An example of a measure quasi-invariant under the action of the diffeomorphism group of the circle

Shavgulidze, E. T.

doi:10.1007/bf01681432

Cited by 20 publications

(14 citation statements)

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“…Note that the functional measure in the equation (19) and the Haar measure dµ H on the group SL(2, R) in the equation (20) are regularized in the same manner.…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

Correlation functions in the Schwarzian theory

Belokurov

Shavgulidze

2018

J. High Energ. Phys.

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A mathematically correct approach to study theories with infinite-dimensional groups of symmetries is presented. It is based on quasi-invariant measures on the groups. In this paper, the properties of the measure on the group of diffeomorphisms are used to evaluate the functional integrals in the Schwarzian theory. As an important example of the application of the new technique, we explicitly evaluate the correlation functions in the Schwarzian theory. * vvbelokurov@yandex.ru † shavgulidze@bk.ru arXiv:1804.00424v2 [hep-th]

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“…Note that the functional measure in the equation (19) and the Haar measure dµ H on the group SL(2, R) in the equation (20) are regularized in the same manner.…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

Correlation functions in the Schwarzian theory

Belokurov

Shavgulidze

2018

J. High Energ. Phys.

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“…Induced representations ofĜ. Our goal now is to classify all irreducible, unitary representations of the warped Virasoro group with vanishing Kac-Moody level, under the assumption that there exists a quasi-invariant measure on all the orbits (see [126][127][128][129] for the construction of such measures). According to the lightning review just displayed, this amounts to the classification of orbits, as defined in (A.23).…”

Section: Jhep03(2016)187mentioning

confidence: 99%

Near-horizon geometry and warped conformal symmetry

Afshar

Detournay

Grumiller

et al. 2016

J. High Energ. Phys.

121

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Abstract:We provide boundary conditions for three-dimensional gravity including boosted Rindler spacetimes, representing the near-horizon geometry of non-extremal black holes or flat space cosmologies. These boundary conditions force us to make some unusual choices, like integrating the canonical boundary currents over retarded time and periodically identifying the latter. The asymptotic symmetry algebra turns out to be a Witt algebra plus a twisted u(1) current algebra with vanishing level, corresponding to a twisted warped CFT that is qualitatively different from the ones studied so far in the literature. We show that this symmetry algebra is related to BMS by a twisted Sugawara construction and exhibit relevant features of our theory, including matching micro-and macroscopic calculations of the entropy of zero-mode solutions. We confirm this match in a generalization to boosted Rindler-AdS. Finally, we show how Rindler entropy emerges in a suitable limit.

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“…The only difference is that now the measure µ is a path integral measure on a supermomentum orbit; such measures were shown to exist in [32]. In addition, this setup provides a simple argument for showing that the representation is irreducible.…”

Section: Massive Modulesmentioning

confidence: 99%

BMS modules in three dimensions

Campoleoni

González

Oblak

et al. 2016

Int. J. Mod. Phys. A

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We build unitary representations of the BMS algebra and its higher-spin extensions in three dimensions, using induced representations as a guide. Our prescription naturally emerges from an ultrarelativistic limit of highest-weight representations of Virasoro and W algebras, which is to be contrasted with non-relativistic limits that typically give non-unitary representations. To support this dichotomy, we also point out that the ultrarelativistic and non-relativistic limits of generic W algebras differ in the structure of their non-linear terms.

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An example of a measure quasi-invariant under the action of the diffeomorphism group of the circle

Cited by 20 publications

References 1 publication

Correlation functions in the Schwarzian theory

Correlation functions in the Schwarzian theory

Near-horizon geometry and warped conformal symmetry

BMS modules in three dimensions

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