arXiv subjects

Laura Donnay

Publications and source records attributed to Laura Donnay.

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arXiv2021

BMS Flux Algebra in Celestial Holography

Starting from gravity in asymptotically flat spacetime, the BMS momentum fluxes are constructed. These are non-local expressions of the solution space living on the celestial Riemann surface. They transform in the coadjoint representation of the extended BMS group and correspond to Virasoro primaries under the action of bulk superrotations. The relation between the BMS momentum fluxes and celestial CFT operators is then established: the supermomentum flux is related to the supertranslation operator and the super angular momentum flux is linked to the stress-energy tensor of the celestial CFT. The transformation under the action of asymptotic symmetries and the OPEs of the celestial CFT currents are deduced from the BMS flux algebra.

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arXiv2020

Quantum BMS transformations in conformally flat space-times and holography

We define and study asymptotic Killing and conformal Killing vectors in $d$-dimensional Minkowski, (A)dS, $\mathbb{R}\times S^{d-1}$ and ${\rm AdS}_2\times S^{d-2}$. We construct the associated quantum charges for an arbitrary CFT and show they satisfy a closed algebra that includes the BMS as a sub-algebra (i.e. supertranslations and superrotations) plus a novel transformation we call `superdilations'. We study representations of this algebra in the Hilbert space of the CFT, as well as the action of the finite transformations obtained by exponentiating the charges. In the context of the AdS/CFT correspondence, we propose a bulk holographic description in semi-classical gravity that reproduces the results obtained from CFT computations. We discuss the implications of our results regarding quantum hairs of asymptotically flat (near-)extremal black holes.

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arXiv2020

Horizon symmetries and hairy black holes in AdS

We investigate whether supertranslation symmetry may appear in a scenario that involves black holes in AdS space. The framework we consider is massive 3D gravity, which admits a rich black hole phase space, including stationary AdS black holes with softly decaying hair. We consider a set of asymptotic conditions that permits such decaying near the boundary, and which, in addition to the local conformal symmetry, is preserved by an extra local current. The corresponding algebra of diffeomorphisms consists of two copies of Virasoro algebra in semi-direct sum with an infinite-dimensional Abelian ideal. We then reorient the analysis to the near horizon region, where infinite-dimensional symmetries also appear. The supertranslation symmetry at the horizon yields an infinite set of non-trivial charges, which we explicitly compute. The zero-mode of these charges correctly reproduces the black hole entropy. In contrast to Einstein gravity, in the higher-derivative theory subleading terms in the near horizon expansion contribute to the near horizon charges. Such terms happen to capture the higher-curvature corrections to the Bekenstein area law.

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arXiv2020

Asymptotic Symmetries and Celestial CFT

We provide a unified treatment of conformally soft Goldstone modes which arise when spin-one or spin-two conformal primary wavefunctions become pure gauge for certain integer values of the conformal dimension $Δ$. This effort lands us at the crossroads of two ongoing debates about what the appropriate conformal basis for celestial CFT is and what the asymptotic symmetry group of Einstein gravity at null infinity should be. Finite energy wavefunctions are captured by the principal continuous series $Δ\in 1+i\mathbb{R}$ and form a complete basis. We show that conformal primaries with analytically continued conformal dimension can be understood as certain contour integrals on the principal series. This clarifies how conformally soft Goldstone modes fit in but do not augment this basis. Conformally soft gravitons of dimension two and zero which are related by a shadow transform are shown to generate superrotations and non-meromorphic diffeomorphisms of the celestial sphere which we refer to as shadow superrotations. This dovetails the Virasoro and Diff(S$^2$) asymptotic symmetry proposals and puts on equal footing the discussion of their associated soft charges, which correspond to the stress tensor and its shadow in the two-dimensional celestial CFT.

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arXiv2020

Carrollian Physics at the Black Hole Horizon

We show that the geometry of a black hole horizon can be described as a Carrollian geometry emerging from an ultra-relativistic limit where the near-horizon radial coordinate plays the role of a virtual velocity of light tending to zero. We prove that the laws governing the dynamics of a black hole horizon, the null Raychaudhuri and Damour equations, are Carrollian conservation laws obtained by taking the ultra-relativistic limit of the conservation of an energy-momentum tensor; we also discuss their physical interpretation. We show that the vector fields preserving the Carrollian geometry of the horizon, dubbed Carrollian Killing vectors, include BMS-like supertranslations and superrotations and that they have non-trivial associated conserved charges on the horizon. In particular, we build a generalization of the angular momentum to the case of non-stationary black holes. Finally, we discuss the relation of these conserved quantities to the infinite tower of charges of the covariant phase space formalism.

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arXiv2019

Cosmological horizons, Noether charges and entropy

It has recently been shown that, in the vicinity of their event horizons, black holes exhibit an infinite-dimensional symmetry. This symmetry captures relevant physical information about the black hole, and in particular about its thermodynamics. Here, we show that the same holds in a cosmological setup. More precisely, we show that around the de Sitter cosmological horizon, an infinite set of diffeomorphisms preserving a sensible set of boundary conditions emerges. These boundary conditions are similar to those considered by Price and Thorne in the context of the membrane paradigm, and permit to accommodate interesting gravity solutions. As for other boundary conditions considered previously, they are preserved by an infinite-dimensional asymptotic isometry algebra that includes supertranslations and two copies of the Virasoro algebra. This symmetry has associated a set of Noether charges that turn out to be conserved, finite, and integrable. We derive these charges explicitly using the covariant formalism and analyze their physical meaning by evaluating them to the case of de Sitter space. In this case, the zero-mode of the charge is found to account for the Gibbons-Hawking entropy of the cosmological horizon. We then consider a much more general set of solutions, including asymptotically de-Sitter black holes and asymptotically Taub-NUT-de Sitter black holes.

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arXiv2019

Extended Symmetries at the Black Hole Horizon

We prove that non-extremal black holes in four-dimensional general relativity exhibit an infinite-dimensional symmetry in their near horizon region. By prescribing a physically sensible set of boundary conditions at the horizon, we derive the algebra of asymptotic Killing vectors, which is shown to be infinite-dimensional and includes, in particular, two sets of supertranslations and two mutually commuting copies of the Virasoro algebra. We define the surface charges associated to the asymptotic diffeomorphisms that preserve the boundary conditions and discuss the subtleties of this definition, such as the integrability conditions and the correct definition of the Dirac brackets. When evaluated on the stationary solutions, the only non-vanishing charges are the zero-modes. One of them reproduces the Bekenstein-Hawking entropy of Kerr black holes. We also study the extremal limit, recovering the NHEK geometry. In this singular case, where the algebra of charges and the integrability conditions get modified, we find that the computation of the zero-modes correctly reproduces the black hole entropy. Furthermore, we analyze the case of three spacetime dimensions, in which the integrability conditions notably simplify and the field equations can be solved analytically to produce a family of exact solutions that realize the boundary conditions explicitly. We examine other features, such as the form of the algebra in the extremal limit and the relation to other works in the literature.

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arXiv2018

Conformally Soft Photons and Gravitons

The four-dimensional $S$-matrix is reconsidered as a correlator on the celestial sphere at null infinity. Asymptotic particle states can be characterized by the point at which they enter or exit the celestial sphere as well as their $SL(2,\mathbb C)$ Lorentz quantum numbers: namely their conformal scaling dimension and spin $h\pm \bar h$ instead of the energy and momentum. This characterization precludes the notion of a soft particle whose energy is taken to zero. We propose it should be replaced by the notion of a conformally soft particle with $h=0$ or $\bar h=0$. For photons we explicitly construct conformally soft $SL(2,\mathbb C)$ currents with dimensions $(1,0)$ and identify them with the generator of a $U(1)$ Kac-Moody symmetry on the celestial sphere. For gravity the generator of celestial conformal symmetry is constructed from a $(2,0)$ $SL(2,\mathbb C)$ primary wavefunction. Interestingly, BMS supertranslations are generated by a spin-one weight $(\frac{3}{2},\frac{1}{2})$ operator, which nevertheless shares holomorphic characteristics of a conformally soft operator. This is because the right hand side of its OPE with a weight $(h,\bar h)$ operator ${\cal O}_{h,\bar h}$ involves the shifted operator ${\cal O}_{h+\frac{1}{2},\bar h+ \frac{1}{2}}$. This OPE relation looks quite unusual from the celestial CFT$_2$ perspective but is equivalent to the leading soft graviton theorem and may usefully constrain celestial correlators in quantum gravity.

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arXiv2018

Black hole memory effect

We compute the memory effect produced at the black hole horizon by a transient gravitational shockwave. As shown by Hawking, Perry, and Strominger (HPS) such a gravitational wave produces a deformation of the black hole geometry which from future null infinity is seen as a Bondi-Metzner-Sachs (BMS) supertranslation. This results in a diffeomorphic but physically distinct geometry which differs from the original black hole by their charges at infinity. Here we give the complementary description of this physical process in the near-horizon region as seen by an observer hovering just outside the event horizon. From this perspective, in addition to a supertranslation the shockwave also induces a horizon superrotation. We compute the associated superrotation charge and show that its form agrees with the one obtained by HPS at infinity. In addition, there is a supertranslation contribution to the horizon charge, which measures the entropy change in the process. We then turn to electrically and magnetically charged black holes and generalize the near-horizon asymptotic symmetry analysis to Einstein-Maxwell theory. This reveals an additional infinite-dimensional current algebra that acts non-trivially on the horizon superrotations. Finally, we generalize the black hole memory effect to Reissner-Nordström black holes.

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arXiv2016

Supertranslations and Superrotations at the Black Hole Horizon

We show that the asymptotic symmetries close to nonextremal black hole horizons are generated by an extension of supertranslations. This group is generated by a semidirect sum of Virasoro and Abelian currents. The charges associated with the asymptotic Killing symmetries satisfy the same algebra. When considering the special case of a stationary black hole, the zero mode charges correspond to the angular momentum and the entropy at the horizon.

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arXiv2016

Asymptotic dynamics of three-dimensional gravity

These are the lectures notes of the course given at the Eleventh Modave Summer School in Mathematical Physics, 2015, aimed at PhD candidates and junior researchers in theoretical physics. We review in details the result of Coussaert-Henneaux-van Driel showing that the asymptotic dynamics of $(2+1)$- dimensional gravity with negative cosmological constant is described at the classical level by Liouville theory. Boundary conditions implement the asymptotic reduction in two steps: the first set reduces the $SL(2,\mathbb R)\times SL(2,\mathbb R)$ Chern-Simons action, equivalent to the Einstein action, to a non-chiral $SL(2,\mathbb R)$ Wess-Zumino-Witten model, while the second set imposes constraints on the WZW currents that reduce further the action to Liouville theory. We discuss the issues of considering the latter as an effective description of the dual conformal field theory describing AdS$_3$ gravity beyond the semi-classical regime.

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arXiv2015

WAdS$_3$/CFT$_2$ correspondence in presence of bulk massive gravitons

In a previous paper, it has been shown that the entropy of non-extremal black holes in Warped Anti-de Sitter (WAdS) spaces in massive gravity can be computed microscopically in terms of a dual conformal field theory. Here, we extend this computation to a set of asymptotic boundary conditions that, while still gathering the WAdS$_3$ black holes, also allow for new solutions that are not locally equivalent to WAdS$_3$ space, and therefore are associated to the local degrees of freedom of the theory (bulk massive gravitons). After presenting explicit examples of such geometries, we compute the asymptotic charge algebra and show that it is generated by the semi-direct sum of Virasoro algebra and an affine Kac-Moody algebra. The value of the central charge turns out to be exactly the one that leads to reproduce the entropy of the WAdS$_3$ black holes. This result probes the WAdS$_3$/CFT$_2$ correspondence in presence of bulk gravitons.

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arXiv2015

Super-BMS$_{3}$ invariant boundary theory from three-dimensional flat supergravity

The two-dimensional super-BMS$_{3}$ invariant theory dual to three-dimensional asymptotically flat $\mathcal{N}=1$ supergravity is constructed. It is described by a constrained or gauged chiral Wess-Zumino-Witten action based on the super-Poincaré algebra in the Hamiltonian, respectively the Lagrangian formulation, whose reduced phase space description corresponds to a supersymmetric extension of flat Liouville theory.

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arXiv2015

Holographic entropy of Warped-AdS$_3$ black holes

We study the asymptotic symmetries of three-dimensional Warped Anti-de Sitter (WAdS) spaces in three-dimensional New Massive Gravity (NMG). For a specific choice of asymptotic boundary conditions, we find that the algebra of charges is infinite-dimensional and coincides with the semidirect sum of Virasoro algebra with non-vanishing central charge and an affine $\hat{u}(1)_k$ Kač-Moody algebra. We show that the WAdS black hole configurations organize in terms of two commuting Virasoro algebras. We identify the Virasoro generators that expand the associated representations in the dual Warped Conformal Field Theory (WCFT) and, by applying the Warped version of the Cardy formula, we prove that the microscopic WCFT computation exactly reproduces the entropy of black holes in WAdS space.

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arXiv2015

Liouville theory beyond the cosmological horizon

The dS/CFT correspondence postulates the existence of a Euclidean CFT dual to a suitable gravity theory with Dirichlet boundary conditions asymptotic to de Sitter spacetime. A semi-classical model of such a correspondence consists of Einstein gravity with positive cosmological constant and without matter which is dual to Euclidean Liouville theory defined at the future conformal boundary. Here we show that Euclidean Liouville theory is also dual to Einstein gravity with Dirichlet boundary conditions on a fixed timelike slice in the static patch. Intriguingly, the spacetime interpretation of Euclidean Liouville time is the physical time of the static observer. As a prerequisite of this correspondence, we show that the asymptotic symmetry algebra which consists of two copies of the Virasoro algebra extends everywhere into the bulk.

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arXiv2014

Asymptotic symmetries and dynamics of three-dimensional flat supergravity

A consistent set of asymptotic conditions for the simplest supergravity theory without cosmological constant in three dimensions is proposed. The canonical generators associated to the asymptotic symmetries are shown to span a supersymmetric extension of the BMS$_3$ algebra with an appropriate central charge. The energy is manifestly bounded from below with the ground state given by the null orbifold or Minkowski spacetime for periodic, respectively antiperiodic boundary conditions on the gravitino. These results are related to the corresponding ones in AdS$_3$ supergravity by a suitable flat limit. The analysis is generalized to the case of minimal flat supergravity with additional parity odd terms for which the Poisson algebra of canonical generators form a representation of the super-BMS$_3$ algebra with an additional central charge.

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