scholarly journals Defect conformal blocks from Appell functions

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ilija Burić ◽  
Volker Schomerus
Keyword(s):  
Field Theory ◽  
Correlation Function ◽  
Conformal Field Theory ◽  
Hypergeometric Functions ◽  
Conformal Symmetry ◽  
Scalar Fields ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Additional Defect ◽  
Appell Functions

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.

scholarly journals NONCOMMUTATIVE CONFORMAL FIELD THEORY IN THE TWIST-DEFORMED CONTEXT

2008 ◽  
Vol 23 (39) ◽  
pp. 3307-3315 ◽  
Author(s):  
FEDELE LIZZI ◽  
PATRIZIA VITALE
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Noncommutative Geometry ◽  
Conformal Symmetry ◽  
Two Dimensional ◽  
Moyal Product ◽  
Conformal Field ◽  
Noncommutative Plane

We discuss conformal symmetry on the two-dimensional noncommutative plane equipped with Moyal product in the twist deformed context. We show that the consistent use of the twist procedure leads to results which are free from ambiguities. This lends support to the importance of the use of twist symmetries in noncommutative geometry.

ANYONS AND GAUSSIAN CONFORMAL FIELD THEORIES

1991 ◽  
Vol 06 (04) ◽  
pp. 289-294 ◽  
Author(s):  
DILEEP P. JATKAR ◽  
SUMATHI RAO
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Mass Parameter ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Conformal Blocks ◽  
Conformal Field ◽  
A Charge ◽  
Chern Simons ◽  
Chern Simons Theory

We identify the spin of the anyons with the holomorphic dimension of the primary fields of a Gaussian conformal field theory. The angular momentum addition rules for anyons go over to the fusion rules for the primary fields and the r↔1/2r duality of the Gaussian CFT is reproduced by a charge-flux duality of the anyons. For a U(1) Chern-Simons theory with topological mass parameter k=2n, N-anyon states on the torus have 2n components, which correspond to the 2n conformal blocks of an N-point function in the Gaussian conformal field theory.

scholarly journals Effects of non-conformal boundary on entanglement entropy

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Andrew Loveridge
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Conformal Field Theory ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Conformal Symmetry ◽  
Entanglement Entropy ◽  
Mixed Boundary Conditions ◽  
De Sitter ◽  
Conformal Field

Abstract Spacetime boundaries with canonical Neuman or Dirichlet conditions preserve conformal invarience, but “mixed” boundary conditions which interpolate linearly between them can break conformal symmetry and generate interesting Renormalization Group flows even when a theory is free, providing soluble models with nontrivial scale dependence. We compute the (Rindler) entanglement entropy for a free scalar field with mixed boundary conditions in half Minkowski space and in Anti-de Sitter space. In the latter case we also compute an additional geometric contribution, which according to a recent proposal then collectively give the 1/N corrections to the entanglement entropy of the conformal field theory dual. We obtain some perturbatively exact results in both cases which illustrate monotonic interpolation between ultraviolet and infrared fixed points. This is consistent with recent work on the irreversibility of renormalization group, allowing some assessment of the aforementioned proposal for holographic entanglement entropy and illustrating the generalization of the g-theorem for boundary conformal field theory.

scholarly journals A CONFORMAL FIELD THEORY DESCRIPTION OF THE PAIRED AND PARAFERMIONIC STATES IN THE QUANTUM HALL EFFECT

2000 ◽  
Vol 15 (27) ◽  
pp. 1679-1688 ◽  
Author(s):  
GERARDO CRISTOFANO ◽  
GIUSEPPE MAIELLA ◽  
VINCENZO MAROTTA
Keyword(s):  
Field Theory ◽  
Wave Function ◽  
Conformal Field Theory ◽  
Quantum Hall Effect ◽  
Ground State ◽  
Quantum Hall ◽  
Scalar Fields ◽  
Neutral Component ◽  
Conformal Field ◽  
Twisted Boundary Conditions

We extend the construction of the effective conformal field theory for the Jain hierarchical fillings proposed in Ref. 1 to the description of a quantum Hall fluid at nonstandard fillings [Formula: see text]. The chiral primary fields are found by using a procedure which induces twisted boundary conditions on the m scalar fields; they appear as composite operators of a charged and neutral component. The neutral modes describe parafermions and contribute to the ground state wave function with a generalized Pfaffian term. Correlators of Ne electrons in the presence of quasi-hole excitations are explicitly given for m=2.

RESHETIKHIN-TURAEV AND CRANE-KOHNO-KONTSEVICH 3-MANIFOLD INVARIANTS COINCIDE

1993 ◽  
Vol 02 (01) ◽  
pp. 65-95 ◽  
Author(s):  
SERGEY PIUNIKHIN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Explicit Formula ◽  
Quantum Groups ◽  
Jones Polynomial ◽  
Matrix Elements ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Wznw Model ◽  
The Matrix

The coincidence of two different presentations of Witten 3-manifold invariants is proved. One of them, invented by Reshetikhin and Turaev, is based on the surgery presentation a of 3-manifold and the representation theory of quantum groups; another one, invented by Kohno and Crane and, in slightly different language by Kontsevich, is based on a Heegaard decomposition of a 3-manifold and representations of the Teichmuller group, arising in conformal field theory. The explicit formula for the matrix elements of generators of the Teichmuller group in the space of conformal blocks in the SU(2) k, WZNW-model is given,using the Jones polynomial of certain links.

scholarly journals 4-point function from conformally coupled scalar in AdS6

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Jae-Hyuk Oh
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Ward Identity ◽  
Conformal Symmetry ◽  
Classical Solutions ◽  
Point Function ◽  
Conformal Theory ◽  
Conformal Field ◽  
Linear Limit

Abstract We explore conformally coupled scalar theory in AdS6 extensively and their classical solutions by employing power expansion order by order in its self-interaction coupling λ. We describe how we get the classical solutions by diagrammatic ways which show general rules constructing the classical solutions. We study holographic correlation functions of scalar operator deformations to a certain 5-dimensional conformal field theory where the operators share the same scaling dimension ∆ = 3, from the classical solutions. We do not assume any specific form of the micro Lagrangian density of the 5-dimensional conformal field theory. For our solutions, we choose a scheme where we remove co-linear divergences of momenta along the AdS boundary directions which frequently appear in the classical solutions. This shows clearly that the holographic correlation functions are free from the co-linear divergences. It turns out that this theory provides correct conformal 2- and 3- point functions of the ∆ = 3 scalar operators as expected in previous literature. It makes sense since 2- and 3- point functions are determined by global conformal symmetry not being dependent on the details of the conformal theory. We also get 4-point function from this holographic model. In fact, it turns out that the 4-point correlation function is not conformal because it does not satisfy the special conformal Ward identity although it does dilation Ward identity and respect SO(5) rotation symmetry. However, in the co-linear limit that all the external momenta are in a same direction, the 4-point function is conformal which means that it satisfy the special conformal Ward identity. We inspect holographic n-point functions of this theory which can be obtained by employing a certain Feynman-like rule. This rule is a construction of n-point function by connecting l-point functions each other where l < n. In the co-linear limit, these n-point functions reproduce the conformal n-point functions of ∆ = 3 scalar operators in d = 5 Euclidean space addressed in arXiv:2001.05379.

scholarly journals SEMICLASSICAL BLOCKS AND CORRELATORS IN RATIONAL AND IRRATIONAL CONFORMAL FIELD THEORY

1996 ◽  
Vol 11 (27) ◽  
pp. 4837-4896 ◽  
Author(s):  
M. B. HALPERN ◽  
N. A. OBERS
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Simple Class ◽  
High Level

The generalized Knizhnik–Zamolodchikov equations of irrational conformal field theory provide a uniform description of rational and irrational conformal field theory. Starting from the known high-level solution of these equations, we first construct the high-level conformal blocks and correlators of all the affine-Sugawara and coset constructions on simple g. Using intuition gained from these cases, we then identify a simple class of irrational processes whose high-level blocks and correlators we are also able to construct.

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