scholarly journals N=1 SUPERCONFORMAL MINIMAL MODEL CORRELATION FUNCTIONS ON THE TORUS

1995 ◽  
Vol 10 (28) ◽  
pp. 3985-4040 ◽  
Author(s):  
A. ABDURRAHMAN ◽  
F. ANTON ◽  
M.A. NAMAZIE ◽  
C. NÚÑEZ
Keyword(s):  
Correlation Functions ◽  
Discrete Series ◽  
Vacuum State ◽  
Coulomb Gas ◽  
Integral Representations ◽  
Conformal Theory ◽  
Fusion Algebra ◽  
Point Correlation ◽  
Superconformal Theories ◽  
Model Correlation

The Coulomb gas formalism is employed to construct contour integral representations of two-point correlation functions on the torus for the N=1 superconformal unitary discrete series, characterized by the single integer p. (For the particular case of the tricritical Ising model, these include the energy and vacancy density operators.) Modular and monodromy properties of the superconformal blocks are examined, and the generalization to superconformal theories of Verlinde’s results on modular transformations and the fusion algebra are discussed in some detail. For p odd the relevant modular matrix is (with respect to a particular basis) symmetric and unitary, as in ordinary rational conformal theory. However, for p even, there appears to be an obstruction due to the Ramond vacuum state.

scholarly journals Line and surface defects for the free scalar field

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Edoardo Lauria ◽  
Pedro Liendo ◽  
Balt C. van Rees ◽  
Xiang Zhao
Keyword(s):  
Scalar Field ◽  
Correlation Functions ◽  
Surface Defects ◽  
Intermediate Result ◽  
Conformal Theory ◽  
Free Theory ◽  
Free Spectrum ◽  
Point Correlation ◽  
Free Scalar ◽  
Almost All

Abstract For a single free scalar field in d ≥ 2 dimensions, almost all the unitary conformal defects must be ‘trivial’ in the sense that they cannot hold interesting dynamics. The only possible exceptions are monodromy defects in d ≥ 4 and co-dimension three defects in d ≥ 5. As an intermediate result we show that the n-point correlation functions of a conformal theory with a generalized free spectrum must be those of the generalized free theory.

scholarly journals A Bäcklund Transformation for Elliptic Four-Point Conformal Blocks

2018 ◽  
Vol 30 (07) ◽  
pp. 1840012
Author(s):  
André Neveu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Correlation Functions ◽  
Integral Transformation ◽  
Bäcklund Transformation ◽  
Integral Representations ◽  
Liouville Theory ◽  
Partial Differential ◽  
Conformal Blocks ◽  
Point Correlation

We apply an integral transformation to solutions of a partial differential equation for the five-point correlation functions in Liouville theory on a sphere with one degenerate field [Formula: see text]. By repeating this transformation, we can reach a whole lattice of values for the conformal dimensions of the four other operators. Factorizing out the degenerate field leads to integral representations of the corresponding four-point conformal blocks. We illustrate this procedure on the elliptic conformal blocks discovered in a previous publication.

scholarly journals THE MASSLESS XXZ CHAIN WITH A BOUNDARY

2001 ◽  
Vol 16 (03) ◽  
pp. 409-424 ◽  
Author(s):  
TAKEO KOJIMA
Keyword(s):  
Correlation Functions ◽  
Free Field ◽  
Vacuum State ◽  
Integral Representations ◽  
Xxz Chain

We study the XXZ chain with a boundary at massless regime -1<Δ<1. We give the free field realizations of the boundary vacuum state and its dual. Using these realizations, we give the integral representations for the correlation functions.

THREE-POINT CORRELATION FUNCTIONS OF THE MINIMAL CONFORMAL THEORIES COUPLED TO 2D GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3601-3612 ◽  
Author(s):  
Vl. S. DOTSENKO
Keyword(s):  
Operator Algebra ◽  
Correlation Functions ◽  
2D Gravity ◽  
Coulomb Gas ◽  
Field Theories ◽  
Algebra Structure ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Point Correlation ◽  
Structure Constants

The general three-point correlation functions of the minimal conformal field theories coupled to gravity are calculated using the specific Coulomb gas type quantization technique. The gravity interaction modifies in an essential way the operator algebra of the corresponding minimal model, in particular in canceling the decoupling of a finite number of primary fields, in case of rational theories. This is suggested to be related to the appearance of new physical states, under the BRST analysis of Lian and Zuckerman. Within the analytic technique, this effect is due to the corresponding singularities of the gravity sector operator algebra structure constants.

scholarly journals THE FREE FIELD REPRESENTATION OF SU(3) CONFORMAL FIELD THEORY

1993 ◽  
Vol 08 (23) ◽  
pp. 4031-4053
Author(s):  
HOVIK D. TOOMASSIAN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Free Field ◽  
Field Representation ◽  
Conformal Field ◽  
Point Correlation

The structure of the free field representation and some four-point correlation functions of the SU(3) conformal field theory are considered.

scholarly journals From correlation functions to event shapes in QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Event Shape ◽  
Proof Of Concept ◽  
Yang Mills ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Event Shapes ◽  
A Charge ◽  
Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

scholarly journals Towards a self-consistent analysis of the anisotropic galaxy two- and three-point correlation functions on large scales: application to mock galaxy catalogues

2020 ◽  
Author(s):  
Naonori S Sugiyama ◽  
Shun Saito ◽  
Florian Beutler ◽  
Hee-Jong Seo
Keyword(s):  
Correlation Functions ◽  
Hubble Parameter ◽  
Theoretical Models ◽  
Practical Method ◽  
Acoustic Oscillation ◽  
Nonlinear Damping ◽  
Joint Analysis ◽  
Angular Diameter Distance ◽  
Point Correlation ◽  
Parameter Constraints

Abstract We establish a practical method for the joint analysis of anisotropic galaxy two- and three-point correlation functions (2PCF and 3PCF) on the basis of the decomposition formalism of the 3PCF using tri-polar spherical harmonics. We perform such an analysis with MultiDark Patchy mock catalogues to demonstrate and understand the benefit of the anisotropic 3PCF. We focus on scales above 80 h−1 Mpc, and use information from the shape and the baryon acoustic oscillation (BAO) signals of the 2PCF and 3PCF. We also apply density field reconstruction to increase the signal-noise ratio of BAO in the 2PCF measurement, but not in the 3PCF measurement. In particular, we study in detail the constraints on the angular diameter distance and the Hubble parameter. We build a model of the bispectrum or 3PCF that includes the nonlinear damping of the BAO signal in redshift space. We carefully account for various uncertainties in our analysis including theoretical models of the 3PCF, window function corrections, biases in estimated parameters from the fiducial values, the number of mock realizations to estimate the covariance matrix, and bin size. The joint analysis of the 2PCF and 3PCF monopole and quadrupole components shows a $30\%$ and $20\%$ improvement in Hubble parameter constraints before and after reconstruction of the 2PCF measurements, respectively, compared to the 2PCF analysis alone. This study clearly shows that the anisotropic 3PCF increases cosmological information from galaxy surveys and encourages further development of the modeling of the 3PCF on smaller scales than we consider.

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.

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.

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