3d gravity and quantum deformations: a Drinfel'd double approach

We construct recently introduced palatial NC twistors by considering the pair of conjugated (Born-dual) twist-deformed D=4 quantum inhomogeneous conformal Hopf algebras Uθ(su(2,2)⋉T4) and Uθ¯(su(2,2)⋉T¯4), where T4 describes complex twistor coordinates and T¯4 the conjugated dual twistor momenta. The palatial twistors are suitably chosen as the quantum-covariant modules (NC representations) of the introduced Born-dual Hopf algebras. Subsequently, we introduce the quantum deformations of D=4 Heisenberg-conformal algebra (HCA) su(2,2)⋉Hℏ4,4 (Hℏ4,4=T¯4⋉ℏT4 is the Heisenberg algebra of twistorial oscillators) providing in twistorial framework the basic covariant quantum elementary system. The class of algebras describing deformation of HCA with dimensionfull deformation parameter, linked with Planck length λp, is called the twistorial DSR (TDSR) algebra, following the terminology of DSR algebra in space-time framework. We describe the examples of TDSR algebra linked with Palatial twistors which are introduced by the Drinfeld twist and the quantization map in Hℏ4,4. We also introduce generalized quantum twistorial phase space by considering the Heisenberg double of Hopf algebra Uθ(su(2,2)⋉T4).

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3D Gravity Data Modelling for Determining a Subsurface structure of The SDP Geothermal Field

Journal of Physics Conference Series ◽

10.1088/1742-6596/1217/1/012042 ◽

2019 ◽

Vol 1217 ◽

pp. 012042

Author(s):

T Meilasandi ◽

A Sugianto ◽

R D Indriana ◽

U Harmoko

Keyword(s):

Gravity Data ◽

Geothermal Field ◽

Data Modelling ◽

Subsurface Structure ◽

3D Gravity

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Poincaré series, 3d gravity and averages of rational CFT

Journal of High Energy Physics ◽

10.1007/jhep04(2021)267 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Viraj Meruliya ◽

Sunil Mukhi ◽

Palash Singh

Keyword(s):

Poincaré Series ◽

Simons Theory ◽

Partition Functions ◽

Moody Algebra ◽

Modular Invariant ◽

Poincare Series ◽

Single Genus ◽

3D Gravity ◽

Chern Simons ◽

Chern Simons Theory

Abstract We investigate the Poincaré series approach to computing 3d gravity partition functions dual to Rational CFT. For a single genus-1 boundary, we show that for certain infinite sets of levels, the SU(2)k WZW models provide unitary examples for which the Poincaré series is a positive linear combination of two modular-invariant partition functions. This supports the interpretation that the bulk gravity theory (a topological Chern-Simons theory in this case) is dual to an average of distinct CFT’s sharing the same Kac-Moody algebra. We compute the weights of this average for all seed primaries and all relevant values of k. We then study other WZW models, notably SU(N)1 and SU(3)k, and find that each class presents rather different features. Finally we consider multiple genus-1 boundaries, where we find a class of seed functions for the Poincaré sum that reproduces both disconnected and connected contributions — the latter corresponding to analogues of 3-manifold “wormholes” — such that the expected average is correctly reproduced.

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The third way to 3D gravity

International Journal of Modern Physics D ◽

10.1142/s0218271815440150 ◽

2015 ◽

Vol 24 (12) ◽

pp. 1544015 ◽

Cited By ~ 11

Author(s):

Eric Bergshoeff ◽

Wout Merbis ◽

Alasdair J. Routh ◽

Paul K. Townsend

Keyword(s):

Equations Of Motion ◽

Massive Gravity ◽

De Sitter ◽

Gravitational Field Equation ◽

Third Way ◽

Metric Tensor ◽

The Third ◽

Higher Dimensional ◽

Conservation Condition ◽

3D Gravity

Consistency of Einstein’s gravitational field equation [Formula: see text] imposes a “conservation condition” on the [Formula: see text]-tensor that is satisfied by (i) matter stress tensors, as a consequence of the matter equations of motion and (ii) identically by certain other tensors, such as the metric tensor. However, there is a third way, overlooked until now because it implies a “nongeometrical” action: one not constructed from the metric and its derivatives alone. The new possibility is exemplified by the 3D “minimal massive gravity” model, which resolves the “bulk versus boundary” unitarity problem of topologically massive gravity with Anti-de Sitter asymptotics. Although all known examples of the third way are in three spacetime dimensions, the idea is general and could, in principle, apply to higher dimensional theories.

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