Conformal field theory on the plane

Ribault, Sylvain

doi:10.48550/arxiv.1406.4290

Cited by 72 publications

(159 citation statements)

References 22 publications

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“…In generalized minimal models, some structure constants do, and some of them don't [16,9]. In our case, the chiral structure constant h r 1 ,r 2 ,k determines the contribution of the degenerate field to an OPE of two twist fields, when we compute this contribution using affine symmetry.…”

Section: Chiral Crossing Symmetry With Degenerate Fieldsmentioning

confidence: 92%

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Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model

Nemkov,

Ribault

2021

Preprint

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We revisit the critical two-dimensional Ashkin-Teller model, i.e. the Z 2 orbifold of the compactified free boson CFT at c = 1. We solve the model on the plane by computing its three-point structure constants and proving crossing symmetry of fourpoint correlation functions. We do this not only for affine primary fields, but also for Virasoro primary fields, i.e. higher twist fields and degenerate fields.This leads us to clarify the analytic properties of Virasoro conformal blocks and fusion kernels at c = 1. We show that blocks with a degenerate channel field should be computed by taking limits in the central charge, rather than in the conformal dimension. In particular, Al. Zamolodchikov's simple explicit expression for the blocks that appear in four-twist correlation functions is only valid in the non-degenerate case: degenerate blocks, starting with the identity block, are more complicated generalized theta functions.

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Section: Chiral Crossing Symmetry With Degenerate Fieldsmentioning

confidence: 92%

“…We will review correlation functions and their properties, while paying particular attention to the nontrivial signs that appear when fields have nonzero conformal spins. For a more detailed review, see [9].…”

Section: Basic Structures Of Two-dimensional Cftmentioning

confidence: 99%

Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model

Nemkov,

Ribault

2021

Preprint

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“…If not stated otherwise, in what follows we consider irreducible Verma module representations [2], i.e. there are not descendant states with vanishing norm, referred here as null vectors.…”

Section: Orbifold Conformal Blocksmentioning

confidence: 99%

“…We consider now a seed theory which is built upon irreducible representations of the Virasoro algebra, labelled by c and h, constructed by removing all the null vectors [2]. A prominent example of such CFTs are the minimal models [1] which have central charge…”

Section: Minimal Model Orbifold Conformal Blocksmentioning

confidence: 99%

“…The conformal bootstrap approach in two-dimensions [1] exploits the infinite-dimensional Virasoro algebra together with the associativity of the Operator Product Expansion (OPE) in the attempt to classify all possible Conformal Field Theories (CFTs). In short [2], the associativity of the conformal algebra leads to functional relations between its special functions dubbed conformal blocks, which can be solved, under certain assumptions on the spectrum of the theory, either analytically or numerically.…”

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confidence: 99%

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Crossing-symmetric Twist Field Correlators and Entanglement Negativity in Minimal CFTs

Ares,

Santachiara,

Viti

2021

Preprint

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We study conformal twist field four-point functions on a Z N orbifold. We examine in detail the case N = 3 and analyze theories obtained by replicated N -times a minimal model with central charge c < 1. A fastly convergent expansion of the twist field correlation function in terms of sphere conformal blocks with central charge N c is obtained by exploiting covering map techniques. We discuss extensive applications of the formalism to the entanglement of two disjoint intervals in CFT, in particular we propose a conformal block expansion for the partially transposed reduced density matrix. Finally, we refine the bounds on the structure constants of unitary CFTs determined previously by the genus two modular bootstrap.

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Instanton Counting, Quantum Geometry and Algebra

Kimura

2021

Mathematical Physics Studies

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Conformal field theory on the plane

Cited by 72 publications

References 22 publications

Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model

Analytic conformal bootstrap and Virasoro primary fields in the Ashkin-Teller model

Crossing-symmetric Twist Field Correlators and Entanglement Negativity in Minimal CFTs

Instanton Counting, Quantum Geometry and Algebra

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