Related papers: Flavored modular differential equations

We construct an orbifold model in which all the standard model particles are unified in a gauge multiplet in higher dimensional supersymmetric gauge theory. We find that a flavor symmetry has to remain in four dimensions due to the discrete…

Let $\fg$ be any untwisted affine Kac-Moody algebra, $\mu$ any fixed complex number, and $\wt\fg(\mu)$ the corresponding toroidal extended affine Lie algebra of nullity two. For any $k$-tuple $\bm{\lambda}=({\lambda}_1, \cdots,…

Let E/Q be a real quadratic field and pi_0 a cuspidal, irreducible, automorphic representation of GL(2,A_E) with trivial central character and infinity type (2,2n+2) for some non-negative integer n. We show that there exists a non-zero…

Within the Dijkgraaf-Vafa correspondence, we study the complete factorization of the Seiberg-Witten curve for U(N_c) gauge theory with N_f<N_c massive flavors. We obtain explicit expressions, from random matrix theory, for the moduli,…

We introduce a new generalisation of partitions, multi-grounded partitions, related to ground state paths indexed by dominant weights of Lie algebras. We use these to express characters of irreducible highest weight modules of Kac-Moody…

We study the modulus stabilization in an $A_4$ model whose $A_4$ flavor symmetry is originated from the $S_4$ modular symmetry. We can stabilize the modulus so that the $A_4$ invariant superpotential leads to the realistic lepton masses and…

Recent work on 6D superconformal field theories (SCFTs) has established an intricate correspondence between certain Higgs branch deformations and nilpotent orbits of flavor symmetry algebras associated with T-branes. In this paper, we…

We perform a comprehensive and systematic analysis of the SUSY flavor structure of generic 5D supergravity models on $S^1/Z_2$ with multiple $Z_2$-odd vector multiplets that generate multiple moduli. The SUSY flavor problem can be avoided…

A simple explanation of the flavor hierarchies can arise if matter fields interact with a conformal sector and different generations have different anomalous dimensions under the CFT. However, in the original study by Nelson and Strassler…

We give the first positive formulas for the weights of every simple highest weight module $L(\lambda)$ over an arbitrary Kac-Moody algebra. Under a mild condition on the highest weight, we also express the weights of $L(\lambda)$ as an…

We revisit the study of singular points in the Coulomb branch of $\mathcal{N}=2$ SQCD in four dimensions with gauge group $SU(N)$ and odd number of flavors. For certain choices of the mass parameters these vacua are not lifted by a mass…

In this paper we construct a modular form f of weight one attached to an imaginary quadratic field K. This form, which is non-holomorphic and not a cusp form, has several curious properties. Its negative Fourier coefficients are non-zero…

Let $\fg$ be a symmetrizable Kac-Moody Lie algebra with the standard Cartan subalgebra $\fh$ and the Weyl group $W$. Let $P_+$ be the set of dominant integral weights. For $\lambda \in P_+$, let $L(\lambda)$ be the irreducible, integrable,…

Modular transformations of string theory are shown to play a crucial role in the discussion of discrete flavor symmetries in the Standard Model. They include CP transformations and provide a unification of CP with traditional flavor…

We propose a grading protocol which assigns global symmetry associated phases to states in the Hilbert space. Without modifying the Hilbert space, this changes the state sum, a process that we call quantum distillation. We describe the…

We study the flavor structure of 4D effective theories, which are derived from extra dimensional theories with magnetic fluxes and non-Abelian Wilson lines. We study zero-mode wavefunctions and compute Yukawa couplings as well as four-point…

We construct from a finitary exact category with duality a module over its Hall algebra, called the Hall module, encoding the first order self-dual extension structure of the category. We study in detail Hall modules arising from the…

In an attempt to understand the observed patterns of lepton and quark masses, models invoking a flavor symmetry $G_f$, under which the Standard Model generations are charged, have been proposed. One particularly successful symmetry, U(2),…

We explore predictive flavor models based on subgroups of the standard-model $SU(3)^5$ flavor symmetry. Restricting to products of $SU(3)$, we find that a global $SU(3)^3$ flavor symmetry, broken only by two Yukawa spurions, leads to a…

It has recently been shown that F-theory based constructions provide a potentially promising avenue for engineering GUT models which descend to the MSSM. In this note we show that in the presence of background fluxes, these models…