Statistics of F-theory flux vacua for particle physics

Abstract

Supersymmetric flux compactification of F-theory in the geometric phase yields numerous vacua, and provides an ensemble of low-energy effective theories with a variety of symmetry, matter multiplicity and Lagrangian parameters. Theoretical tools have already been developed so that we can study how the statistics of those flux vacua depend on the choice of symmetry and some of the Lagrangian parameters. In this article, we estimate the fraction of i) vacua that have a U(1) symmetry for spontaneous R-parity violation, and ii) those that realise ideas which achieve hierarchical eigenvalues of the Yukawa matrices. We also learn a lesson that the number of flux vacua is reduced very much when the unbroken U(1)Y symmetry is obtained from a non-trivial Mordell-Weil group, while it is not, when U(1)Y is in SU(5) unification. It also turns out to be likely that vacua with an approximate U(1) symmetry form a locus of accumulation points of the flux vacua distribution.

Fluxes in F-theory compactifications on genus-one fibrations

“…Our focus here will be on the gauge sector. The explicit construction of such G 4 gauge fluxes in globally defined F-theory compactifications on elliptic fibrations has been studied in great detail recently, including the works [27,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. First steps in extending these results to F-theory compactifications without a section have already been undertaken in [11].…”

Scanning the skeleton of the 4D F-theory landscape

“…(3) Classify other non-geometric information that affects the low energy physics, such as G 4 flux [16][17][18][19][20][21][22] or T-brane structures [23][24][25]. The G 4 flux has especially important impact on the physics of 4D F-theory compactifications, such as producing net chirality for matter and generating the Gukov-Vafa-Witten superpotential [26].…”

Learning non-Higgsable gauge groups in 4D F-theory

“…(3) For a given geometry, classify other non-geometric information relevant to the low energy physics, such as the G 4 flux in 4D F-theory [20][21][22][23][24][25][26].…”