arXiv:1809.03722 · SciPost Physics

On 2d CFTs that interpolate between minimal models

Sylvain Ribault

Published Jun 25, 2019• 18 citations

Abstract

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.

DOI: 10.21468/scipostphys.6.6.075

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arXiv:1809.03722 · SciPost Physics

On 2d CFTs that interpolate between minimal models

Sylvain Ribault

Published Jun 25, 2019• 18 citations

arXiv HTML PDF

Abstract

DOI: 10.21468/scipostphys.6.6.075

Related papers

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{\mathbb{Z}}_2

twist field in the symmetric product orbifold, we produce the Hellerman bound and the logarithmically corrected Cardy formula that is valid for h ≥ c/12.

H_3^+

model, and the

SU_2

and

\widetilde{SL}_2(\mathbb{R})

WZW models. We also discuss relations between some of these models, and limits of these models when the central charge and/or conformal dimensions tend to particular values.

A bstract We propose a method to challenge the calculation of genus- g , bulk n -point, b -boundary, c -crosscap correlation functions with x boundary operators

{\mathcal{F}}_{g,n,b,c}^x

F g , n , b , c x in two-dimensional conformal field theories (CFT 2 ). We show that

{\mathcal{F}}_{g,n,b,c}^x

F g , n , b , c x are infinite linear combinations of genus- g , bulk ( n + b + c )-point functions F g , ( n + b + c ) , and try to obtain the linear coefficients in this work. We show the existence of a single pole structure in the linear coefficients at degenerate limits. A practical method to obtain the infinite linear coefficients is the free field realizations of Ishibashi states. We review the results in Virasoro minimal models

\mathcal{M}

M ( p, p ′) and extend it to the N = 1 minimal models

\mathcal{SM}

SM ( p, p ′).

d+1

dimensional quantum gravity and

d

dimensional CFT. Within this correspondence, the CFT appears as a non-perturbative formulation of quantum gravity. Except in special cases, this CFT belongs to ICFT. Against this backdrop, the methods for ICFTs have developed rapidly in recent years. Many of these ICFT methods are indispensable for modern quantum gravity research. Unfortunately, these cannot be learned from textbooks on 2D CFTs, such as Yellow book. These lecture notes aim to fill this gap. Specifically, we will cover techniques that have already been applied in many studies, such as HHLL block and monodromy method, and significant results that have become proper nouns, such as Hellerman bound and HKS bound.