Hilbert Series for Moduli Spaces of Two Instantons

The Hilbert Series (HS) of the moduli space of two G instantons on C^2, where G is a simple gauge group, is studied in detail. For a given G, the moduli space is a singular hyperKahler cone with a symmetry group U(2) \times G, where U(2) is the natural symmetry group of C^2. Holomorphic functions on the moduli space transform in irreducible representations of the symmetry group and hence the Hilbert series admits a character expansion. For cases that G is a classical group (of type A, B, C, or D), there is an ADHM construction which allows us to compute the HS explicitly using a contour integral. For cases that G is of E-type, recent index results allow for an explicit computation of the HS. The character expansion can be expressed as an infinite sum which lives on a Cartesian lattice that is generated by a small number of representations. This structure persists for all G and allows for an explicit expressions of the HS to all simple groups. For cases that G is of type G_2 or F_4, discrete symmetries are enough to evaluate the HS exactly, even though neither ADHM construction nor index is known for these cases.Comment: 53 pages, 9 tables, 24 figure

Conformal Aspects of Spinor-Vector Duality

We present a detailed study of various aspects of Spinor-Vector duality in Heterotic string compactifications and expose its origin in terms of the internal conformal field theory. In particular, we illustrate the main features of the duality map by using simple toroidal orbifolds preserving N_4 = 1 and N_4 = 2 spacetime supersymmetries in four dimensions. We explain how the duality map arises in this context by turning on special values of the Wilson lines around the compact cycles of the manifold. We argue that in models with N_4 = 2 spacetime supersymmetry, the interpolation between the Spinor-Vector dual vacua can be continuously realized. We trace the origin of the Spinor-Vector duality map to the presence of underlying N = (2, 2) and N = (4, 4) SCFTs, and explicitly show that the induced spectral-flow in the twisted sectors is responsible for the observed duality. The isomorphism between current algebra representations gives rise to a number of chiral character identities, reminiscent of the recently-discovered MSDS symmetry.Comment: 49 page

Monte Carlo simulation of SU(2) Yang-Mills theory with light gluinos

In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with light dynamical gluinos the low energy features of the dynamics as confinement and bound state mass spectrum are investigated. The motivation is supersymmetry at vanishing gluino mass. The performance of the applied two-step multi-bosonic dynamical fermion algorithm is discussed.Comment: latex, 48 pages, 16 figures with epsfi

Hamiltonian Theory of the Composite Fermion Wigner Crystal

Experimental results indicating the existence of the high magnetic field Wigner Crystal have been available for a number of years. While variational wavefunctions have demonstrated the instability of the Laughlin liquid to a Wigner Crystal at sufficiently small filling, calculations of the excitation gaps have been hampered by the strong correlations. Recently a new Hamiltonian formulation of the fractional quantum Hall problem has been developed. In this work we extend the Hamiltonian approach to include states of nonuniform density, and use it to compute the excitation gaps of the Wigner Crystal states. We find that the Wigner Crystal states near $\nu=1/5$ are quantitatively well described as crystals of Composite Fermions with four vortices attached. Predictions for gaps and the shear modulus of the crystal are presented, and found to be in reasonable agreement with experiments.Comment: 41 page, 6 figures, 3 table

On quantization of weakly nonlinear lattices. Envelope solitons

A way of quantizing weakly nonlinear lattices is proposed. It is based on introducing "pseudo-field" operators. In the new formalism quantum envelope solitons together with phonons are regarded as elementary quasi-particles making up boson gas. In the classical limit the excitations corresponding to frequencies above linear cut-off frequency are reduced to conventional envelope solitons. The approach allows one to identify the quantum soliton which is localized in space and understand existence of a narrow soliton frequency band.Comment: 5 pages. Phys. Rev. E (to appear