Superconformal Field Theory with Boundary: Fermionic Model

Fermionic model of Superconformal field theory with boundary is considered. There were written the ''boundary'' Ward Identity for this theory and also constructed boundary states for fermionic and spin models. For this model were derived ''bootstrap'' equations for boundary structure constants.Comment: 12 page

Conformal blocks related to the R-R states in the \hat c =1 SCFT

We derive an explicit form of a family of four-point Neveu-Schwarz blocks with $\hat c =1,$ external weights $\Delta_i = 1/8$ and arbitrary intermediate weight. The derivation is based on a set of identities obeyed in the free superscalar theory by correlation functions of fields satisfying Ramond condition with respect to the bosonic (dimension 1) and the fermionic (dimension 1/2) currents.Comment: 15 pages, no figure

Minimal Models of CFT on Z_N-Surfaces

The conformal field theory on a Z_N-surface is studied by mapping it on the branched sphere. Using a coulomb gas formalism we construct the minimal models of the theory.Comment: 16 pages, latex, no figures; two important early references on the coset construction have been included; to appear in Mod. Phys. Let

Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks

Liouville field theory on a sphere is considered. We explicitly derive a differential equation for four-point correlation functions with one degenerate field $V_{-\frac{mb}{2}}$. We introduce and study also a class of four-point conformal blocks which can be calculated exactly and represented by finite dimensional integrals of elliptic theta-functions for arbitrary intermediate dimension. We study also the bootstrap equations for these conformal blocks and derive integral representations for corresponding four-point correlation functions. A relation between the one-point correlation function of a primary field on a torus and a special four-point correlation function on a sphere is proposed

Consistent superconformal boundary states

We propose a supersymmetric generalization of Cardy's equation for consistent N=1 superconformal boundary states. We solve this equation for the superconformal minimal models SM(p/p+2) with p odd, and thereby provide a classification of the possible superconformal boundary conditions. In addition to the Neveu-Schwarz (NS) and Ramond (R) boundary states, there are NS~ states. The NS and NS~ boundary states are related by a Z_2 "spin-reversal" transformation. We treat the tricritical Ising model as an example, and in an appendix we discuss the (non-superconformal) case of the Ising model.Comment: 23 pages, LaTeX; amssymb, epsf, 1 eps figure; v2: references adde

Twisting the N=2 String

The most general homogeneous monodromy conditions in $N{=}2$ string theory are classified in terms of the conjugacy classes of the global symmetry group $U(1,1)\otimes{\bf Z}_2$. For classes which generate a discrete subgroup \G, the corresponding target space backgrounds {\bf C}^{1,1}/\G include half spaces, complex orbifolds and tori. We propose a generalization of the intercept formula to matrix-valued twists, but find massless physical states only for $\Gamma{=}{\bf 1}$ (untwisted) and $\Gamma{=}{\bf Z}_2$ (\`a la Mathur and Mukhi), as well as for $\Gamma$ being a parabolic element of $U(1,1)$. In particular, the sixteen ${\bf Z}_2$-twisted sectors of the $N{=}2$ string are investigated, and the corresponding ground states are identified via bosonization and BRST cohomology. We find enough room for an extended multiplet of `spacetime' supersymmetry, with the number of supersymmetries being dependent on global `spacetime' topology. However, world-sheet locality for the chiral vertex operators does not permit interactions among all massless `spacetime' fermions.Comment: 42 pages, LaTeX, no figures, 120 kb, ITP-UH-24/93, DESY 93-191 (abstract and introduction clarified, minor corrections added