Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Rational F-Theory GUTs without exotics

Sven Krippendorf, Damian Kaloni Mayorga Pena, Paul-Konstantin Oehlmann, Fabian Ruehle

TL;DR

The paper tackles the problem of engineering F-theory GUTs that reproduce the MSSM spectrum without exotics while maintaining phenomenologically viable couplings. It contrasts spectral-cover constructions with models based on rational sections, showing that the former struggle to satisfy all anomaly and coupling constraints, whereas the latter, including toric and bottom-up approaches with up to two additional U(1) factors, yield promising, benchmark realizations. A systematic search identifies four viable rational-section models (two inequivalent) and two explicit benchmark examples, highlighting a half-complete multiplet structure that permits realistic Yukawas while forbidding dangerous operators, potentially via a residual matter parity. The results provide concrete guidance for global geometric embeddings and future studies of moduli stabilization and Green–Schwarz anomaly cancellation mechanisms, advancing the prospects for exotic-free, phenomenologically viable F-theory GUTs with controlled U(1) gauge sectors.

Abstract

We construct F-theory GUT models without exotic matter, leading to the MSSM matter spectrum with potential singlet extensions. The interplay of engineering explicit geometric setups, absence of four-dimensional anomalies, and realistic phenomenology of the couplings places severe constraints on the allowed local models in a given geometry. In constructions based on the spectral cover we find no model satisfying all these requirements. We then provide a survey of models with additional U(1) symmetries arising from rational sections of the elliptic fibration in toric constructions and obtain phenomenologically appealing models based on SU(5) tops. Furthermore we perform a bottom-up exploration beyond the toric section constructions discussed in the literature so far and identify benchmark models passing all our criteria, which can serve as a guideline for future geometric engineering.

Rational F-Theory GUTs without exotics

TL;DR

The paper tackles the problem of engineering F-theory GUTs that reproduce the MSSM spectrum without exotics while maintaining phenomenologically viable couplings. It contrasts spectral-cover constructions with models based on rational sections, showing that the former struggle to satisfy all anomaly and coupling constraints, whereas the latter, including toric and bottom-up approaches with up to two additional U(1) factors, yield promising, benchmark realizations. A systematic search identifies four viable rational-section models (two inequivalent) and two explicit benchmark examples, highlighting a half-complete multiplet structure that permits realistic Yukawas while forbidding dangerous operators, potentially via a residual matter parity. The results provide concrete guidance for global geometric embeddings and future studies of moduli stabilization and Green–Schwarz anomaly cancellation mechanisms, advancing the prospects for exotic-free, phenomenologically viable F-theory GUTs with controlled U(1) gauge sectors.

Abstract

We construct F-theory GUT models without exotic matter, leading to the MSSM matter spectrum with potential singlet extensions. The interplay of engineering explicit geometric setups, absence of four-dimensional anomalies, and realistic phenomenology of the couplings places severe constraints on the allowed local models in a given geometry. In constructions based on the spectral cover we find no model satisfying all these requirements. We then provide a survey of models with additional U(1) symmetries arising from rational sections of the elliptic fibration in toric constructions and obtain phenomenologically appealing models based on SU(5) tops. Furthermore we perform a bottom-up exploration beyond the toric section constructions discussed in the literature so far and identify benchmark models passing all our criteria, which can serve as a guideline for future geometric engineering.

Paper Structure

This paper contains 14 sections, 51 equations, 1 figure, 9 tables.

Table of Contents

  1. Introduction and summary of results
  2. Review of F-theory model building techniques
  3. The spectral cover
  4. Compactifications with multiple sections
  5. Explicit examples from toric constructions
  6. Fluxes and anomaly cancellation
  7. Status of spectral cover model building
  8. Systematic F-theory model building
  9. Search strategy
  10. Models from spectral cover constructions
  11. Constructions with rational sections
  12. Beyond toric sections
  13. Conclusions and outlook
  14. Second benchmark model

Figures (1)

  • Figure 1: (a) Toric diagram for the polygon $F_5$. It has the sections $\sigma_0$: $s_0=0$ (the zero section), $\sigma_1$: $s_1=0$ and $\sigma_2$: $u=0$, which are marked as red points in the diagram. (b) The polygon is set as the basis for the SU(5) top at $z=0$. The intersections of the sections with the tree of $\mathbb{P}^1$'s at $z=1$ (see the red lines in the diagram) serve to compute the charges of the fields via the Shioda map. From the intersections one can also deduce the splitting for each of the inequivalent flat SU(5) tops allowed for $F_5$: (c) 2-3, 1-4 (d) 3-2, 1-4 (e) 2-3, 2-3 and (f) 1-4, 5-0.