COSET CONSTRUCTION SU(2)k × SU(2)l/SU(2)k+l AND MINIMAL-LIKE THEORIES

1993 ◽  
Vol 08 (13) ◽  
pp. 1243-1258
Author(s):  
M. YU. LASHKEVICH
Keyword(s):  
Conformal Blocks ◽  
Coset Construction

The equivalence of SU (2)k × SU (2)l/ SU (2)k+l coset constructions and some bosonic theories are proved. The connection between conformal blocks of coset construction and of SU (2)N theories has been found. Currents in coset construction are discussed.

Coset Constructions of Conformal Blocks

1997 ◽  
Vol 11 (19) ◽  
pp. 2311-2332
Author(s):  
Takeshi Ikeda
Keyword(s):  
Ising Model ◽  
Minimal Model ◽  
Virasoro Algebra ◽  
Conformal Blocks ◽  
Coset Construction

On the basis of the coset construction, we obtained canonical maps that relate the sheaf of conformal blocks of the Wess–Zumino–Witten model to those of the unitarizable Virasoro minimal model. We conjectured that the maps are isomorphisms. Making use of spinor realizations, we confirmed the conjecture for the case of the Ising model. We also discussed the coherency of the sheaf of conformal blocks for the Virasoro algebra.

scholarly journals Towards Feynman rules for conformal blocks

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.

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.

scholarly journals Dispersion formulas in QFTs, CFTs and holography

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.

scholarly journals Combinatorial expansions of conformal blocks

2010 ◽  
Vol 164 (1) ◽  
pp. 831-852 ◽  
Author(s):  
A. V. Marshakov ◽  
A. D. Mironov ◽  
A. Yu. Morozov
Keyword(s):  
Conformal Blocks

scholarly journals U(1) Chern-Simons theory and c=1 conformal blocks

1989 ◽  
Vol 223 (1) ◽  
pp. 61-66 ◽  
Author(s):  
Michiel Bos ◽  
V.P. Nair
Keyword(s):  
Simons Theory ◽  
Conformal Blocks ◽  
Chern Simons ◽  
Chern Simons Theory

TETRAHEDRA AND POLYNOMIAL EQUATIONS IN TOPOLOGICAL FIELD THEORY

1991 ◽  
Vol 06 (20) ◽  
pp. 3571-3598 ◽  
Author(s):  
NOUREDDINE CHAIR ◽  
CHUAN-JIE ZHU
Keyword(s):  
Field Theory ◽  
Topological Field Theory ◽  
Fundamental Representation ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Witten Theory ◽  
Topological Field ◽  
General Program ◽  
The One ◽  
Chern Simons

Some tetrahedra in SUk(2) Chern-Simons-Witten theory are computed. The results can be used to compute an arbitrary tetrahedron inductively by fusing with the fundamental representation. The results obtained are in agreement with those of quantum groups. By associating a (finite) topological field theory (FTFT) to every rational conformal field theory (RCFT), we show that the pentagon and hexagon equations in RCFT follow directly from some skein relations in FTFT. By generalizing the operation of surgery on links in FTFT, we also derive an explicit expression for the modular transformation matrix S(k) of the one-point conformal blocks on a torus in RCFT and the equations satisfied by S(k), in agreement with those required in RCFT. The implication of our results on the general program of classifying RCFT is also discussed.

scholarly journals Isomonodromic Tau-Functions from Liouville Conformal Blocks

2014 ◽  
Vol 336 (2) ◽  
pp. 671-694 ◽  
Author(s):  
N. Iorgov ◽  
O. Lisovyy ◽  
J. Teschner
Keyword(s):  
Conformal Blocks ◽  
Tau Functions

scholarly journals Conformal blocks on elliptic curves and the Knizhnik-Zamolodchikov-Bernard equations

1996 ◽  
Vol 176 (1) ◽  
pp. 133-161 ◽  
Author(s):  
Giovanni Felder ◽  
Christian Wieczerkowski
Keyword(s):  
Elliptic Curves ◽  
Conformal Blocks
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