scholarly journals General solution of an exact correlation function factorization in conformal field theory

2009 ◽  
Vol 2009 (10) ◽  
pp. P10002 ◽  
Author(s):  
Jacob J H Simmons ◽  
Peter Kleban
2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ilija Burić ◽  
Volker Schomerus

Abstract We develop a group theoretical formalism to study correlation functions in defect conformal field theory, with multiple insertions of bulk and defect fields. This formalism is applied to construct the defect conformal blocks for three-point functions of scalar fields. Starting from a configuration with one bulk and one defect field, for which the correlation function is determined by conformal symmetry, we explore two possibilities, adding either one additional defect or bulk field. In both cases it is possible to express the blocks in terms of classical hypergeometric functions, though the case of two bulk and one defect field requires Appell’s function F4.


2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  


1993 ◽  
Vol 08 (23) ◽  
pp. 4031-4053
Author(s):  
HOVIK D. TOOMASSIAN

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


2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Adolfo del Campo ◽  
Tadashi Takayanagi

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yuan Yao ◽  
Akira Furusaki

AbstractWe formulate a ℤk-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising duality atk= 2. The ℤk-parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their criticality cannot be described by any existing conformal field theory. The modular transformations of these parafermionic low-energy critical theories as general consistency conditions are found to be unconventional in that their partition functions on a torus transform differently from any conformal field theory whenk >2. Explicit forms of partition functions are obtained by the developed parafermionization for a large class of critical ℤk-parafermionic chains, whose operator contents are intrinsically distinct from any bosonic or fermionic model in terms of conformal spins and statistics. We also use the parafermionization to exhaust all the ℤk-parafermionic minimal models, complementing earlier works on fermionic cases.


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