scholarly journals The light asymptotic limit of conformal blocks in Toda field theory

2016 ◽  
Vol 2016 (5) ◽  
Author(s):  
Hasmik Poghosyan ◽  
Rubik Poghossian ◽  
Gor Sarkissian
Keyword(s):  
Field Theory ◽  
Asymptotic Limit ◽  
Conformal Blocks ◽  
Toda Field Theory

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.

CONFORMAL AFFINE TODA FIELD THEORIES

1992 ◽  
Vol 06 (11n12) ◽  
pp. 2015-2040 ◽  
Author(s):  
L. BONORA
Keyword(s):  
Field Theory ◽  
Field Theories ◽  
The Continuum ◽  
Toda Field Theory

The conformal affine sl2 Toda field theory is introduced and analyzed both in the continuum and on the lattice.

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 WZW-TODA REDUCTION USING THE CASIMIR OPERATOR

1994 ◽  
Vol 09 (05) ◽  
pp. 745-758 ◽  
Author(s):  
I. JACK ◽  
J. PANVEL
Keyword(s):  
Field Theory ◽  
Casimir Operator ◽  
Central Charge ◽  
Hamiltonian Operator ◽  
Quantum Level ◽  
Quantum Hamiltonian ◽  
Toda Field Theory

We construct a quantum Hamiltonian operator for the Wess-Zumino-Witten (WZW) model in terms of the Casimir operator. This facilitates the discussion of the reduction of the WZW model to the Toda field theory at the quantum level and provides a very straightforward derivation of the quantum central charge for the Toda field theory.

Multiple poles and other features of affine Toda field theory

1991 ◽  
Vol 356 (2) ◽  
pp. 469-498 ◽  
Author(s):  
H.W. Braden ◽  
E. Corrigan ◽  
P.E. Dorey ◽  
R. Sasaki
Keyword(s):  
Field Theory ◽  
Multiple Poles ◽  
Toda Field Theory

scholarly journals Aspects of Affine Toda Field Theory on a Half Line

1995 ◽  
Vol 118 ◽  
pp. 143-164 ◽  
Author(s):  
E. Corrigan ◽  
P. E. Dorey ◽  
R. H. Rietdijk
Keyword(s):  
Field Theory ◽  
Half Line ◽  
Toda Field Theory

scholarly journals Affine Toda field theory from tree unitarity

2004 ◽  
Vol 33 (1) ◽  
pp. 137-148 ◽  
Author(s):  
S. Pratik Khastgir
Keyword(s):  
Field Theory ◽  
Toda Field Theory

ON THE VANISHING COUPLINGS IN $\hat{A}\hat{D}\hat{E}$ AFFINE TODA FIELD THEORIES

1992 ◽  
Vol 07 (23) ◽  
pp. 5707-5718
Author(s):  
YOSHIHIRO SAITOH ◽  
TOKUZO SHIMADA
Keyword(s):  
Field Theory ◽  
Field Theories ◽  
Charge Balance ◽  
Massless Theory ◽  
Balance Condition ◽  
Interaction Terms ◽  
Exponential Interaction ◽  
A Charge ◽  
Higher Order Corrections ◽  
Toda Field Theory

We show that certain vanishing couplings in the [Formula: see text] affine Toda field theories remain vanishing even after higher-order corrections are included. This is a requisite property for the Lagrangian formulation of the theory. We develop a new perturbative formulation and treat affine Toda field theories as a massless theory with exponential interaction terms. We show that the nonrenormalization comes from the Dynkin automorphism of the Lie algebra associated with these theories. A charge balance condition plays an important role in our scheme. The all-order nonrenormalization of vanishing couplings in [Formula: see text] affine Toda field theory is also proved in a standard massive scheme.

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