Degenerate conformal field theories and explicit expressions for some null vectors

Benoit, Louis; Saint‐Aubin, Yvan

doi:10.1016/0370-2693(88)91352-4

Cited by 76 publications

(77 citation statements)

References 8 publications

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“…In general, one obtains an (rs) th order differential equation for correlators of O r,s (z). For the fairly wide range of cases of degenerate states with dimension h r,1 , the null descendant can be written in closed form as [62,64] …”

Section: Jhep05(2016)109mentioning

confidence: 99%

On information loss in AdS3/CFT2

Fitzpatrick

Kaplan

et al. 2016

J. High Energ. Phys.

114

183

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We discuss information loss from black hole physics in AdS 3 , focusing on two sharp signatures infecting CFT 2 correlators at large central charge c: 'forbidden singularities' arising from Euclidean-time periodicity due to the effective Hawking temperature, and late-time exponential decay in the Lorentzian region. We study an infinite class of examples where forbidden singularities can be resolved by non-perturbative effects at finite c, and we show that the resolution has certain universal features that also apply in the general case. Analytically continuing to the Lorentzian regime, we find that the non-perturbative effects that resolve forbidden singularities qualitatively change the behavior of correlators at times t ∼ S BH , the black hole entropy. This may resolve the exponential decay of correlators at late times in black hole backgrounds. By Borel resumming the 1/c expansion of exact examples, we explicitly identify 'information-restoring' effects from heavy states that should correspond to classical solutions in AdS 3 . Our results suggest a line of inquiry towards a more precise formulation of the gravitational path integral in AdS 3 .

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Section: Jhep05(2016)109mentioning

confidence: 99%

On information loss in AdS3/CFT2

Fitzpatrick

Kaplan

et al. 2016

J. High Energ. Phys.

114

183

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“…Such features distinguish our approach from the previous definitions of covariant operators generalizing the Schwarzian derivative (e.g. [7][6] [8]). …”

Section: Uniformizing Schwarzian Operatorsmentioning

confidence: 99%

Zamolodchikov relations and Liouville hierarchy in SL(2,R)k WZNW model

et al. 2005

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We study the connection between Zamolodchikov operator-valued relations in Liouville field theory and in the SL(2, R) k WZNW model. In particular, the classical relations in SL(2, R) k can be formulated as a classical Liouville hierarchy in terms of the isotopic coordinates, and their covariance is easily understood in the framework of the AdS 3 /CF T 2 correspondence.Conversely, we find a closed expression for the classical Liouville decoupling operators in terms of the so called uniformizing Schwarzian operators and show that the associated uniformizing parameter plays the same role as the isotopic coordinates in SL(2, R) k . The solutions of the j-th classical decoupling equation in the WZNW model span a spin j reducible representation of SL(2, R). Likewise, we show that in Liouville theory solutions of the classical decoupling equations span spin j representations of SL(2, R), which is interpreted as the isometry group of the hyperbolic upper half-plane. We also discuss the connection with the Hamiltonian reduction of SL(2, R) k WZNW model to Liouville theory.

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“…Основным результатом является теорема 3.1, утверждаю-щая, что алгебра когомологий H * (L 1 ) порождается при помощи нетривиаль-ных произведений Масси двумя базисными коциклами из H 1 (L 1 ). В ее дока-зательстве существенную роль играет техника, развитая Фейгиным, Фуксом и Ретахом в [13], а также формула Бенуа-Сент-Обана [5] для особых векторов модулей Верма над алгеброй Вирасоро.…”

Section: предисловиеunclassified

Алгебра Формальных Векторных Полей На Прямой И Гипотеза Бухштабера

Миллионщиков¹

2009

Функц. анализ и его прил.

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Degenerate conformal field theories and explicit expressions for some null vectors

Cited by 76 publications

References 8 publications

On information loss in AdS3/CFT2

On information loss in AdS3/CFT2

Zamolodchikov relations and Liouville hierarchy in SL(2,R)k WZNW model

Алгебра Формальных Векторных Полей На Прямой И Гипотеза Бухштабера

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