Sung-Kil Yang

Elliptic genera and N=2 superconformal field theory

Abstract Recently Witten proposed to consider the 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, i.e. the ones orbifoldized by e2πiJ0 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) holomony.

Study of N = 2 superconformal field theories in 4 dimensions

Making use of the exact solutions of the N = 2 supersymmetric gauge theories, we construct new classes of superconformal field theories (SCFTs) by fine-tuning the moduli parameters and bringing the theories to critical points. SCFTs we have constructed represent universality classes of the 4-dimensional N = 2 SCFTs.

THE TOPOLOGICAL CP1 MODEL AND THE LARGE-N MATRIX INTEGRAL

We discuss the topological CP1 model which consists of the holomorphic maps from Riemann surfaces onto CP1. We construct a large-N matrix model which reproduces precisely the partition function of the CP1 model at all genera of Riemann surfaces. The action of our matrix model has the form where M is an N × N Hermitian matrix and tn,P(tn,Q), (n = 0, 1, 2, …) are the coupling constants of the nth descendant of the puncture (Kahler) operator.

Modular invariance in N=2 superconformal field theories

The modular invariance properties of two-dimensional N=2 superconformal field theories are studied. It is shown that the character formulae of the central charge c<3 unitary highest weight representation for the untwisted algebras can be written in terms of the string functions and the theta functions of the affine su(2) Kac-Moody algebra. Deriving the modular transformation of the characters we construct the modular invariant partition functions on a torus. The character relation corresponding to the coset space construction of the unitary discrete series in the N=2 algebra is also obtained.

Modular Invariant Partition Function of the Ashkin-teller Model on the Critical Line and

Abstract The modular invariant partition function of the two-dimensional Ashkin-Teller model on a line of continuously varying critically is obtained. The second magnetic exponent is predicted to be 9 8 . Derivation of the partition function in terms of gaussian field theories is also presented. Using chiral gaussian fields we construct the partition function for free boundary conditions, in terms of which the numerically observed spectrum is reproduced and, in particular, the appearance of N = 2 supersymmetry at three particular points on the critical line is demonstrated. We discuss the fermion operator content by constructing the partition function for antiperiodic boundary conditions.

N=2

In this paper we describe in some detail the representation of the topological CP1 model in terms of a matrix integral which we have introduced in a previous article. We first discuss the integrable structure of the CP1 model and show that it is governed by an extension of the one-dimensional Toda hierarchy. We then introduce a matrix model which reproduces the sum over holomorphic maps from arbitrary Riemann surfaces onto CP1. We compute intersection numbers on the moduli space of curves using a geometrical method and show that the results agree with those predicted by the matrix model. We also develop a Landau-Ginzburg (LG) description of the CP1 model using a superpotential eX + et0,Q e-X given by the Lax operator of the Toda hierarchy (X is the LG field and t0,Q is the coupling constant of the Kahler class). The form of the superpotential indicates the close connection between CP1 and N=2 supersymmetric sine-Gordon theory which was noted sometime ago by several authors. We also discuss possible generalizations of our construction to other manifolds and present an LG formulation of the topological CP2 model.

Superconformal Invariance

A systematic formulation of the higher genus expansion in topological string theory is considered. We also develop a simple way of evaluating genus zero correlation functions. At higher genera we derive some interesting formulas for the free energy in the

TOPOLOGICAL σ MODELS AND LARGE N MATRIX INTEGRAL

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ON THE GENUS EXPANSION IN THE TOPOLOGICAL STRING THEORY

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Topological strings, flat coordinates and gravitational descendants

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