Related papers: Spin Leonard pairs and the zero diagonal space

It was earlier shown that an SO(9,1) $\theta^\a$ spinor variable can be constructed from RNS matter and ghost fields. $\theta^\a$ has a bosonic worldsheet super-partner $\lambda^\a$ which plays the role of a twistor variable, satisfying…

We show that the conditions which originate the spin and pseudospin symmetries in the Dirac equation are the same that produce equivalent energy spectra of relativistic spin-1/2 and spin-0 particles in the presence of vector and scalar…

A proof is presented for the absence of gap for spin $1/2$ ladders with an odd number of legs, in the infinite leg length limit. This result is relevant to the current discussion of coupled one--dimensional spin systems, a physical…

In a space of d $(d > 5) $ ordinary and d Grassmann coordinates, fields manifest in an ordinary four-dimensional subspace as spinor (1/2, 3/2), scalar, vector or tensor fields with the corresponding charges, according to two kinds of…

For $g \ge 5$, we give a complete classification of the connected components of strata of abelian differentials over Teichm\"uller space, establishing an analogue of Kontsevich and Zorich's classification of their components over moduli…

A vector space S of linear operators between vector spaces U and V is called locally linearly dependent (in abbreviated form: LLD) when every vector x of U is annihilated by a non-zero operator in S. A duality argument bridges the theory of…

Several possible odd-parity states are listed up group-theoretically and examined in light of recent experiments on Sr$_2$RuO$_4$. Those include some of the $f$-wave pairing states, ${\mib d}({\mib k})\propto{\hat{\mib z}} k_xk_y(k_x + {\rm…

The isotropic limit of spin systems with orbital degeneracy is shown to have global SU(4) symmetry. On many 2D lattices, the ground state does not posses long range order, which may explain the observed spin liquid properties of $LiNiO_2$.…

We show that scalar chiral order can be induced by four-spin exchanges in the two-leg spin ladder, using the spin-chirality duality transformation and matrix-product ansatz. Scalar-chiral-ordered states are found to be exact ground states…

Possible anisotropic spin singlet pairings in Bi$_2$X$_3$ (X is Se or Te) are studied. Among six pairings compatible with the crystal symmetry, two novel pairings show nontrivial surface Andreev bound states, which form flat bands and could…

We address here a few classical lattice--spin models, involving $n-$component unit vectors ($n=2,3$), associated with a $D-$dimensional lattice $\mathbb{Z}^D,\,D=1,2$, and interacting via a pair potential restricted to nearest neighbours…

We review the general formalism of duality rotations for $\cal N$-extended (super)conformal gauge multiplets of arbitrary (super)spin in four dimensions, with ${\cal N} \geq 0$. Self-dual models for a vector field (${\cal N}=0$) and for…

Let K be an arbitrary (commutative) field and L be an algebraic closure of it. Let V be a linear subspace of M_n(K), with n>2. We show that if every matrix of V has at most one eigenvalue in K, then dim V<=1+n(n-1)/2. If every matrix of V…

The spectrum of integrable spin chains are shown to be independent of the ordering of their spins. As an application we introduce defects (local spin inhomogeneities in homogenous chains) in two-boundary spin systems and, by changing their…

We give necessary and sufficient conditions for the existence of pin+, pin- and spin structures on Riemannian manifolds with holonomy group $Z_2^k$. For any n>3 (resp. n>5) we give examples of pairs of compact manifolds (resp. compact…

For a given $3 \times 3$ real matrix $A$, the eigenvalue complementarity problem relative to the Lorentz cone consists of finding a real number $\lambda$ and a nonzero vector $x \in \mathbb{R}^3$ such that $x^T(A-\lambda I)x=0$ and both $x$…

In zero magnetic field the superconductor Sr$_2$RuO$_4$ is believed to have a chiral spin triplet pairing state in which the gap function d-vector is aligned along the crystal c-axis. Using a phenomenological but orbital specific…

We use group theory to classify the superconducting states of systems with two orbitals on a tetragonal lattice. The orbital part of the superconducting gap function can be either symmetric or anti-symmetric. For the orbital symmetric…

Let $\mathbb F$ denote a field, and let $V$ denote a vector space over $\mathbb F$ with finite positive dimension. We consider an ordered pair of $\mathbb F$-linear maps $A: V \to V$ and $A^*:V\to V$ such that (i) each of $A,A^*$ is…

Anomalous dimensions of Wilson operators with large Lorentz spin scale logarithmically with the spin. Recent multi-loop QCD calculations of twist-two anomalous dimensions revealed the existence of interesting structure of the subleading…