Chern-Simons-like Theories of Gravity

In this PhD thesis, we investigate a wide class of three-dimensional massive gravity models and show how most of them (if not all) can be brought in a first-order, Chern-Simons-like, formulation. This allows for a general analysis of the Hamiltonian for this wide class of models. From the Chern-Simons-like perspective, the known higher-derivative theories of 3D massive gravity, like Topologically Massive Gravity and New Massive Gravity, can be extended to a wider class of models. These models are shown to be free of (possibly ghost-like) scalar excitations and exhibit improved behavior with respect to Anti-de Sitter holography; the new models have regions in their parameter space where positive boundary central charge is compatible with positive mass and energy for the massive spin-2 mode. We discuss the construction of several of these improved models in detail and derive the necessary constraints needed to remove any unphysical degree of freedom. We also comment on the AdS/LCFT correspondence which arises when the massive spin-2 mode becomes massless and is replaced by a logarithmic mode. Most of the results have been published elsewhere, however, a special effort is made here to present the aspects of Chern-Simons-like theories in a pedagogical and comprehensive way.Comment: 201 pages, 3 figures, PhD thesis defended at the University of Groningen on September 26, 2014. Contains results previously obtained in arXiv:1307.2774, arXiv:1401.5386, arXiv:1402.1688, arXiv:1404.2867, arXiv:1405.6213 and arXiv:1410.616

Soft hairy warped black hole entropy

We reconsider warped black hole solutions in topologically massive gravity and find novel boundary conditions that allow for soft hairy excitations on the horizon. To compute the associated symmetry algebra we develop a general framework to compute asymptotic symmetries in any Chern-Simons-like theory of gravity. We use this to show that the near horizon symmetry algebra consists of two u(1) current algebras and recover the surprisingly simple entropy formula $S=2\pi (J_0^+ + J_0^-)$, where $J_0^\pm$ are zero mode charges of the current algebras. This provides the first example of a locally non-maximally symmetric configuration exhibiting this entropy law and thus non-trivial evidence for its universality.Comment: 24pp, v2: added appendix C and minor edit

Most general flat space boundary conditions in three-dimensional Einstein gravity

We consider the most general asymptotically flat boundary conditions in three-dimensional Einstein gravity in the sense that we allow for the maximal number of independent free functions in the metric, leading to six towers of boundary charges and six associated chemical potentials. We find as associated asymptotic symmetry algebra an isl(2)_k current algebra. Restricting the charges and chemical potentials in various ways recovers previous cases, such as BMS_3, Heisenberg or Detournay-Riegler, all of which can be obtained as contractions of corresponding AdS_3 constructions. Finally, we show that a flat space contraction can induce an additional Carrollian contraction. As examples we provide two novel sets of boundary conditions for Carroll gravity.Comment: 23 pp, invited for CQG BMS Focus Issue edited by Geoffrey Compere, v2: added minor clarifications and ref

Stress tensor correlators in three-dimensional gravity

We calculate holographically arbitrary n-point correlators of the boundary stress tensor in three-dimensional Einstein gravity with negative or vanishing cosmological constant. We provide explicit expressions up to 5-point (connected) correlators and show consistency with the Galilean conformal field theory Ward identities and recursion relations of correlators, which we derive. This provides a novel check of flat space holography in three dimensions.Comment: 6 pages, v2: corrected sign

Logistic growth on networks: exact solutions for the SI model

The SI model is the most basic of all compartmental models used to describe the spreading of information through a population. Despite its apparent simplicity, the analytic solution of this model on networks is still lacking. We address this problem here, using a novel formulation inspired by the mathematical treatment of many-body quantum systems. This allows us to organize the time-dependent expectation values for the state of individual nodes in terms of contributions from subgraphs of the network. We compute these contributions systematically and find a set of symmetry relations among subgraphs of differing topologies. We use our novel approach to compute the spreading of information on three different sample networks. The exact solution, which matches with Monte-Carlo simulations, visibly departs from the mean-field results.Comment: 15 pages, 4 figures, accompanied by a software package at https://doi.org/10.6084/m9.figshare.14872182.v4. v2: extended explanation and incorporated supplemental material into the main text. Accepted for publication in Phys.Rev.

Extended massive gravity in three dimensions

Using a first order Chern-Simons-like formulation of gravity we systematically construct higher-derivative extensions of general relativity in three dimensions. The construction ensures that the resulting higher-derivative gravity theories are free of scalar ghosts. We canonically analyze these theories and construct the gauge generators and the boundary central charges. The models we construct are all consistent with a holographic c-theorem which, however, does not imply that they are unitary. We find that Born-Infeld gravity in three dimensions is contained within these models as a subclass.Comment: 35p, v2; minor changes, references adde

Supersymmetric Galilean conformal blocks

We set up the bootstrap procedure for supersymmetric Galilean Conformal (SGC) field theories in two dimensions by constructing the SGC blocks in the $\mathcal{N}=1$ and two possible $\mathcal{N} =2$ extensions of the Galilean conformal algebra. In all analyzed cases, we present the bootstrap equations by crossing symmetry of the four point function. In addition, we compute the global SGC blocks analytically by solving the differential equations obtained by acting with the Casimirs of the global subalgebras inside the four point function. These global blocks agree with the general SGC blocks in the limit of large central charge. We comment on possible applications to supersymmetric BMS$_3$ invariant field theories and flat holography.Comment: 43 pages, v2: references added and typos fixed, v3: refs added, minor errors in the expression for the despotic blocks fixed. Matches published versio

Emergent information dynamics in many-body interconnected systems

The information implicitly represented in the state of physical systems allows one to analyze them with analytical techniques from statistical mechanics and information theory. In the case of complex networks such techniques are inspired by quantum statistical physics and have been used to analyze biophysical systems, from virus-host protein-protein interactions to whole-brain models of humans in health and disease. Here, instead of node-node interactions, we focus on the flow of information between network configurations. Our numerical results unravel fundamental differences between widely used spin models on networks, such as voter and kinetic dynamics, which cannot be found from classical node-based analysis. Our model opens the door to adapting powerful analytical methods from quantum many-body systems to study the interplay between structure and dynamics in interconnected systems.Comment: 7 pages, 3 figure

Logarithmic AdS Waves and Zwei-Dreibein Gravity

We show that the parameter space of Zwei-Dreibein Gravity (ZDG) in AdS3 exhibits critical points, where massive graviton modes coincide with pure gauge modes and new `logarithmic' modes appear, similar to what happens in New Massive Gravity. The existence of critical points is shown both at the linearized level, as well as by finding AdS wave solutions of the full non-linear theory, that behave as logarithmic modes towards the AdS boundary. In order to find these solutions explicitly, we give a reformulation of ZDG in terms of a single Dreibein, that involves an infinite number of derivatives. At the critical points, ZDG can be conjectured to be dual to a logarithmic conformal field theory with zero central charges, characterized by new anomalies whose conjectured values are calculated.Comment: 20 page