiteness theorems and counting conjectures for the flux landscape

Grimm,

Monnee

2024

In this paper, we explore the string theory landscape obtained from type IIB and F-theory flux compactifications. We first give a comprehensive introduction to a number of mathematical finiteness theorems, indicate how they have been obtained, and clarify their implications for the structure of the locus of flux vacua. Subsequently, in order to address finer details of the locus of flux vacua, we propose three mathematically precise conjectures on the expected number of connected components, geometric complexity, and dimensionality of the vacuum locus. With the recent breakthroughs on the tameness of Hodge theory, we believe that they are attainable to rigorous mathematical tools and can be successfully addressed in the near future. The remainder of the paper is concerned with more technical aspects of the finiteness theorems. In particular, we investigate their local implications and explain how infinite tails of disconnected vacua approaching the boundaries of the moduli space are forbidden. To make this precise, we present new results on asymptotic expansions of Hodge inner products near arbitrary boundaries of the complex structure moduli space.