scholarly journals ON THE LIOUVILLE APPROACH TO CORRELATION FUNCTIONS FOR 2D QUANTUM GRAVITY

1992 ◽  
Vol 07 (03) ◽  
pp. 235-249 ◽  
Author(s):  
KENICHIRO AOKI ◽  
ERIC D’HOKER
Keyword(s):  
Quantum Gravity ◽  
Correlation Functions ◽  
Functional Integral ◽  
Two Dimensions ◽  
Minimal Models ◽  
Point Function

We evaluate the three-point function for arbitrary states in bosonic minimal models on the sphere coupled to quantum gravity in two dimensions. The validity of the formal continuation in the number of Liouville screening charge insertions is shown directly from the Liouville functional integral using semi-classical methods.

CORRELATION FUNCTIONS OF σ FIELDS WITH VALUES IN A HYPERBOLIC SPACE

1989 ◽  
Vol 04 (01) ◽  
pp. 267-286 ◽  
Author(s):  
Z. HABA
Keyword(s):  
Field Theory ◽  
Hyperbolic Space ◽  
Half Plane ◽  
Correlation Functions ◽  
Functional Integral ◽  
Two Dimensions ◽  
Hyperbolic Spaces ◽  
Conformal Invariant ◽  
Upper Half Plane

It is shown that the functional integral for a σ field with values in the Poincare upper half-plane (and some other hyperbolic spaces) can be performed explicitly resulting in a conformal invariant noncanonical field theory in two dimensions.

QUANTUM GRAVITY IN TWO DIMENSIONS

1987 ◽  
Vol 02 (11) ◽  
pp. 893-898 ◽  
Author(s):  
A. M. POLYAKOV
Keyword(s):  
Differential Equations ◽  
Quantum Gravity ◽  
Current Algebra ◽  
Correlation Functions ◽  
Light Cone ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Light Cone Gauge

Two dimensional induced quantum gravity is analyzed. By the use of light-cone gauge we derive a gravitational analogue of the Wess-Zumino action and discover its amazing connection with SL (2, ℝ) current algebra. The latter permits us to find differential equations for the correlation functions.

scholarly journals CORRELATION FUNCTIONS OF MINIMAL MODELS COUPLED TO TWO-DIMENSIONAL QUANTUM SUPERGRAVITY

1992 ◽  
Vol 07 (04) ◽  
pp. 333-343 ◽  
Author(s):  
KENICHIRO AOKI ◽  
ERIC D’HOKER
Keyword(s):  
Correlation Functions ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Minimal Models ◽  
Point Correlation ◽  
Bosonic Case

We compute the three-point functions of Neveu-Schwarz primary fields of the minimal models on the sphere when coupled to supergravity in two dimensions. The results show that the three-point correlation functions are determined by the scaling dimensions of the fields, as in the bosonic case.

Radiative corrections in two-dimensional gravity

1992 ◽  
Vol 70 (2-3) ◽  
pp. 110-113
Author(s):  
D. G. C. McKeon ◽  
C. Wong
Keyword(s):  
Models Of Quantum Gravity ◽  
Quantum Gravity ◽  
Two Dimensions ◽  
Radiative Corrections ◽  
Two Dimensional ◽  
Point Function ◽  
Perturbative Calculations ◽  
Gravitational Action ◽  
Flat Background ◽  
Dimensional Gravity

It is shown how one can do perturbative calculations about a flat background in two-dimensional models of quantum gravity. The Jackiw–Teitelboim model and the induced gravitational action of Polyakov are considered. A suitable choice of gauge allows one to employ operator regularization, a symmetry-preserving procedure that is particularly convenient as it does not alter the dimensionality of these models, allowing one to exploit some properties peculiar to two dimensions. A specific example is provided by the graviton two-point function.

scholarly journals Correlation functions in finite temperature CFT and black hole singularities

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
D. Rodriguez-Gomez ◽  
J.G. Russo
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Correlation Functions ◽  
Finite Temperature ◽  
Proper Time ◽  
Black Brane ◽  
Point Function ◽  
Black Hole Singularity ◽  
Point Correlation ◽  
Scaling Dimension

Abstract We compute thermal 2-point correlation functions in the black brane AdS5 background dual to 4d CFT’s at finite temperature for operators of large scaling dimension. We find a formula that matches the expected structure of the OPE. It exhibits an exponentiation property, whose origin we explain. We also compute the first correction to the two-point function due to graviton emission, which encodes the proper time from the event horizon to the black hole singularity.

Functional Solution Scheme for Relativistic Strong Coupling Theor

1964 ◽  
Vol 19 (7-8) ◽  
pp. 828-834
Author(s):  
G. Heber ◽  
H. J. Kaiser
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Functional Integral ◽  
The Self ◽  
Matrix Elements ◽  
Point Function ◽  
Expectation Value ◽  
Lattice Space ◽  
S Matrix ◽  
Functional Solution

The vacuum expectation value of the S-matrix is represented, following HORI, as a functional integral and separated according to Svac=exp( — i W) ∫ D φ exp( —i ∫ dx Lw). Now, the functional integral involves only the part Lw of the Lagrangian without derivatives and can be easily calculated in lattice space. We propose a graphical scheme which formalizes the action of the operator W = f dx dy δ (x—y) (δ/δ(y))⬜x(δ/δ(x)) . The scheme is worked out in some detail for the calculation of the two-point-function of neutral BOSE fields with the self-interaction λ φM for even M. A method is proposed which under certain convergence assumptions should yield in a finite number of steps the lowest mass eigenvalues and the related matrix elements. The method exhibits characteristic differences between renormalizable and nonrenormalizable theories.

scholarly journals SUPERCONFORMAL 2D MINIMAL MODELS AND AN UNUSUAL COSET CONSTRUCTION

1993 ◽  
Vol 08 (09) ◽  
pp. 851-859 ◽  
Author(s):  
M. YU. LASHKEVICH
Keyword(s):  
Correlation Functions ◽  
Minimal Models ◽  
Coset Construction ◽  
Point Correlation

We consider a coset construction of minimal models. We define it rigorously and prove that it gives superconformal minimal models. This construction allows us to build all primary fields of superconformal models and to calculate their tree-point correlation functions.

scholarly journals On 2d CFTs that interpolate between minimal models

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Sylvain Ribault
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Exactly Solvable ◽  
Structure Constants

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.

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