Coulomb integrals and conformal blocks in theAdS3-WZNW model

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.

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MONODROMY OF SOLUTIONS OF THE KNIZHNIK-ZAMOLODCHIKOV EQUATION: SL(2)k WZNW MODEL

International Journal of Modern Physics A ◽

10.1142/s0217751x04020506 ◽

2004 ◽

Vol 19 (supp02) ◽

pp. 336-347

Author(s):

B. PONSOT

Keyword(s):

Field Theory ◽

Conformal Blocks ◽

Wznw Model ◽

Liouville Field Theory ◽

Zamolodchikov Equation

Three explicit and equivalent representations for the monodromy of the conformal blocks in the non compact SL(2)k WZNW model are proposed in terms of the same quantity computed in Liouville field theory.

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Conformal blocks and correlators in a bosonized WZNW model

JETP Letters ◽

10.1134/1.568242 ◽

1999 ◽

Vol 70 (10) ◽

pp. 659-665

Author(s):

K. A. Saraikin

Keyword(s):

Conformal Blocks ◽

Wznw Model

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N = 3 AND N = 4 SUPERCONFORMAL WZNW SIGMA MODELS IN SUPERSPACE II: THE N = 4 CASE

International Journal of Modern Physics A ◽

10.1142/s0217751x92000181 ◽

1992 ◽

Vol 07 (02) ◽

pp. 287-316 ◽

Cited By ~ 8

Author(s):

E. A. IVANOV ◽

S. O. KRIVONOS ◽

V. M. LEVIANT

Keyword(s):

Sigma Models ◽

Conformal Blocks ◽

Wznw Model ◽

Chiral Superfields ◽

Zamolodchikov Equation

The issues related to the U (1) × O (4) N = 4 superconformal WZNW sigma models [with the bosonic target spaces U (1) × SU (2) and U (1) × U (1) × O (4)] are investigated in the framework of a 2D N = 4 superspace. We define the corresponding N = 4 supercurrents, both on classical and quantum levels, in terms of the basic primary N = 4 WZNW superfields and show that the generalized Sugawara form for the dimension 3/2 and 2 component currents directly follows from the constraints on the basic superfields. The N = 4 superfield analog of the Knizhnik–Zamolodchikov equation for conformal blocks in WZNW sigma models is derived. We also analyze the N = 4 WZNW superfields from the standpoint of two SU(2) N = 4 SCAs entering as subalgebras into the underlying U (1) × O (4) N = 4 SCA. We demonstrate that in the linearizing limit the U (1) × SU (2) WZNW model reproduces the recently discussed SU(2) N = 4 superconformal system of free chiral superfields.

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Towards Feynman rules for conformal blocks

Journal of High Energy Physics ◽

10.1007/jhep01(2021)005 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Sarah Hoback ◽

Sarthak Parikh

Keyword(s):

Field Theory ◽

Effective Field Theory ◽

Hypergeometric Functions ◽

Power Series Expansion ◽

Effective Field ◽

Conformal Block ◽

Tree Level ◽

Conformal Blocks ◽

Simple Set ◽

Feynman Rules

Abstract We conjecture a simple set of “Feynman rules” for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the “OPE channel.” The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper.

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A simple approximation for inverse distance with application to the one‐center and two‐center Coulomb integrals

The Journal of Chemical Physics ◽

10.1063/1.449258 ◽

1985 ◽

Vol 83 (5) ◽

pp. 2616-2618 ◽

Cited By ~ 2

Author(s):

S. Noor Mohammad

Keyword(s):

Simple Approximation ◽

The One ◽

Coulomb Integrals ◽

Inverse Distance

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Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

Journal of High Energy Physics ◽

10.1007/jhep12(2020)019 ◽

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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Dispersion formulas in QFTs, CFTs and holography

Journal of High Energy Physics ◽

10.1007/jhep05(2021)098 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

David Meltzer

Keyword(s):

Fourier Transform ◽

Correlation Functions ◽

Momentum Space ◽

Conformal Blocks ◽

Dispersion Formula ◽

Space Dispersion

Abstract We study momentum space dispersion formulas in general QFTs and their applications for CFT correlation functions. We show, using two independent methods, that QFT dispersion formulas can be written in terms of causal commutators. The first derivation uses analyticity properties of retarded correlators in momentum space. The second derivation uses the largest time equation and the defining properties of the time-ordered product. At four points we show that the momentum space QFT dispersion formula depends on the same causal double-commutators as the CFT dispersion formula. At n-points, the QFT dispersion formula depends on a sum of nested advanced commutators. For CFT four-point functions, we show that the momentum space dispersion formula is equivalent to the CFT dispersion formula, up to possible semi-local terms. We also show that the Polyakov-Regge expansions associated to the momentum space and CFT dispersion formulas are related by a Fourier transform. In the process, we prove that the momentum space conformal blocks of the causal double-commutator are equal to cut Witten diagrams. Finally, by combining the momentum space dispersion formulas with the AdS Cutkosky rules, we find a complete, bulk unitarity method for AdS/CFT correlators in momentum space.

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