Geometric actions for three-dimensional gravity

Barnich, Glenn; González, Hernán A.; Salgado-Rebolledo, Patricio

doi:10.1088/1361-6382/aa9806

Cited by 67 publications

(111 citation statements)

References 70 publications

(107 reference statements)

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“…Here M 0 and L 0 are proportional to the mass and angular momentum of the gravitational saddle and f and α are fields which generate BMS 3 superrotations and supertranslations, respectively. The boundary theory coincides with the geometric action on the coadjoint orbit of the BMS 3 group of [62], where the orbit representatives are given by M 0 and L 0 and the BMS 3 central charges are c 1 = 0 and c 2 = 3/G N . This provides a map between the bulk gravitational solutions and the coadjoint orbit of the BMS 3 group [76] with constant representatives.…”

Section: Introductionmentioning

confidence: 83%

“…Another accomplishment of the work [62] was to show how the geometric action on the coadjoint orbits of any gauge group can be deformed by adding Hamiltonians that preserve the global symmetries of the theory. One can add to the kinetic term (2.32) as Hamiltonian the Noether charge Q ( L , M ) of a global symmetry (generated by bms 3 vector fields ( L (ϕ), M (ϕ))) and the resulting action will by construction preserve the global symmetries of (2.32).…”

Section: Geometric Actionmentioning

confidence: 99%

“…The action is one-loop exact [63], which can be shown by suitable adaptation of the Duistermaat-Heckman theorem [73] (see also [74]). A given generic Virasoro orbit can be related by a field redefinition to the b 0 = 0 orbit [62]. This is in essence the uniformizing transformation that proved useful in computing Virasoro blocks in the heavy-light limit from AdS 3 geometry [75].…”

Section: Introductionmentioning

confidence: 99%

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Geometric actions and flat space holography

Merbis

Riegler²

2020

J. High Energ. Phys.

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In this paper we perform the Hamiltonian reduction of the action for three-dimensional Einstein gravity with vanishing cosmological constant using the Chern-Simons formulation and Bondi-van der Burg-Metzner-Sachs (BMS) boundary conditions. An equivalent formulation of the boundary action is the geometric action on BMS 3 coadjoint orbits, where the orbit representative is identified as the bulk holonomy. We use this reduced action to compute one-loop contributions to the torus partition function of all BMS 3 descendants of Minkowski spacetime and cosmological solutions in flat space. We then consider Wilson lines in the ISO(2, 1) Chern-Simons theory with endpoints on the boundary, whose reduction to the boundary theory gives a bilocal operator. We use the expectation values and two-point correlation functions of these bilocal operators to compute quantum contributions to the entanglement entropy of a single interval for BMS 3 invariant field theories and BMS 3 blocks, respectively. While semi-classically the BMS 3 boundary theory has central charges c 1 = 0 and c 2 = 3/G N , we find that quantum corrections in flat space do not renormalize G N , but rather lead to a non-zero c 1 .

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Section: Introductionmentioning

confidence: 83%

Section: Geometric Actionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Geometric actions and flat space holography

Merbis

Riegler²

2020

J. High Energ. Phys.

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“…The similarity of warped conformal boundary conditions in section 6.3 to conformal ones in section 6.2, together with the relation of the latter to SYK, suggests the possibility of SYK-like models that exhibit an off-shell warped conformal symmetry that is largely broken on-shell. This may provide a new and interesting angle on SYK-like model building on the field theory side and lead to a generalized Schwarzian action along the lines of [109].…”

Section: Discussionmentioning

confidence: 99%

Menagerie of AdS2 boundary conditions

Grumiller

McNees

Salzer

et al. 2017

J. High Energ. Phys.

154

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Abstract:We consider different sets of AdS 2 boundary conditions for the JackiwTeitelboim model in the linear dilaton sector where the dilaton is allowed to fluctuate to leading order at the boundary of the Poincaré disk. The most general set of boundary conditions is easily motivated in the gauge theoretic formulation as a Poisson sigma model and has an sl(2) current algebra as asymptotic symmetries. Consistency of the variational principle requires a novel boundary counterterm in the holographically renormalized action, namely a kinetic term for the dilaton. The on-shell action can be naturally reformulated as a Schwarzian boundary action. While there can be at most three canonical boundary charges on an equal-time slice, we consider all Fourier modes of these charges with respect to the Euclidean boundary time and study their associated algebras. Besides the (centerless) sl(2) current algebra we find for stricter boundary conditions a Virasoro algebra, a warped conformal algebra and a u(1) current algebra. In each of these cases we get one half of a corresponding symmetry algebra in three-dimensional Einstein gravity with negative cosmological constant and analogous boundary conditions. However, on-shell some of these algebras reduce to finite-dimensional ones, reminiscent of the on-shell breaking of conformal invariance in SYK. We conclude with a discussion of thermodynamical aspects, in particular the entropy and some Cardyology.

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“…Previous work on boundary dynamics in three-dimensional asymptotically flat gravity and BMS 3 -invariant actions has appeared in [16][17][18][19][20][21]. That work has some overlap with the present paper but our emphasis on the relationship to fluid dynamics and the Lie-Poisson bracket, and our use of the membrane paradigm as starting point, are new.…”

Section: Introductionmentioning

confidence: 84%

BMS₃invariant fluid dynamics at null infinity

Penna¹

2018

Class. Quantum Grav.

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Abstract:We revisit the boundary dynamics of asymptotically flat, three dimensional gravity. The boundary is governed by a momentum conservation equation and an energy conservation equation, which we interpret as fluid equations, following the membrane paradigm. We reformulate the boundary's equations of motion as Hamiltonian flow on the dual of an infinite-dimensional, semi-direct product Lie algebra equipped with a Lie-Poisson bracket. This gives the analogue for boundary fluid dynamics of the Marsden-Ratiu-Weinstein formulation of the compressible Euler equations on a manifold, M , as Hamiltonian flow on the dual of the Lie algebra of Diff(M ) C ∞ (M ). The Lie group for boundary fluid dynamics turns out to be Diff(S 1 ) Ad vir, with central charge c = 3/G. This gives a new derivation of the centrally extended, three-dimensional Bondi-van der Burg-Metzner-Sachs (BMS 3 ) group. The relationship with fluid dynamics helps to streamline and physically motivate the derivation. For example, the central charge, c = 3/G, is simply read off of a fluid equation in much the same way as one reads off a viscosity coefficient. The perspective presented here may useful for understanding the still mysterious four-dimensional BMS group.

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Geometric actions for three-dimensional gravity

Cited by 67 publications

References 70 publications

Geometric actions and flat space holography

Geometric actions and flat space holography

Menagerie of AdS2 boundary conditions

BMS₃invariant fluid dynamics at null infinity

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Geometric actions for three-dimensional gravity

Cited by 67 publications

References 70 publications

Geometric actions and flat space holography

Geometric actions and flat space holography

Menagerie of AdS2 boundary conditions

BMS3invariant fluid dynamics at null infinity

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Product

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BMS₃invariant fluid dynamics at null infinity