arXiv subjects
Publications and source records attributed to Sung-Kil Yang.
Applying boundary conformal field theory we study the low-energy critical behavior of the Calogero-Sutherland model of $BC_N$-type. The universality class of the model is found to be a {\it chiral} Tomonaga-Luttinger liquid. Various correlation exponents depending on the interaction strength are obtained.
Using recently proposed soliton equations we derive a basic identity for the scaling violation of $N=2$ supersymmetric gauge theories $\sum_i a_i\partial F/\partial a_i-2F=8 πi b_1 u$. Here $F$ is the prepotential, $a_i$'s are the expectation values of the scalar fields in the vector multiplet, $u=1/2\, {\rm Tr}\, \langleϕ^2\rangle$ and $b_1$ is the coefficient of the one-loop $β$-function. This equation holds in the Coulomb branch of all $N=2$ supersymmetric gauge theories coupled with massless matter.
The Landau-Ginzburg formulation of two-dimensional topological sigma models on the target space with positive first Chern class is considered. The effective Landau-Ginzburg superpotential takes the form of logarithmic type which is characteristic of supersymmetric theories with the mass gap. The equations of motion yield the defining relations of the quantum cohomology ring. Topological correlation functions in the $CP^{n-1}$ and Grassmannian models are explicitly evaluated with the use of the logarithmic superpotential.
Critical properties of the Calogero-Sutherland model of $BC_N$-type ($BC_N$-CS model) are studied. Using the asymptotic Bethe-ansatz spectrum of the $BC_N$-CS model, we calculate finite-size corrections in the energy spectrum. Since the $BC_N$-CS model does not possess translational invariance, the finite-size spectrum acquires the contributions coming from ``boundaries''. We show that the low-energy critical behavior of the model is described by $c=1$ boundary conformal field theory. Thus the universality class of the model is identified as a chiral Tomonaga-Luttinger liquid.
We calculate the prepotential of the low-energy effective action for $N=2$ $SU(2)$ supersymmetric Yang-Mills theory with $N_f$ massless hypermultiplets ($N_f=1,\, 2,\, 3$). The precise evaluation of the instanton corrections is performed by making use of the Picard-Fuchs equations associated with elliptic curves. The flavor dependence of the instanton effect is determined explicitly both in the weak- and strong-coupling regimes.
We discuss duality and mirror symmetry phenomena of Landau-Ginzburg orbifolds considering their elliptic genera. Under the duality (or mirror) transform performed by orbifoldizing the Landau-Ginzburg model via some discrete group of the superpotential we observe that the roles of the untwisted and twisted sectors are exchanged. As explicit evidence detailed orbifold data are presented for $N=2$ minimal models, Arnold's exceptional singularities, $K3$ surfaces constructed from Arnold's singularities and Fermat hypersurfaces. (To appear in the proceedings of the workshop, ``Quantum Field Theory, Integrable Models and Beyond'', Yukawa Institute for Theoretical Physics, Kyoto University, 14-18 February 1994.)
Recently Witten proposed to consider elliptic genus in $N=2$ superconformal field theory to understand the relation between $N=2$ minimal models and Landau-Ginzburg theories. In this paper we first discuss the basic properties satisfied by elliptic genera in $N=2$ theories. These properties are confirmed by some fundamental class of examples. Then we introduce a generic procedure to compute the elliptic genera of a particular class of orbifold theories, {\it i.e.\/} the ones orbifoldized by $e^{2πiJ_0}$ in the Neveu-Schwarz sector. This enables us to calculate the elliptic genera for Landau-Ginzburg orbifolds. When the Landau-Ginzburg orbifolds allow an interpretation as target manifolds with $SU(N)$ holonomy we can compare the expressions with the ones obtained by orbifoldizing tensor products of $N=2$ minimal models. We also give sigma model expressions of the elliptic genera for manifolds of $SU(N)$ holonomy.
In the first part of this paper we investigate the operator aspect of higher-rank supersymmetric model which is introduced as a Lie theoretic extension of the $N=2$ minimal model with the simplest case $su(2)$ corresponding to the $N=2$ minimal model. In particular we identify the analogs of chirality conditions and chiral ring. In the second part we construct a class of topological conformal field theories starting with this higher-rank supersymmetric model. We show the BRST-exactness of the twisted stress-energy tensor, find out physical observables and discuss how to make their correlation functions. It is emphasized that in the case of $su(2)$ the topological field theory constructed in this paper is distinct from the one obtained by twisting the $N=2$ minimal model through the usual procedure.