Akishi Kato

CLASSIFICATION OF MODULAR INVARIANT PARTITION FUNCTIONS IN TWO DIMENSIONS

The partition functions of c < 1 minimal unitary conformal theories are completely classified. It is proven that the list given by Cappelli, Itzykson and Zuber exhausts the set of physically acceptable solutions.

D-brane actions on Kahler manifolds

We consider actions for N D-branes at points in a general Kahler manifold, which satisfy the axioms of D-geometry, and could be used as starting points for defining M(atrix)-theory in curved space. We show that the axioms cannot be satisfied unless the metric is Ricci flat, and argue that such actions do exist when the metric is Ricci flat. This may provide an argument for Ricci flatness in M(atrix)-theory.

Free boson representation of

A bosonization scheme of theq-vertex operators of Uq(sl2) for arbitrary level is obtained. They act as intertwiners among the highest weight modules constructed in a bosonic Fock space. An integral formula is proposed forN-point functions and explicit calculation for two-point function is presented.

q

Abstract We have computed general four-point functions and obtained the operator-product-expansion coefficients in the discrete N = 1 superconformal theories using the method developed by Dotsenko and Fateev. As an application of our results, we have considered the effect of applying the slightly relevant perturbation on superconformal theories. For large m it is shown that the central charge c(m) shifts twice the minimal possible amount as c(m) → c(m − 2), in accordance with what the Witten index tr(−1)F suggests.

-vertex operators and their correlation functions

Abstract Gepners model has realized string propagation on Calabi-Yau type manifolds in terms of conformal field theories. We study the correlation functions in E 7 type modular-invariant Wess-Zumino-Witten theory which is relevant to a three-generation model. Our procedure is applicable to general off-diagonal modular-invariant theories. We determine the Yukawa couplings of the model and discuss their geometrical and phenomenological implications. We also clarify Verlindes fusion rule in E 7 modular-invariant theory.

Operator product expansion coefficients in N = 1 superconformal theory and slightly relevant perturbation

We discuss the modular invariance of the SL(2,R) WZW model. In particular, we discuss in detail the modular invariants using the sl(2,R) characters based on the discrete unitary series of the SL(2,R) representations. The explicit forms of the corresponding characters are known when no singular vectors appear. We show, for example, that from such characters modular invariants can be obtained only when the level k<2 and infinitely large spins are included. In fact, we give a modular invariant with three variables Z(z,τ,u) in this case. We also argue that the discrete series characters are not sufficient to construct a modular invariant compatible with the unitarity bound, which was proposed to resolve the ghost problem of the SL(2,R) strings.

E7 type modular invariant Wess-Zumino theory and Gepner's string compactification

Abstract An explicit formula is obtained for the two-loop vacuum amplitude of the closed bosonic string in terms of a Siegel modular form (cusp form) of weight ten.

Modular invariance of string theory on AdS3

Abstract We study the relation between topological string theory and singularity theory using the partition function of the AN−1 topological string defined by a matrix integral of Kontsevich type. A genus expansion of the free energy is considered, and the genus g = 0 contribution is shown to be described by a special solution of the N-reduced dispersionless KP system. We show universal correspondences between the time variables of the dispersionless KP hierarchy and the flat coordinates associated with versal deformations of simple singularities of type A. We also study the behavior of topological matter theory on the sphere in a topological gravity background, in order to clarify the role of the topological string in the singularity theory. Finally we make some comment on gravitational phase transitions.

Modular invariance and two-loop bosonic string vacuum amplitude

AbstractA quiver mutation loop is a sequence of mutations and vertex relabelings, along which a quiver transforms back to the original form. For a given mutation loop