scholarly journals Generating Functional in CFT and Effective Action for Two-Dimensional Quantum Gravity on Higher Genus Riemann Surfaces

1997 ◽  
Vol 188 (1) ◽  
pp. 29-67 ◽  
Author(s):  
Ettore Aldrovandi ◽  
Leon A. Takhtajan
Keyword(s):  
Quantum Gravity ◽  
Effective Action ◽  
Riemann Surfaces ◽  
Two Dimensional ◽  
Generating Functional ◽  
Higher Genus

A COMPACT BOSON COUPLED TO TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (15) ◽  
pp. 2743-2754 ◽  
Author(s):  
NORISUKE SAKAI ◽  
YOSHIAKI TANII
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Riemann Surfaces ◽  
Partition Functions ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
The Continuum ◽  
Continuum Field

The radius dependence of partition functions is explicitly evaluated in the continuum field theory of a compactified boson, interacting with two-dimensional quantum gravity (noncritical string) on Riemann surfaces for the first few genera. The partition function for the torus is found to be a sum of terms proportional to R and 1/R. This is in agreement with the result of a discretized version (matrix models), but is quite different from the critical string. The supersymmetric case is also explicitly evaluated.

scholarly journals 2D QUANTUM GRAVITY COUPLED TO RENORMALIZABLE MATTER FIELDS

1994 ◽  
Vol 09 (32) ◽  
pp. 5689-5709 ◽  
Author(s):  
JAN AMBJØRN ◽  
KAZUO GHOROKU
Keyword(s):  
Renormalization Group ◽  
Quantum Gravity ◽  
Effective Action ◽  
Two Dimensional ◽  
Conformally Invariant ◽  
Renormalization Group Equations ◽  
Β Function ◽  
Matter Fields

We consider two-dimensional quantum gravity coupled to matter fields which are renormalizable but not conformally invariant. Questions concerning the β function and the effective action are addressed, and the effective action and the dressed renormalization group equations are determined for various matter potentials.

scholarly journals ANOMALIES AND EFFECTIVE ACTIONS IN TWO-DIMENSIONAL SUPERSPACE

1992 ◽  
Vol 07 (08) ◽  
pp. 1685-1704 ◽  
Author(s):  
FRANÇOIS DELDUC ◽  
FRANÇOIS GIERES
Keyword(s):  
Effective Action ◽  
Riemann Surfaces ◽  
Two Dimensional ◽  
Ward Identities ◽  
Stress Energy ◽  
Super Riemann Surfaces

We derive a chirally split expression for the superdiffeomorphism anomaly in the two-dimensional superplane. The effective action from which this anomaly was obtained is related to the WZ-action associated with the superdiffeomorphism group. Furthermore, we show that the anomalous Ward identities generated by supercoordinate transformations encompass the wellknown OPE’s for the stress-energy supertensor. In conclusion, the extension to generic super Riemann surfaces is discussed.

CORRELATION FUNCTIONS AND ZERO MODES ON HIGHER GENUS RIEMANN SURFACES

1988 ◽  
Vol 03 (04) ◽  
pp. 841-860 ◽  
Author(s):  
M. BONINI ◽  
R. IENGO
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Correlation Functions ◽  
Riemann Surfaces ◽  
Covariant Formulation ◽  
Two Dimensional ◽  
Zero Modes ◽  
Modular Transformation ◽  
Higher Genus

We describe systematically the propagators and the zero modes of the various two dimensional fields which appear in the construction of the scattering amplitudes in the string theory, within the framework of the covariant formulation, and we discuss also their modular transformation properties.

scholarly journals INTERACTIONS OF DISCRETE STATES WITH NONZERO GHOST NUMBER IN c = 1 2D GRAVITY

1992 ◽  
Vol 07 (29) ◽  
pp. 2723-2730 ◽  
Author(s):  
NOBUYOSHI OHTA ◽  
HISAO SUZUKI
Keyword(s):  
Quantum Gravity ◽  
Vertex Operator ◽  
Effective Action ◽  
2D Gravity ◽  
Ghost Number ◽  
Two Dimensional ◽  
Discrete States ◽  
Structure Constants ◽  
Area Preserving ◽  
Operator Representations

We study the interactions of the discrete states with nonzero ghost number in c = 1 two-dimensional (2D) quantum gravity. By using the vertex operator representations, it is shown that their interactions are given by the structure constants of the group of the area preserving diffeomorphism similar to those of vanishing ghost number. The effective action for these states is also worked out. The result suggests that the whole system has a BRST-like symmetry.

THE ORIGIN OF SL(nC) CURRENT ALGEBRA IN GENERALIZED TWO-DIMENSIONAL GRAVITY

1992 ◽  
Vol 07 (18) ◽  
pp. 4353-4375 ◽  
Author(s):  
K. YOSHIDA
Keyword(s):  
Current Algebra ◽  
Riemann Surfaces ◽  
Mathematical Structure ◽  
Two Dimensions ◽  
Projective Structure ◽  
Two Dimensional ◽  
Induced Gravity ◽  
Higher Genus ◽  
Dimensional Gravity

The origin of local SL(nC) symmetry in induced gravity in two dimensions, enlarged with the so-called W fields, is considered on higher genus Riemann surfaces. In the simplest case of W2, the mathematical structure of Polyakov’s two-dimensional gravity precisely corresponds to the projective structure of Riemann surfaces. Some speculations on the generalization to higher Wn algebras are presented.

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