Related papers: Flavored modular differential equations

An irreducible weight module of an affine Kac-Moody algebra $\mathfrak{g}$ is called dense if its support is equal to a coset in $\mathfrak{h}^{*}/Q$. Following a conjecture of V. Futorny about affine Kac-Moody algebras $\mathfrak{g}$, an…

Let $C$ be a symmetrizable generalized Cartan Matrix, and $q$ an indeterminate. ${\fg}(C)$ is the Kac-Moody Lie algebra and $U=U_q({\fg}(C))$ the associated quantum enveloping algebra over $ k={\Bbb Q}(q)$. The quantum function algebra…

We use vector flavor symmetry to relate form factors of isospin changing operators to isovector form factors. Flavor twisted boundary conditions in lattice QCD thus allow isovector form factors of twist-two operators, e.g, to be computed at…

This paper investigates an inverse seesaw model of neutrino masses based on non-holomorphic modular $A_4$ symmetry, extending the framework of modular-invariant flavor models beyond the conventional holomorphic paradigm. After the general…

An extension of the Standard Model with anomaly free $U(1)_F$ flavor symmetry is studied in this paper. With this extension and the addition of the right-handed neutrino states, the solution of anomaly free charge assignments is found,…

Let $\mathfrak{g}$ be a simple finite dimensional complex Lie algebra and let $\widehat{\mathfrak{g}}$ be the corresponding affine Lie algebra. Kac and Wakimoto observed that in some cases the coefficients in the character formula for a…

After a very brief overview recollecting the `classic' parts of QCD, that is its application to describe hard processes and static properties of hadrons, I survey recent work -- some very recent -- on QCD at non-zero temperature and…

Matrix-valued holomorphic quantum modular forms are intricate objects that arise in successive refinements of the Volume Conjecture of knots and involve three holomorphic, asymptotic and arithmetic objects. It is expected that the algebraic…

It is well known that because of the axial anomaly in QCD, mesons with $J^P = 0^-$ are close to $SU(3)_{\mathrm{V}}$ eigenstates: the $eta^\prime(958)$ meson is largely a singlet, and the $\eta$ meson an octet. In contrast, states with $J^P…

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 $Sp(2h+2, \mathbb{C})$…

Form factor sequences of an integrable QFT can be defined axiomatically as solutions of a system of recursive functional equations, known as ``form factor equations''. We show that their solution can be replaced with the study of the…

String compactifications on an orbi-folded torus with complex structure give rise to chiral fermions, spontaneously broken CP, modular invariance. We show that this allows simple effective theories of flavour and CP where: i) the QCD angle…

We examine symmetries of chiral four-dimensional vacua of Type IIB flux compactifications with vanishing superpotential $W=0$. We find that the ${\cal N}=1$ supersymmetric MSSM-like and Pati-Salam vacua possess enhanced discrete symmetries…

We propose a novel approach to study hyperbolic Kac-Moody algebras, and more specifically, the Feingold-Frenkel algebra $\mathfrak{F}$, which is based on considering the tensor algebra of level-one states before descending to the Lie…

We consider supersymmetric domain walls of four-dimensional $\mathcal{N}\!=\!1$ $Sp(N)$ SQCD with $F\!=\!N+1$ and $F\!=\!N+2$ flavors. First, we study numerically the differential equations defining the walls, classifying the solutions.…

Let g be an affine Kac-Moody Lie algebra and let $\lambda, \mu$ be two dominant integral weights for g. We prove that under some mild restriction, for any positive root $\beta$, $V(\lambda)\otimes V(\mu)$ contains $V(\lambda+\mu-\beta)$ as…

First, we prove the Kac-Wakimoto conjecture on modular invariance of characters of exceptional affine W-algebras. In fact more generally we prove modular invariance of characters of all lisse W-algebras obtained through Hamiltonian…

We discuss methods, based on the theory of vector-valued modular forms, to determine all modular differential equations satisfied by the conformal characters of RCFT; these modular equations are related to the null vector relations of the…

We give a new interpretation of representation theory of the finite-dimensional half-integer weight modules over the queer Lie superalgebra $\mathfrak{q}(n)$. It is given in terms of Brundan's work of finite-dimensional integer weight…

Given a Hilbert cuspidal newform $g$ we construct a family of modular forms of half-integral weight whose Fourier coefficients give the central values of the twisted $L$-series of $g$ by fundamental discriminants. The family is parametrized…