scholarly journals Gaudin models and multipoint cnformal blocks: general theory

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Ilija Burić ◽  
Sylvain Lacroix ◽  
Jeremy A. Mann ◽  
Lorenzo Quintavalle ◽  
Volker Schomerus
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Differential Operators ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Commuting Differential Operators ◽  
Higher Dimensional ◽  
Important Open Problem ◽  
Complete Set ◽  
Gaudin Models

Abstract The construction of conformal blocks for the analysis of multipoint correlation functions with N > 4 local field insertions is an important open problem in higher dimensional conformal field theory. This is the first in a series of papers in which we address this challenge, following and extending our short announcement in [1]. According to Dolan and Osborn, conformal blocks can be determined from the set of differential eigenvalue equations that they satisfy. We construct a complete set of commuting differential operators that characterize multipoint conformal blocks for any number N of points in any dimension and for any choice of OPE channel through the relation with Gaudin integrable models we uncovered in [1]. For 5-point conformal blocks, there exist five such operators which are worked out smoothly in the dimension d.

scholarly journals Gaudin models and multipoint conformal blocks. Part II. Comb channel vertices in 3D and 4D

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Ilija Burić ◽  
Sylvain Lacroix ◽  
Jeremy Mann ◽  
Lorenzo Quintavalle ◽  
Volker Schomerus
Keyword(s):  
Differential Operators ◽  
Arbitrary Dimension ◽  
Tensor Fields ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Higher Dimensional ◽  
Sutherland Model ◽  
Joint Eigenfunctions ◽  
Space Formalism ◽  
Gaudin Models

Abstract It was recently shown that multi-point conformal blocks in higher dimensional conformal field theory can be considered as joint eigenfunctions for a system of commuting differential operators. The latter arise as Hamiltonians of a Gaudin integrable system. In this work we address the reduced fourth order differential operators that measure the choice of 3-point tensor structures for all vertices of 3- and 4-dimensional comb channel conformal blocks. These vertices come associated with a single cross ratio. Remarkably, we identify the vertex operators as Hamiltonians of a crystallographic elliptic Calogero-Moser-Sutherland model that was discovered originally by Etingof, Felder, Ma and Veselov. Our construction is based on a further development of the embedding space formalism for mixed-symmetry tensor fields. The results thereby also apply to comb channel vertices of 5- and 6-point functions in arbitrary dimension.

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.

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.

The search for higher symmetry in string theory

1989 ◽  
Vol 329 (1605) ◽  
pp. 349-357 ◽  
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
String Theory ◽  
Vantage Point ◽  
Higher Symmetry ◽  
Conformal Field ◽  
Soluble Model ◽  
Higher Dimensional ◽  
Dimensional Gravity

Some remarks are made about the nature and role of the search for higher symmetry in string theory. These symmetries are most likely to be uncovered in a mysterious ‘unbroken phase’, for which (2+ 1)-dimensional gravity provides an interesting and soluble model. New insights about conformal field theory, in which one gets ‘out of flatland’ to see a wider symmetry from a higher-dimensional vantage point, may offer clues to the unbroken phase of string theory

scholarly journals KERR–BOLT SPACETIMES AND KERR/CFT CORRESPONDENCE

2012 ◽  
Vol 27 (08) ◽  
pp. 1250046 ◽  
Author(s):  
A. M. GHEZELBASH
Keyword(s):  
Field Theory ◽  
Boundary Condition ◽  
Black Hole ◽  
Conformal Field Theory ◽  
Virasoro Algebra ◽  
Conformal Field ◽  
Higher Dimensional ◽  
Dimensional Black Hole ◽  
Horizon Geometry ◽  
Cardy Formula

We study the extremal rotating spacetimes with a NUT twist in the context of recently proposed Kerr/CFT correspondence. The Kerr/CFT correspondence states that the near-horizon states of an extremal four (or higher) dimensional black hole could be identified with a certain chiral conformal field theory. The corresponding Virasoro algebra is generated with a class of diffeomorphism which preserves an appropriate boundary condition on the near-horizon geometry. We combine the calculated central charges with the expected form of the temperature, using the Cardy formula to obtain the microscopically entropy of the extremal rotating spacetimes with a NUT twist. All results are in agreement with the macroscopic entropy of the extremal spacetimes.

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 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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