Related papers: Notes on the BMS group in three dimensions: II. Co…
The worldvolume theory of membrane is mathematically equivalent to three-dimensional quantum gravity coupled to matter fields corresponding to the target space coordinates of embedded membrane. In a recent paper [arXiv:1503.08812] a new…
Just as 3d state sum models, including 3d quantum gravity, can be built using categories of group representations, "2-categories of 2-group representations" may provide interesting state sum models for 4d quantum topology, if not quantum…
We demonstrate how some problems arising in simplicial quantum gravity can be successfully addressed within the framework of combinatorial group theory. In particular, we argue that the number of simplicial 3-manifolds having a fixed…
We study the construction of a manifestly covariant worldline action from a coadjoint orbit. A coadjoint orbit is a submanifold in the dual vector space of a Lie algebra, generated by coadjoint actions. Since a coadjoint orbit is a…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
Two-dimensional (2d) field theories invariant under the Bondi-Metzner-Sachs algebra, or 2d BMSFTs in short, are putative holographic duals of Einstein gravity in 3d asymptotically flat spacetimes. When defined on a torus, these field…
Three-dimensional Einstein-Maxwell theory with non trivial asymptotics at null infinity is solved. The symmetry algebra is a Virasoro-Kac-Moody type algebra that extends the bms3 algebra of the purely gravitational case. Solution space…
We describe some results concerning the phase space of 3-dimensional Einstein gravity when space is a torus and with negative cosmological constant. The approach uses the holonomy matrices of flat SL(2,R) connections on the torus to…
We analyze the geometric aspects of unitary evolution of general states for a multilevel quantum system by exploiting the structure of coadjoint orbits in the unitary group Lie algebra. Using the same method in the case of SU(3) we study…
In the Chern-Simons formulation of Einstein gravity in 2+1 dimensions the phase space of gravity is the moduli space of flat G-connections, where G is a typically non-compact Lie group which depends on the signature of space-time and the…
We investigate the quantum aspects of three-dimensional gravity with a positive cosmological constant. The reduced phase space of the three-dimensional de Sitter gravity is obtained as the space which consists of the Kerr-de Sitter…
We study flat space cosmologies in two dimensions by taking the flat space limit of the Achucarro-Ortiz model. We unravel a phase transition between hot flat space and flat space cosmologies, and derive a new dilaton-dependent counterterm…
We study the representations of the three-dimensional Euclidean Snyder-de Sitter algebra. This algebra generates the symmetries of a model admitting two fundamental scales (Planck mass and cosmological constant) and is invariant under the…
We study several aspects of holographic entanglement in two models known as flat$_3$/BMSFT and (W)AdS$_3$/WCFT. These are two examples of holography beyond AdS/CFT where the the boundary field theories are not Lorentz invariant but still…
Massless higher-spin fields show no preference for any value of the cosmological constant in $3d$. All matter-free higher-spin gravities in 3d are equivalent to Chern-Simons theories with an appropriate choice of gauge algebra. For various…
We show that the effective dynamics of matter fields coupled to 3d quantum gravity is described after integration over the gravitational degrees of freedom by a braided non-commutative quantum field theory symmetric under a…
A homology cylinder over a compact manifold is a homology cobordism between two copies of the manifold together with a boundary parametrization. We study abelian quotients of the homology cobordism group of homology cylinders. For homology…
Organization and ordering from interactions in many-body systems underlies our understanding of phases of classical and quantum matter. Magnetism has played a particularly foundational role in the study of many-body phases. Here, we explore…
We establish the phase diagram of three--dimensional quantum gravity coupled to Ising matter. We find that in the negative curvature phase of the quantum gravity there is no disordered phase for ferromagnetic Ising matter because the…
We further develop a noncommutative model unifying quantum mechanics and general relativity proposed in {\it Gen. Rel. Grav.} (2004) {\bf 36}, 111-126. Generalized symmetries of the model are defined by a groupoid $\Gamma $ given by the…