Quaternion-K\"ahler N=4 Supersymmetric Mechanics

Using the N=4, 1D harmonic superspace approach, we construct a new type of N=4 supersymmetric mechanics involving 4n-dimensional Quaternion-K\"ahler (QK) 1D sigma models as the bosonic core. The basic ingredients of our construction are {\it local} N=4, 1D supersymmetry realized by the appropriate transformations in 1D harmonic superspace, the general N=4, 1D superfield vielbein and a set of 2(n+1) analytic "matter" superfields representing (n+1) off-shell supermultiplets (4, 4, 0). Both superfield and component actions are given for the simplest QK models with the manifolds \mathbb{H}H^n = Sp(1,n)/[Sp(1) x Sp(n)] and \mathbb{H}P^n = Sp(1+n)/[Sp(1) x Sp(n)] as the bosonic targets. For the general case the relevant superfield action and constraints on the (4, 4, 0) "matter" superfields are presented. Further generalizations are briefly discussed.Comment: further minor corrections in eqs. (2.21), (4.24) and (A9

Anyons from Strings

The Nambu-Goto string in a 3-dimensional (3D) Minkowski spacetime is quantized preserving Lorentz invariance and parity. The spectrum of massive states contains anyons. An ambiguity in the ground state energy is resolved by the 3D N=1 Green-Schwarz superstring, which has massless ground states describing a dilaton and dilatino, and first-excited states of spin 1/4.Comment: 4 pages, two additional refs. in v

Addendum to ``Integrability of Open Spin Chains with Quantum Algebra Symmetry''

We show that the quantum-algebra-invariant open spin chains associated with the affine Lie algebras $A^{(1)}_n$ for $n>1$ are integrable. The argument, which applies to a large class of other quantum-algebra-invariant chains, does not require that the corresponding $R$ matrix have crossing symmetry.Comment: 4 pages, plain tex, UMTG-16

A Super-Flag Landau Model

We consider the quantum mechanics of a particle on the coset superspace $SU(2|1)/[U(1)\times U(1)]$, which is a super-flag manifold with $SU(2)/U(1)\cong S^2$ `body'. By incorporating the Wess-Zumino terms associated with the $U(1)\times U(1)$ stability group, we obtain an exactly solvable super-generalization of the Landau model for a charged particle on the sphere. We solve this model using the factorization method. Remarkably, the physical Hilbert space is finite-dimensional because the number of admissible Landau levels is bounded by a combination of the U(1) charges. The level saturating the bound has a wavefunction in a shortened, degenerate, irrep of $SU(2|1)$

Boundary S Matrix for the XXZ Chain

We compute by means of the Bethe Ansatz the boundary S matrix for the open anisotropic spin-1/2 chain with diagonal boundary magnetic fields in the noncritical regime (Delta > 1). Our result, which is formulated in terms of q-gamma functions, agrees with the vertex-operator result of Jimbo et al.Comment: 9 pages, LaTeX, no figure