Related papers: Conjugate Bailey pairs
We discuss the lattice formulation of gauge theories with fermions in arbitrary representations of the color group, and present the implementation of the RHMC algorithm for simulating dynamical Wilson fermions. A first dataset is presented…
We present results from a lattice study of SU(2) color, N=1 supersymmetric Yang-Mills theory using domain wall fermions. Supersymmetry in this particular lattice formulation is expected to emerge in the continuum and chiral limits without…
By using generalized vertex algebras associated to rational lattices, we construct explicitly the admissible modules for the affine Lie algebra $A_1 ^{(1)}$ of level $-{4/3}$. As an application, we show that the W(2,5) algebra with central…
A flavor-unified theory based on the simple Lie algebra of ${\mathfrak{s}\mathfrak{u}}(8)$ was previously proposed to generate the observed Standard Model quark/lepton mass hierarchies and the Cabibbo-Kobayashi-Maskawa mixing pattern due to…
We consider string junctions with endpoints on a set of branes of IIB string theory defining an ADE-type gauge Lie algebra. We show how to characterize uniquely equivalence classes of junctions related by string/brane crossing through…
In this paper, we recall Lepowsky's and Wakimoto's product character formulas formulated in a new way by using arrays of specialized weighted crystals of negative roots for affine Lie algebras of type $C_l^{(1)}$, $D_{l+1}^{(2)}$ and…
We establish a weight-preserving bijection between the index sets of the spectral data of row-to-row and corner transfer matrices for $U_q\widehat{sl(n)}$ restricted interaction round a face (IRF) models. The evaluation of momenta by adding…
We present a non-perturbative lattice study of SU(4) gauge theory with two flavors of fermions in the fundamental representation and two in the two-index antisymmetric representation: a theory closely related to a minimal…
A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…
The second $\mathbb{Z}_{3}$ parafermionic conformal theories are associated with the coset construction $\frac{SU(2)_{k}\times SU(2)_{4}}{SU(2)_{k+4}} $. Solid-on-solid integrable lattice models obtained by fusion of the model based on…
We construct composite operators in two-dimensional bosonized QCD, which obey a $W_\infty$ algebra, and discuss their relation to analogous objects recently obtained in the fermionic language. A complex algebraic structure is unravelled,…
We review some basic features of the Lie-algebraic classification of W-algebras and related integrable hierarchies in 1+1 dimensions, pointing out the role of affine Lie algebras. We emphasize that the supersymmetric extensions of the above…
The Q1 lattice equation, a member in the Adler-Bobenko-Suris list of 3D consistent lattices, is investigated. By using the multidimensional consistency, a novel Lax pair for Q1 equation is given, which can be nonlinearised to produce…
We give a purely combinatorial proof of the positivity of the stabilized forms of the generalized exponents associated to each classical root system. In finite type A_{n-1}, we rederive the description of the generalized exponents in terms…
A consistent realization of the quantum operators corresponding to the canonically conjugate phase and number variables is proposed, resorting to the irreducible unitary representations of the Lie algebra su(1,1), as proposed by Kastrup.
We present results from a numerical study of N=1 supersymmetric Yang-Mills theory using domain wall fermions. In this particular lattice formulation of the theory, supersymmetry is expected to emerge accidentally in the continuum and chiral…
We study various aspects of parafermionic theories such as the precise field content, a description of a basis of states (that is, the counting of independent states in a freely generated highest-weight module) and the explicit expression…
We present an algorithm for the construction of the branching functions in the vacuum sector for affine Lie algebras based on the string hypothesis solution to a system of Bethe equations for generalized RSOS models. We also mention how the…
By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on…
We obtain a characterization of the real Lie algebras admitting abelian complex structures in terms of certain affine Lie algebras $\frak a \frak f \frak f (A)$, where $A$ is a commutative algebra. These affine Lie algebras are natural…