Tohru Eguchi

Superconformal Algebras and String Compactification on Manifolds with SU(N) Holonomy

Abstract We discuss string compactifications on manifolds with SU( n ) holonomy by making use of representation theories of extended superconformal algebras. In particular, string compactification on K 3 surfaces is discussed in detail. We calculate loop-space indices and show that all c = 6 superconformal field theories describe string propagation on manifolds with SU(2) holonomy. We study Gepners models based on the tensoring of N = 2 minimal series and point out that some of these models are identified as orbifolds. We also discuss c = 9 superconformal field theories and their relation to Calabi-Yau manifolds.

Notes on the K3 Surface and the Mathieu Group M 24

We point out that the elliptic genus of the K3 surface has a natural decomposition in terms of dimensions of irreducible representations of the largest Mathieu group M 24. The reason remains a mystery.

N=2 superconformal models as topological field theories

We present simple observations on the topological nature of N=2 superconformal field theories. We point out that under a suitable redefinition of the energy-momentum tensor the central charge of N=2 theory vanishes and the theory is transformed into a topological quantum field theory. BRST invariant observables are given by chiral primary fields. We also discuss the relevant perturbations of N=2 and SU(2) coset models.

Conformal and current algebras on a general Riemann surface

Abstract Starting from a path integral formulation, Ward identities are derived for conformal and current algebras on a general Riemann surface. An n+1-point amplitude with energy-momentum tensor insertion is related by the Ward identity to an n-point amplitude and its derivative with respect to the modular parameters. Similarly, an n+1-point function with current insertion is related to an n-point function and its derivative with respect to an harmonic background gauge field. We discuss how conformal and current algebras, defined in each coordinate patch, are glued together to form a global algebraic structure on the Riemann surface.

Penner type matrix model and Seiberg-Witten theory

We discuss the Penner type matrix model recently proposed by Dijkgraaf and Vafa for a possible explanation of the relation between four-dimensional gauge theory and Liouville theory by making use of the connection of the matrix model to two-dimensional CFT. We first consider the relation of gauge couplings defined in UV and IR regimes of Nf = 4,

On the unitary representations of N=2 and N=4 superconformal algebras

\mathcal{N}

Seiberg-Witten theory, matrix model and AGT relation

= 2 supersymmetric gauge theory being related as qUV = ϑ2(qIR)4/ϑ3(qIR)4. We then use this relation to discuss the action of modular transformation on the matrix model and determine its spectral curve.We also discuss the decoupling of massive flavors from the Nf = 4 matrix model and derive matrix models describing asymptotically free