GUTs and exceptional branes in F-theory — II. Experimental predictions

We discuss the period geometry and the topological string amplitudes on elliptically fibered Calabi-Yau fourfolds in toric ambient spaces. In particular, we describe a general procedure to fix integral periods. Using some elementary facts from homological mirror symmetry we then obtain Bridgelands involution and its monodromy action on the integral basis for non-singular elliptically fibered fourfolds. The full monodromy group contains a subgroup that acts as PSL(2,Z) on the Kähler modulus of the fiber and we analyze the consequences of this modularity for the genus zero and genus one amplitudes as well as the associated geometric invariants. We find holomorphic anomaly equations for the amplitudes, reflecting precisely the failure of exact PSL(2,Z) invariance that relates them to quasi-modular forms. Finally we use the integral basis of periods to study the horizontal flux superpotential and the leading order Kähler potential for the moduli fields in F-theory compactifications globally on the complex structure moduli space. For a particular example we verify attractor behaviour at the generic conifold given an aligned choice of flux which we expect to be universal. Furthermore we analyze the superpotential at the orbifold points but find no stable vacua.

Section: Quasi Modular Forms and Holomorphic Anomaly Equationsmentioning

confidence: 99%

“…Ignoring the details of how this happens for the concrete geometry under consideration it has been shown that by degenerating the fourfold in a controlled way viable phenomenological low energy particle spectra will emerge in four dimensions as was worked out in the F-theory revival starting with the papers of [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Modular amplitudes and flux-superpotentials on elliptic Calabi-Yau fourfolds

Cota¹,

Klemm

Schimannek³

2018

“…This way, F-theory can be considered as a 12-dimensional string theory compactified on a torus characterised by the above modulus τ . Algebraically, the fibration is described by a birationally equivalent complex cubic equation, the so called Weierstraß model [2][3][4]. Depending on the specific structure of its coefficients, at certain points of the fibration the torus degenerates and the fibration becomes singular.…”

Section: Jhep10(2015)041mentioning

confidence: 99%

“…If we then substitute this into the equation for the fiveplets of the GUT group, (3.8), we get an equation factorised into 3 parts, 4) which indicates that we have at least 3 distinct matter curves by the usual interpretation. The so obtained splittings of the non-trivial SU(5) representations are collected in table 2.…”

Section: Jhep10(2015)041mentioning

confidence: 99%

Phenomenological implications of a minimal F-theory GUT with discrete symmetry

Karozas

King

Leontaris

et al. 2015

Abstract:We discuss the origin of both non-Abelian discrete family symmetry and Abelian continuous family symmetry, as well as matter parity, from F-theory SUSY GUTs. We propose a minimal model based on the smallest GUT group SU(5), together with the non-Abelian family symmetry D 4 plus an Abelian family symmetry, where fluxes are responsible for doublet-triplet splitting, leading to a realistic low energy spectrum with phenomenologically acceptable quark and lepton masses and mixing. We show how a Z 2 matter parity emerging from F-theory can suppress proton decay while allowing neutronantineutron oscillations, providing a distinctive signature of the set-up.

“…Recently, F-theory has been used to obtain local models of Grand Unified Theories (GUTs), starting from the papers [30][31][32][33]. Global completions of GUT models have also been intensively studied [35][36][37][38][39][40][41][42][43], with special focus on SU(5) configurations.…”

Section: Absractmentioning

confidence: 99%

Tate form and weak coupling limits in F-theory

Esole

Savelli

2013

AbsractWe consider the weak coupling limit of F-theory in the presence of non-Abelian gauge groups implemented using the traditional ansatz coming from Tate's algorithm. We classify the types of singularities that could appear in the weak coupling limit and explain their resolution. In particular, the weak coupling limit of SU(n) gauge groups leads to an orientifold theory which suffers from conifold singulaties that do not admit a crepant resolution compatible with the orientifold involution. We present a simple resolution to this problem by introducing a new weak coupling regime that admits singularities compatible with both a crepant resolution and an orientifold symmetry. We also comment on possible applications of the new limit to model building. We finally discuss other unexpected phenomena as for example the existence of several non-equivalent directions to flow from strong to weak coupling leading to different gauge groups.