Superstring theoryをめぐって(放談室)

http://cds.cern.ch/record/241379/files/arXiv:hep-th_9210010.pdf

W symmetry in conformal field theory

We review recent developments (up to January 2004) of the Liouville field theory and its matrix model dual. This review consists of three parts. In part I, we review the bosonic Liouville theory. After briefly reviewing the necessary background, we discuss the bulk structure constants (the DOZZ formula) and the boundary states (the FZZT brane and the ZZ brane). Various applications are also presented. In part II, we review the supersymmetric extension of the Liouville theory. We first discuss the bulk structure constants and the branes as in the bosonic Liouville theory, and then we present the matrix dual descriptions with some applications. In part III, the Liouville theory on unoriented surfaces is reviewed. After introducing the crosscap state, we discuss the matrix model dual description and the tadpole cancellation condition. This review also includes some original material such as the derivation of the conjectured dual action for the N = 2 Liouville theory from other known dualities and the comparison of the Liouville crosscap state with the c = 0 unoriented matrix model. This is based on my master’s thesis submitted to Department of Physics, Faculty of Science, University of Tokyo on January 2004.

http://cds.cern.ch/record/709154/files/0402009.pdf

Liouville Field Theory — A decade after the revolution

I review recent results on the infrared properties of QCD from Dyson-Schwinger equations. The topics include infrared exponents of one-particle irreducible Green's functions, the fixed point behaviour of the running coupling at zero momentum, the pattern of dynamical quark mass generation and properties of light mesons.

http://iopscience.iop.org/article/10.1088/0954-3899/32/8/R02/pdf

Infrared properties of QCD from Dyson-Schwinger equations

We study D-branes on the quintic CY by combining results from several directions: general results on holomorphic curves and vector bundles, stringy geometry and mirror symmetry, and the boundary states in Gepner models recently constructed by Recknagel and Schomerus, to begin sketching a picture of D-branes in the stringy regime. We also make first steps towards computing superpotentials on the D-brane world-volumes.

https://iopscience.iop.org/article/10.1088/1126-6708/2000/08/015/pdf

D-branes on the quintic

Fusion rules, structure constants and 4-point functions for all the fields in the Neveu-Schwarz, Ramond and twisted sectors of N = 2 minimal models are presented. It is shown that the additional Zp+2 symmetries of these models are generated by specific chiral N = 2 superfields. The structure of the corresponding N = 2 superparafermionic models is discussed.

N=2 superconformal minimal models

Renormalization group flow for general SU(2) coset models

Fusions of conformal models

Affine geometry and WN-Gravities

We study conformal boundary conditions and corresponding one-point functions of the N = 2 super-Liouville theory using both conformal and modular bootstrap methods. We have found both continuous (`FZZT-branes') and discrete (`ZZ-branes') boundary conditions. In particular, we identify two different types of the discrete ZZ-brane solutions, which are associated with degenerate fields of the N = 2 super-Liouville theory.

Marian Stanishkov

Papers

N=2 superconformal minimal models

Renormalization group flow for general SU(2) coset models

Fusions of conformal models

Affine geometry and WN-Gravities

ZZ-branes of N = 2 super-Liouville theory