Related papers: On the $D_n$ Spin Vertex Models for Odd $n$
Given a weight of sl(n), we derive a system of variable-coefficient second-order linear partial differential equations that determines the singular vectors in the corresponding Verma module. Moreover, we completely solve the system in a…
We construct superconformal gauged sigma models with extended rigid supersymmetry in three dimensions. Those with N>4 have necessarily flat targets, but the models with N \leq 4 admit non-flat targets, which are cones with appropriate…
By extending the six-dimensional hybrid formalism for the superstring to include $d=6$ $\mathcal{N}=1$ superspace variables along with unconstrained bosonic ghost fields, we construct a manifestly spacetime supersymmetric vertex operator…
We take first steps toward a theory of ``conformal twists'' for superconformal field theories in dimension 3 to 6, extending the well-known analysis of twists for supersymmetric theories. A conformal twist is a square-zero odd element in…
We elaborate on conformal higher-spin gauge theory in three-dimensional (3D) curved space. For any integer $n>2$ we introduce a conformal spin-$\frac{n}{2}$ gauge field $h_{(n)} =h_{\alpha_1\dots \alpha_n}$ (with $n$ spinor indices) of…
We investigate various aspects of the integrability of the vertex models associated to the $D_n^2$ affine Lie algebra with open boundaries. We first study the solutions of the corresponding reflection equation compatible with the minimal…
We provide a linear analysis on normal modes of the spin Boltzmann equation proposed in \cite{Weickgenannt:2021cuo}, where the non-diagonal or polarized part of the transition rate is neglected to ensure the Hermitian property of linearized…
A non-isospectral (2+1) dimensional integrable spin equation is investigated. It is shown that its geometrical and gauge equivalent counterparts is the (2+1) dimensional nonlinear Schr\"odinger equation introduced by Zakharov and studied…
We develop the analytic bootstrap in several directions. First, we discuss the appearance of nonperturbative effects in the Lorentzian inversion formula, which are exponentially suppressed at large spin but important at finite spin. We show…
We calculate the scaling dimensions of operators with large global charge and spin in 2+1 dimensional conformal field theories. By the state-operator correspondence, these operators correspond to superfluids with vortices and can be…
We construct, for spin $0,1,2$ tensor fields on S$^d$, a set of ladder operators that connect the distinct UIRs of SO$(d+1)$. This is achieved by relying on the conformal Killing vectors of S$^d$. For the case of spinning fields, the ladder…
Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, ... This has led to numerous exact (but non-rigorous) predictions of their scaling…
The extension of nonlinear higher-spin equations in d=4 proposed in [arXiv:1504.07289] for the construction of invariant functional is shown to respect local Lorentz symmetry. The equations are rewritten in a manifestly Lorentz covariant…
We consider the construction of a general tree level amplitude for the interactions between dynamical D-branes where the configurations have non-zero odd spin structure. Using Riemann Theta Identities we map the conditions for the…
$\mathcal{N}=2$ supersymmetric $Spin(n)$ gauge theory admits hypermultiplets in spinor representations of the gauge group, compatible with $\beta\leq0$, for $n\leq 14$. The theories with $\beta<0$ can be obtained as mass-deformations of the…
We construct massless infinite spin irreducible representations of the six-dimensional Poincar\'{e} group in the space of fields depending on twistor variables. It is shown that the massless infinite spin representation is realized on the…
We introduce a spin ladder with discrete symmetries designed to emulate a two-dimensional spin-1/2 boson system at half-filling. Using global properties, such as the structure of topological defects, we establish a correspondence between…
$Vect(N)$, the algebra of vector fields in $N$ dimensions, is studied. Some aspects of local differential geometry are formulated as $Vect(N)$ representation theory. There is a new class of modules, {\it conformal fields}, whose…
We construct a parafermionic conformal theory with the symmetry Z_N, for N odd, based on the second solution of Fateev-Zamolodchikov for the corresponding parafermionic chiral algebra. Primary operators are classified according to their…
The vector system of linear differential equations for a field with arbitrary fractional spin is proposed using infinite-dimensional half-bounded unitary representations of the $\overline{SL(2,R)}$ group. In the case of $(2j+1)$-dimensional…