scholarly journals Correlation functions and vertex operators of Liouville theory

2004 ◽  
Vol 581 (1-2) ◽  
pp. 133-140 ◽  
Author(s):  
George Jorjadze ◽  
Gerhard Weigt
Keyword(s):  
Correlation Functions ◽  
Liouville Theory ◽  
Vertex Operators

scholarly journals Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yifei He ◽  
Jesper Lykke Jacobsen ◽  
Hubert Saleur
Keyword(s):  
Potts Model ◽  
Correlation Functions ◽  
Liouville Theory ◽  
Analytical Determination ◽  
Conformal Weight ◽  
Two Dimensional ◽  
Conformal Blocks ◽  
Conformal Bootstrap ◽  
Point Correlation

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

LANDAU LEVELS AND VERTEX OPERATIONS FOR ANYONS

1991 ◽  
Vol 06 (30) ◽  
pp. 2819-2826 ◽  
Author(s):  
GERALD V. DUNNE ◽  
ALBERTO LERDA ◽  
CARLO A. TRUGENBERGER
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
External Magnetic Field ◽  
String Theory ◽  
Ground State ◽  
Correlation Functions ◽  
Landau Levels ◽  
Vertex Operators ◽  
Many Body

We construct exact many-body eigenstates of both energy and angular momentum for the N-anyon problem in an external magnetic field. We show that such states span the full ground state eigenspace and arise as correlation functions of Fubini-Veneziano vertex operators of string theory.

RANDOM SURFACES AND THE LIOUVILLE THEORY

1992 ◽  
Vol 07 (15) ◽  
pp. 3403-3433 ◽  
Author(s):  
Y. KITAZAWA
Keyword(s):  
Black Holes ◽  
Physical Properties ◽  
Correlation Functions ◽  
Two Dimensions ◽  
Liouville Theory ◽  
View Point ◽  
Complete Understanding ◽  
Random Surfaces ◽  
Dimensional Gravity ◽  
The Continuum

We review the physical properties of random surfaces from the view point of the continuum Liouville theory. We shall summarize physical motivations of this subject and the field-theoretic treatment of the random surfaces. In the case of subcritical strings propagating in less than two dimensions, a complete understanding has been obtained recently through matrix models. We discuss the Liouville theory understanding of these results by studying the correlation functions. We also discuss promising avenues of further investigations such as black holes in 2-dimensional gravity and 3- and 4-dimensional string theory which may be relevant to Ising 3 and QCD 4.

Correlation functions in Liouville theory

1991 ◽  
Vol 66 (16) ◽  
pp. 2051-2055 ◽  
Author(s):  
M. Goulian ◽  
M. Li
Keyword(s):  
Correlation Functions ◽  
Liouville Theory

scholarly journals Free boson representation ofq-vertex operators and their correlation functions

1993 ◽  
Vol 157 (1) ◽  
pp. 119-137 ◽  
Author(s):  
Akishi Kato ◽  
Yas-Hiro Quano ◽  
Jun'ichi Shiraishi
Keyword(s):  
Correlation Functions ◽  
Vertex Operators ◽  
Free Boson ◽  
Boson Representation

scholarly journals A LECTURE ON THE LIOUVILLE VERTEX OPERATORS (REVIEW)

2004 ◽  
Vol 19 (supp02) ◽  
pp. 436-458 ◽  
Author(s):  
J. TESCHNER
Keyword(s):  
Free Field ◽  
Liouville Theory ◽  
Vertex Operators ◽  
Continuous Family ◽  
Matrix Elements ◽  
Crossing Symmetry ◽  
The Matrix

We reconsider the construction of exponential fields in the quantized Liouville theory. It is based on a free-field construction of a continuous family or chiral vertex operators. We derive the fusion and braid relations of the chiral vertex operators. This allows us to simplify the verification of locality and crossing symmetry of the exponential fields considerably. The calculation of the matrix elements of the exponential fields leads to a constructive derivation of the formula proposed by Dorn/Otto and the brothers Zamolodchikov.

scholarly journals LIOUVILLE THEORY: WARD IDENTITIES FOR GENERATING FUNCTIONAL AND MODULAR GEOMETRY

1994 ◽  
Vol 09 (25) ◽  
pp. 2293-2299 ◽  
Author(s):  
LEON A. TAKHTAJAN
Keyword(s):  
Moduli Spaces ◽  
Correlation Functions ◽  
Riemann Surfaces ◽  
Central Charge ◽  
Perturbation Expansion ◽  
Liouville Theory ◽  
Energy Tensor ◽  
Ward Identities ◽  
Generating Functional ◽  
Local Index

We continue the study of quantum Liouville theory through Polyakov’s functional integral,1,2 started in Ref. 3. We derive the perturbation expansion for Schwinger’s generating functional for connected multi-point correlation functions involving stress-energy tensor, give the “dynamical” proof of the Virasoro symmetry of the theory and compute the value of the central charge, confirming previous calculation in Ref. 3. We show that conformal Ward identities for these correlation functions contain such basic facts from Kähler geometry of moduli spaces of Riemann surfaces, as relation between accessory parameters for the Fuchsian uniformization, Liouville action and Eichler integrals, Kähler potential for the Weil-Petersson metric, and local index theorem. These results affirm the fundamental role that universal Ward identities for the generating functional play in Friedan-Shenker modular geometry.4

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