Related papers: Flavored modular differential equations

Every 4d $\mathcal{N} = 2$ SCFT $\mathcal{T}$ corresponds to an associated VOA $\mathbb{V}(\mathcal{T})$, which is in general non-rational with a more involved representation theory. Null states in $\mathbb{V}(\mathcal{T})$ can give rise to…

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),…

The formalism of non-holomorphic modular flavor symmetry is developed, and the Yukawa couplings are level $N$ polyharmonic Maa{\ss} forms satisfying the Laplacian condition. We find that the integer (even) weight polyharmonic Maa{\ss} forms…

We study a scenario to derive four-dimensional modular flavor symmetric models from higher dimensional theory by assuming the compactification consistent with the modular symmetry. In our scenario, wavefunctions in extra dimensional compact…

In this paper we analytically explore the modularity of the flavored Schur index of 4d $\mathcal{N} = 2$ SCFTs. We focus on the $A_1$ theories of class-$\mathcal{S}$ and $\mathcal{N} = 4$ theories with $SU(N)$ gauge group. We work out the…

We show that the bases of irreducible integrable highest weight module of a non-symmetric Kac-Moody algebra, which is associated to a quiver with a nontrivial admissible automorphism, can be naturally identified with a set of certain…

Modular flavor symmetries provide us with a new, promising approach to the flavor problem. However, in their original formulation the kinetic terms of the standard model fields do not have a preferred form, thus introducing additional…

Modular symmetry offers the possibility to provide an origin of discrete flavour symmetry and to break it along particular symmetry preserving directions without introducing flavons or driving fields. It is also possible to use a weighton…

We study the modular invariance in magnetized torus models. Modular invariant flavor model is a recently proposed hypothesis for solving the flavor puzzle, where the flavor symmetry originates from modular invariance. In this framework…

We recently showed, in hep-ph/0406101, that warped extra dimensional models with bulk custodial symmetry and few TeV KK masses lead to striking signals at $B$-factories. In this paper, using a spurion analysis, we systematically study the…

We review the modular flavor symmetric models of quarks and leptons focusing on our works. We present some flavor models of quarks and leptons by using finite modular groups and discuss the phenomenological implications. The modular flavor…

We study quark and lepton flavor structures on magnetized $T^2/\mathbb{Z}_2$ twisted orbifold model. There are 6,460 number of flavor models but most of them cannot lead to realistic flavor observables because of the difficulties on…

In the formalism of the non-supersymmetric modular invariance approach to the flavour problem the elements of the Yukawa coupling and fermion mass matrices are expressed in terms of polyharmonic Maa{\ss} modular forms of level $N$ in…

Discrete flavor symmetries have been an appealing approach for explaining the observed flavor structure, which is not justified in the Standard Model (SM). Typically, these models require a so-called flavon field in order to give rise to…

We propose models to explain the hierarchies of the quark masses and mixing by utilizing the $S_4^\prime$ modular flavor symmetry. The hierarchy is realized by the modulus $\tau$ stabilized at $\mathrm{Im}\,\tau \gg 1$, where the residual…

We revisit the modular flavor symmetry from a more general perspective. The scalar modular forms of principal congruence subgroups are extended to the vector-valued modular forms, then we have more possible finite modular groups including…

We study modular symmetric quark flavor models without fine-tuning. Mass matrices are written in terms of modular forms, and modular forms in the vicinity of the modular fixed points become hierarchical depending on their residual charges.…

Generalizing the super duality formalism for finite-dimensional Lie superalgebras of type $ABCD$, we establish an equivalence between parabolic BGG categories of a Kac-Moody Lie superalgebra and a Kac-Moody Lie algebra. The characters for a…

Over-extended Kac-Moody algebras contain so-called gradient structures - a gl(d)-covariant level decomposition of the algebra contains strings of modules at different levels that can be interpreted as spatial gradients. We present an…

We study the flavor structures of zero-modes, which are originated from the modular symmetry on $T^2_1\times T^2_2$ and its orbifold with magnetic fluxes. We introduce the constraint on the moduli parameters by $\tau_2=N\tau_1$, where…