Abstract Recently, lattice formulations of Abelian chiral gauge theory in two dimensions have been devised on the basis of the Abelian bosonization. A salient feature of these 2D lattice formulations is that the gauge invariance is exactly preserved for anomaly-free theories and thus is completely free from the question of the gauge mode decoupling. In the present paper, we propose yet another lattice formulation sharing this desired property. A particularly unique point in our formulation is that the vertex operator of the dual scalar field, which carries the vector charge of the fermion and the “magnetic charge” in the bosonization, is represented by a “hole” excised from the lattice; this is the excision method formulated recently by Abe et al. in a somewhat different context.

Japan

Okuto Morikawa

Soma Onoda

Hiroshi Suzuki

Yet Another Lattice Formulation of 2D (1) Chiral Gauge Theory via Bosonization David Tong: lectures on gauge theory

We study black strings/funnels and other black hole configurations in AdS that correspond to different phases of the dual CFT in black hole backgrounds, employing different approaches at large D. We assemble the phase diagram of uniform and non-uniform black strings/funnels and study their dynamical stability. We also construct flowing horizons. Many of our results are available analytically, though some are only known numerically.

Israel

Spain

David Licht

Ryotaku Suzuki

Benson Way

The large D effective theory of black strings in AdS

We explore the phase space of non-uniform black branes compactified on oblique lattices with a large number of dimensions. We find the phase diagrams for different periodicities and angles, and determine the thermodynamically preferred phases for each lattice configuration. In a range of angles, we observe that some phases become metastable.

Portugal

Raimon Luna

Lattice black branes at large D

We study the evolution of the Gregory-Laflamme instability for black strings in global AdS spacetime, and investigate the CFT dual of the formation of a bulk naked singularity. Using an effective theory in the large D limit, we uncover a rich variety of dynamical behaviour, depending on the thickness of the string and on initial perturbations. These include: large inflows of horizon generators from the asymptotic boundary (a ‘black tsunami’); a pinch-off of the horizon that likely reveals a naked singularity; and competition between these two behaviours, such as a nakedly singular pinch-off that subsequently gets covered by a black tsunami. The holographic dual describes different patterns of heat flow due to the Hawking radiation of two black holes placed at the antipodes of a spherical universe. We also present a model that describes, in any D, the burst in the holographic stress-energy tensor when the signal from a bulk self-similar naked singularity reaches the boundary. The model shows that the shear components of the boundary stress diverge in finite time, while the energy density and pressures from the burst vanish.

Roberto Emparan

France

Marija Tomašević

Black tsunamis and naked singularities in AdS

We study how black hole entropy is generated and the role it plays in several highly dynamical processes: the decay of unstable black strings and ultraspinning black holes; the fusion of two rotating black holes; and the subsequent fission of the merged system into two black holes that fly apart (which can occur in dimension D ≥ 6, with a mild violation of cosmic censorship). Our approach uses the effective theory of black holes at D → ∞, but we expect our main conclusions to hold at finite D. Black hole fusion is highly irreversible, while fission, which follows the pattern of the decay of black strings, generates comparatively less entropy. In 2 → 1 → 2 black hole collisions an intermediate, quasi-thermalized state forms that then fissions. This intermediate state erases much of the memory of the initial states and acts as an attractor funneling the evolution of the collision towards a small subset of outgoing parameters, which is narrower the closer the total angular momentum is to the critical value for fission. Entropy maximization provides a very good guide for predicting the final outgoing states. Along our study, we clarify how entropy production and irreversibility appear in the large D effective theory. We also extend the study of the stability of new black hole phases (black bars and dumbbells). Finally, we discuss entropy production through charge diffusion in collisions of charged black holes.

Tomás Andrade

Aron Jansen

Entropy production and entropic attractors in black hole fusion and fission

We explore the rich phase space of singly spinning (both neutral and charged) black hole solutions in the large limit. We find several ‘bumpy’ branches which are connected to multiple (concentric) black rings, and black Saturns. Additionally, we obtain stationary solutions without axisymmetry that are only stationary at ∞, but correspond to long-lived black hole solutions at finite . These multipolar solutions can appear as intermediate configurations in the decay of ultra-spinning Myers-Perry black holes into stable black holes. Finally, we also construct stationary solutions corresponding to the instability of such a multipolar solution.

Black ripples, flowers and dumbbells at large

We study the evolution of black hole collisions and ultraspinning black hole instabilities in higher dimensions. These processes can be efficiently solved numerically in an effective theory in the limit of large number of dimensions D. We present evidence that they lead to violations of cosmic censorship. The post-merger evolution of the collision of two black holes with total angular momentum above a certain value is governed by the properties of a resonance-like intermediate state: a long-lived, rotating black bar, which pinches off towards a naked singularity due to an instability akin to that of black strings. We compute the radiative loss of spin for a rotating bar using the quadrupole formula at finite D, and argue that at large enough D — very likely for D ≳ 8, but possibly down to D = 6 — the spin-down is too inefficient to quench this instability. We also study the instabilities of ultraspinning black holes by solving numerically the time evolution of axisymmetric and non-axisymmetric perturbations. We demonstrate the development of transient black rings in the former case, and of multi-pronged horizons in the latter, which then proceed to pinch and, arguably, fragment into smaller black holes.

Black hole collisions, instabilities, and cosmic censorship violation at large D

We use a recent implementation of the large D expansion in order to construct the higher-dimensional Kerr-Newman black hole and also new charged rotating black bar solutions of the Einstein-Maxwell theory, all with rotation along a single plane. We describe the space of solutions, obtain their quasinormal modes, and study the appearance of instabilities as the horizons spread along the plane of rotation. Generically, the presence of charge makes the solutions less stable. Instabilities can appear even when the angular momentum of the black hole is small, as long as the charge is sufficiently large. We expect that, although our study is performed in the limit D → ∞, the results provide a good approximation for charged rotating black holes at finite D ≥ 6.

Charged rotating black holes in higher dimensions

We argue that cosmic censorship is violated in the collision of two black holes in high spacetime dimension D when the initial total angular momentum is sufficiently large. The two black holes merge and form an unstable bar-like horizon, which grows a neck in its middle that pinches down with diverging curvature. When D is large, the emission of gravitational radiation is strongly suppressed and cannot spin down the system to a stable rotating black hole before the neck grows. The phenomenon is demonstrated using simple numerical simulations of the effective theory in the 1/D expansion. We propose that, even though cosmic censorship is violated, the loss of predictability is small independently of D.

Cosmic censorship violation in black hole collisions in higher dimensions

We propose and demonstrate a new and efficient approach to investigate black hole dynamics in the limit of large number of dimensions D. The basic idea is that an asymptotically flat black brane evolving under the Gregory-Laflamme instability forms lumps that closely resemble a localized black hole. In this manner, the large-D effective equations for extended black branes can be used to study localized black holes. We show that these equations have exact solutions for black-hole-like lumps on the brane, which correctly capture the main properties of Schwarzschild and Myers-Perry black holes at large D, including their slow quasinormal modes and the ultraspinning instabilities (axisymmetric or not) at large angular momenta. Furthermore, we obtain a novel class of rotating ‘black bar’ solutions, which are stationary when D → ∞, and are long-lived when D is finite but large, since their gravitational wave emission is strongly suppressed. The leading large D approximation reproduces to per-cent level accuracy previous numerical calculations of the bar-mode growth rate in D = 6, 7.