8 research outputs found
Fusion rules and singular vectors of the osp(1|2) current algebra
The fusion of Verma modules of the osp(1|2) current algebra is studied. In
the framework of an isotopic formalism, the singular vector decoupling
conditions are analyzed. The fusion rules corresponding to the admissible
representations of the osp(1|2) algebra are determined. A relation between the
characters of these last representations and those corresponding to the minimal
superconformal models is found. A series of equations that relate the
descendants of the highest weight vectors resulting from a fusion of Verma
modules are obtained. Solving these equations the singular vectors of the
theory can be determined.Comment: 63 pages, phyzz
Cubic curves from instanton counting
We investigate the possibility to extract Seiberg-Witten curves from the
formal series for the prepotential, which was obtained by the Nekrasov
approach. A method for models whose Seiberg-Witten curves are not hyperelliptic
is proposed. It is applied to the SU(N) model with one symmetric or
antisymmetric representations as well as for SU(N_1)xSU(N_2) model with
(N_1,N_2) or (N_1,\bar{N}_2) bifundamental matter. Solutions are compared with
known results. For the gauge group product we have checked the instanton
corrections which follow from our curves against direct instanton counting
computations up to two instantons.Comment: 30 pages, v2. typos fixed, referenced adde
On the free field realization of the osp(1|2) current algebra
The free field representation of the osp(1|2) current algebra is analyzed.
The four point conformal blocks of the theory are studied. The structure
constants for the product of an arbitrary primary operator and a primary field
that transforms according to the fundamental representation of osp(1|2) are
explicitly calculated.Comment: 11 pages, phyzz
Prepotential and Instanton Corrections in N=2 Supersymmetric SU(N_1)xSU(N_2) Yang Mills Theories
In this paper we analyse the non-hyperelliptic Seiberg-Witten curves derived
from M-theory that encode the low energy solution of N=2 supersymmetric
theories with product gauge groups. We consider the case of a SU(N_1)xSU(N_2)
gauge theory with a hypermultiplet in the bifundamental representation together
with matter in the fundamental representations of SU(N_1) and SU(N_2). By means
of the Riemann bilinear relations that hold on the Riemann surface defined by
the Seiberg--Witten curve, we compute the logarithmic derivative of the
prepotential with respect to the quantum scales of both gauge groups. As an
application we develop a method to compute recursively the instanton
corrections to the prepotential in a straightforward way. We present explicit
formulas for up to third order on both quantum scales. Furthermore, we extend
those results to SU(N) gauge theories with a matter hypermultiplet in the
symmetric and antisymmetric representation. We also present some non-trivial
checks of our results.Comment: 21 pages, 2 figures, minor changes and references adde
Structure constants for the osp(1|2) current algebra
We study the free field realization of the two-dimensional osp(1|2) current
algebra. We consider the case in which the level of the affine osp(1|2)
symmetry is a positive integer. Using the Coulomb gas technique we obtain
integral representations for the conformal blocks of the model. In particular,
from the behaviour of the four-point function, we extract the structure
constants for the product of two arbitrary primary operators of the theory.
From this result we derive the fusion rules of the osp(1|2) conformal field
theory and we explore the connections between the osp(1|2) affine symmetry and
the N=1 superconformal field theories.Comment: 64 pages, phyzzx, no figure