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A bstract The simultaneous study of top-down and bottom-up approaches to modular flavor symmetry leads necessarily to the concept of eclectic flavor groups. These are non-trivial products of modular and traditional flavor symmetries that exhibit the phenomenon of local flavor enhancement in moduli space. We develop methods to determine the eclectic flavor groups that can be consistently associated with a given traditional flavor symmetry. Applying these methods to a large family of prominent traditional flavor symmetries, we try to identify potential candidates for realistic eclectic flavor groups and show that they are relatively rare. Model building with finite modular flavor symmetries thus appears to be much more restrictive than previously thought.

A bstract Eclectic flavor groups arising from string compactifications combine the power of modular and traditional flavor symmetries to address the flavor puzzle. This top-down scheme determines the representations and modular weights of all matter fields, imposing strict constraints on the structure of the effective potential, which result in controlled corrections. We study the lepton and quark flavor phenomenology of an explicit, potentially realistic example model based on a 𝕋 6 /ℤ 3 × ℤ 3 orbifold compactification of the heterotic string that gives rise to an Ω(2) eclectic flavor symmetry. We find that the interplay of flavon alignment and the localization of the modulus in the vicinity of a symmetry-enhanced point leads to naturally protected fermion mass hierarchies, favoring normal-ordered neutrino masses arising from a see-saw mechanism. We show that our model can reproduce all observables in the lepton sector with a small number of parameters and deliver predictions for so far undetermined neutrino observables. Furthermore, we extend the fit to quarks and find that Kähler corrections are instrumental in obtaining a successful simultaneous fit to the quark and lepton sectors.

A bstract Modular symmetries naturally combine with traditional flavor symmetries and CP , giving rise to the so-called eclectic flavor symmetry. We apply this scheme to the two-dimensional ℤ 2 orbifold, which is equipped with two modular symmetries SL(2 , ℤ) T and SL(2 , ℤ) U associated with two moduli: the Kähler modulus T and the complex structure modulus U . The resulting finite modular group is (( S 3 × S 3 ) ⋊ ℤ 4 ) × ℤ 2 including mirror symmetry (that exchanges T and U ) and a generalized CP -transformation. Together with the traditional flavor symmetry ( D 8 × D 8 )/ℤ 2 , this leads to a huge eclectic flavor group with 4608 elements. At specific regions in moduli space we observe enhanced unified flavor symmetries with as many as 1152 elements for the tetrahedral shaped orbifold and T = U = exp π i 3 . This rich eclectic structure implies interesting (modular) flavor groups for particle physics models derived form string theory.

A bstract Modular flavor symmetries have been proposed as a new way to address the flavor problem. It is known that they can emerge from string compactifications. We discuss this connection in detail, and show how the congruence subgroups of SL(2 , ℤ), which underlie many modular flavor symmetries, emerge from stringy duality symmetries by orbifolding. This requires an analysis of massive states, which reveals a picture that is more intricate than the well-known situation on the torus. It involves towers of states of different quantum numbers, related by modular transformations. Members of different towers become massless at different points in moduli space. We also show that, at least in the ℤ 3 orbifold, the string selection rules can be understood as discrete remnants of continuous gauge symmetries. Non-Abelian discrete flavor symmetries arise as relics of various, relatively misaligned, continuous Abelian gauge symmetries. The generators of these U(1) symmetries give rise to CP -violating Clebsch-Gordan coefficients. If the modulus settles close to a critical point, the corresponding gauge bosons may be light enough to be searched for at future colliders.

A bstract Predictions of inflationary schemes can be influenced by the presence of extra dimensions. This could be of particular relevance for the spectrum of gravitational waves in models where the extra dimensions provide a brane-world solution to the hierarchy problem. Apart from models of large as well as exponentially warped extra dimensions, we analyze the size of tensor modes in the Linear Dilaton scheme recently revived in the discussion of the “clockwork mechanism”. The results are model dependent, significantly enhanced tensor modes on one side and a suppression on the other. In some cases we are led to a scheme of “remote inflation”, where the expansion is driven by energies at a hidden brane. In all cases where tensor modes are enhanced, the requirement of perturbativity of gravity leads to a stringent upper limit on the allowed Hubble rate during inflation.

Discrete flavor symmetries provide a promising approach to understand the flavor sector of the standard model of particle physics. Top-down (TD) explanations from string theory reveal two different types of such flavor symmetries: traditional and modular flavor symmetries that combine to the eclectic flavor group. There have been many bottom-up (BU) constructions to fit experimental data within this scheme. We compare TD and BU constructions to identify the most promising groups and try to give a unified description. Although there is some progress in joining BU and TD approaches, we point out some gaps that have to be closed with future model building.

A bstract We present a detailed analysis of the eclectic flavor structure of the two-dimensional ℤ 2 orbifold with its two unconstrained moduli T and U as well as SL(2 , ℤ) T × SL(2 , ℤ) U modular symmetry. This provides a thorough understanding of mirror symmetry as well as the R -symmetries that appear as a consequence of the automorphy factors of modular transformations. It leads to a complete picture of local flavor unification in the ( T , U ) modulus landscape. In view of applications towards the flavor structure of particle physics models, we are led to top-down constructions with high predictive power. The first reason is the very limited availability of flavor representations of twisted matter fields as well as their (fixed) modular weights. This is followed by severe restrictions from traditional and (finite) modular flavor symmetries, mirror symmetry, CP and R -symmetries on the superpotential and Kähler potential of the theory.

A bstract A previously discussed clockwork mechanism within heterotic M-theory is applied to its axion landscape. We identify a unique candidate for a QCD-axion with a decay constant in the preferred “axion window” around 10 11 GeV. It is accompanied by at least one ultra-light axion that couples predominantly to hidden sector gauge groups.

A bstract Compactifications of heterotic M-theory are shown to provide solutions to the weak- and axion-scale hierarchy problems as a consequence of warped large extra dimensions. They allow a description that is reminiscent of the so-called continuous clockwork mechanism. The models constructed here cover a new region of clockwork parameter space and exhibit unexplored spectra and couplings of Kaluza-Klein modes. Previously discussed models are outside this region of parameter space and do seem to require an ultraviolet completion other than that of perturbative higher dimensional D = 10 , 11 string- or M-theory. A 5D-supergravity description can be given for all explicitly known continuous clockwork models. The various classes of models can be distinguished through the different roles played by vector multiplets and the universal hypermultiplet in 5D-supergravity.

We use string theory constructions towards the generalisation of the supersymmetric standard model of strong and electroweak interactions. Properties of the models depend crucially on the location of fields in extradimensional compact space. This allows us to extract some generic lessons for the phenomenological properties of the low energy effective action. Within this scheme we present a compelling model based on local grand unification and mirage mediation of supersymmetry breakdown. We analyse the properties of the specific model towards its possible tests at the LHC and the complementarity to direct dark matter searches.