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Abstract We study a flavor model with A 4 symmetry which originates from S 4 modular group. In S 4 symmetry, Z 2 subgroup can be anomalous, and then S 4 can be violated to A 4. Starting with a S 4 symmetric Lagrangian at the tree level, the Lagrangian at the quantum level has only A 4 symmetry when Z 2 in S 4 is anomalous. We obtain modular forms of two singlets and a triplet representations of A 4 by decomposing S 4 modular forms into A 4 representations. We propose a new A 4 flavor model of leptons by using those A 4 modular forms. We succeed in constructing a viable neutrino mass matrix through the Weinberg operator for both normal hierarchy (NH) and inverted hierarchy (IH) of neutrino masses. Our predictions of the CP violating Dirac phase δ CP and the mixing sin2 θ 23 depend on the sum of neutrino masses for NH.

A bstract In this paper, we propose a new Swampland condition, the Trans-Planckian Censorship Conjecture (TCC), based on the idea that in a consistent quantum theory of gravity sub-Planckian quantum fluctuations should remain quantum and never become larger than the Hubble horizon and freeze in an expanding universe. Applied to the case of scalar fields, it leads to conditions that are similar to the refined dS Swampland conjecture. For large field ranges, TCC is stronger than the dS Swampland conjecture but it is weaker for small field ranges. In particular for asymptotic regions of field space, TCC leads to a bound V ′ ≥ 2 d − 1 d − 2 V , which is consistent with all known cases in string theory. Like the dS Swampland conjecture, the TCC forbids long-lived meta-stable dS spaces, but it does allow sufficiently short-lived ones.

A bstract We discuss fermion mass hierarchies within modular invariant flavour models. We analyse the neighbourhood of the self-dual point τ = i , where modular invariant theories possess a residual Z 4 invariance. In this region the breaking of Z 4 can be fully described by the spurion ϵ ≈ τ − i , that flips its sign under Z 4 . Degeneracies or vanishing eigenvalues of fermion mass matrices, forced by the Z 4 symmetry at τ = i , are removed by slightly deviating from the self-dual point. Relevant mass ratios are controlled by powers of |ϵ| . We present examples where this mechanism is a key ingredient to successfully implement an hierarchical spectrum in the lepton sector, even in the presence of a non-minimal Kähler potential.

A bstract We study the phenomenological implications of the modular symmetry Γ(3) ≃ A 4 of lepton flavors facing recent experimental data of neutrino oscillations. The mass matrices of neutrinos and charged leptons are essentially given by fixing the expectation value of modulus τ , which is the only source of modular invariance breaking. We introduce no flavons in contrast with the conventional flavor models with A 4 symmetry. We classify our neutrino models along with the type I seesaw model, the Weinberg operator model and the Dirac neutrino model. In the normal hierarchy of neutrino masses, the seesaw model is available by taking account of recent experimental data of neutrino oscillations and the cosmological bound of sum of neutrino masses. The predicted sin 2 θ 23 is restricted to be larger than 0 . 54 and δ CP = ±(50°-180°). Since the correlation of sin 2 θ 23 and δ CP is sharp, the prediction is testable in the future. It is remarkable that the effective mass m ee of the neutrinoless double beta decay is around 22 meV while the sum of neutrino masses is predicted to be 145 meV. On the other hand, for the inverted hierarchy of neutrino masses, only the Dirac neutrino model is consistent with the experimental data.

A bstract We investigate the swampland distance conjecture (SDC) in the complex moduli space of type II compactifications on one-parameter Calabi-Yau threefolds. This class of manifolds contains hundreds of examples and, in particular, a subset of 14 geometries with hypergeometric differential Picard-Fuchs operators. Of the four principal types of singularities that can occur — specified by their limiting mixed Hodge structure — only the K -points and the large radius points (or more generally the M -points) are at infinite distance and therefore of interest to the SDC. We argue that the conjecture is fulfilled at the K - and the M -points, including models with several M -points, using explicit calculations in hypergeometric models which contain typical examples of all these degenerations. Together with previous work on the large radius points, this suggests that the SDC is indeed fulfilled for one-parameter Calabi-Yau spaces.

A bstract A low-energy effective theory is said to be in the swampland if it does not have any consistent UV completion inside a theory of quantum gravity. The natural question is if the standard model of particle physics, possibly with some minimal extensions, are in the swampland — we are in trouble if the answer to this question is yes. We discuss this question in view of the recent swampland conjectures. We prove a no-go theorem concerning the modification of the Higgs sector. Moreover, we find that QCD axion is incompatible with the recent swampland conjectures, unless some sophisticated possibilities are considered. We discuss the implications of this result for spontaneous breaking of CP symmetry. We comment on dynamical supersymmetry breaking as well as the issue of multi-valuedness of the potential. We also propose a refinement of the de Sitter swampland conjecture.

A bstract The recently proposed relaxion models require extremely large trans-Planckian axion excursions as well as a potential explicitly violating the axion shift symmetry. The latter property is however inconsistent with the axion periodicity, which corresponds to a gauged discrete shift symmetry. A way to make things consistent is to use monodromy, i.e. both the axion and the potential parameters transform under the discrete shift symmetry. The structure is better described in terms of a 3-form field C μνρ coupling to the SM Higgs through its field strength F 4 . The 4-form also couples linearly to the relaxion, in the Kaloper-Sorbo fashion. The extremely small relaxion-Higgs coupling arises in a see-saw fashion as g ≃ F 4 /f , with f being the axion decay constant. We discuss constraints on this type of constructions from membrane nucleation and the Weak Gravity Conjecture. The latter requires the existence of membranes, whose too fast nucleation could in principle drive the theory out of control, unless the cut-off scale is lowered. This allows to rule out the simplest models with the QCD axion as relaxion candidate on purely theoretical grounds. We also discuss possible avenues to embed this structure into string theory.

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 We examine a common origin of four-dimensional flavor, CP, and U(1) R symmetries in the context of heterotic string theory with standard embedding. We find that flavor and U(1) R symmetries are unified into the Sp(2 h + 2 , ℂ) modular symmetries of Calabi-Yau threefolds with h being the number of moduli fields. Together with the ℤ 2 CP CP symmetry, they are enhanced to G Sp(2 h + 2 , ℂ) ≃ Sp(2 h + 2 , ℂ) ⋊ ℤ 2 CP generalized symplectic modular symmetry. We exemplify the S 3 , S 4 , T ′ , S 9 non-Abelian flavor symmetries on explicit toroidal orbifolds with and without resolutions and ℤ 2 , S 4 flavor symmetries on three-parameter examples of Calabi-Yau threefolds. Thus, non-trivial flavor symmetries appear in not only the exact orbifold limit but also a certain class of Calabi-Yau three-folds. These flavor symmetries are further enlarged to non-Abelian discrete groups by the CP symmetry.

A bstract String theory has been claimed to give rise to natural fuzzy dark matter candidates in the form of ultralight axions. In this paper we revisit this claim by a detailed study of how moduli stabilisation affects the masses and decay constants of different axion fields which arise in type IIB flux compactifications. We find that obtaining a considerable contribution to the observed dark matter abundance without tuning the axion initial misalignment angle is not a generic feature of 4D string models since it requires a mild violation of the Sf ≲ M P bound, where S is the instanton action and f the axion decay constant. Our analysis singles out C 4 -axions, C 2 -axions and thraxions as the best candidates to realise fuzzy dark matter in string theory. For all these ultralight axions we provide predictions which can be confronted with present and forthcoming observations.