Algorithmic universality in F-theory compactifications

Abstract

We study universality of geometric gauge sectors in the string landscape in the context of Ftheory compactifications. A finite time construction algorithm is presented for 4 3 × 2.96 × 10 755 Ftheory geometries that are connected by a network of topological transitions in a connected moduli space. High probability geometric assumptions uncover universal structures in the ensemble without explicitly constructing it. For example, non-Higgsable clusters of seven-branes with intricate gauge sectors occur with probability above 1 − 1.01 × 10 −755 , and the geometric gauge group rank is above 160 with probability .999995. In the latter case there are at least 10 E8 factors, the structure of which fixes the gauge groups on certain nearby seven-branes. Visible sectors may arise from E6 or SU (3) seven-branes, which occur in certain random samples with probability ≃ 1 200.

Connecting Dualities and Machine Learning

“…For explicit constructions of these dualities and more details see for instance. [17][18][19][20] Note that the reduced calculational complexity required to calculate the Yukawa couplings in the dual frame was mentioned in [21].…”

Systematics of aligned axions

“…12 It may be useful to reduce the basis for the lattice spanned by the t i . 13 And vice-versa, modulo those related by m ↔ −m, as the P -cube grid and N -parallelepiped domains in Σ are symmetric under the reflection about any of the P Cartesian coordinate axes.…”

“…Axions were originally proposed to solve the strong CP problem of QCD [1], and many (∼ 100) axions often arise in compactifications of string theory (see e.g. [2][3][4][5][6][7][8][9][10][11][12]). Axions can be dark matter [13][14][15][16][17], drive inflation [18][19][20][21][22][23][24] and (similar to quantized fluxes [25]) can account for the observed vacuum energy [26].…”

Kähler moduli stabilization and the propagation of decidability

“…In [1], which introduced computational complexity into studies of the string landscape, it was shown that a version of the Bousso-Polchinski model [2] for the cosmological constant is NP-complete. Furthermore, computing the scalar potential in string theory, finding its critical points, and establishing that they are metastable vacua all require solving NP-hard or co-NP-hard problems [3]. Within the last two years, machine learning was introduced into the study of string theory problems [4][5][6][7] to make progress on computationally hard problems.…”

“…For physics examples, the question can be posed of how the Universe "found" the state it is currently in if this requires solving a hard or undecidable problem. For instance, when applied to finding a small cosmological constant in an eternally inflating universe [1,3,[14][15][16], this gives a measure that differs significantly from others [17][18][19][20].…”