Related papers: BMS-like algebras: canonical realisations and BRST…
We compute completely the BRST--antibracket cohomology on local functionals in two-dimensional Weyl invariant gravity for given classical field content (two dimensional metric and scalar matter fields) and gauge symmetries (two dimensional…
The surface charges associated with the symmetries of asymptotically flat four dimensional spacetimes at null infinity are constructed. They realize the symmetry algebra in general only up to a field-dependent central extension that…
Starting from the asymptotic kinematics of massless scalar fields near null infinity in any spacetime dimension, we build two higher-spin extensions of the Carrollian definition of the BMS group and its generalisations. The first extension…
We construct several quantum coset W-algebras, e.g. sl(2,R)/U(1) and sl(2,R)+sl(2,R) / sl(2,R), and argue that they are finitely nonfreely generated. Furthermore, we discuss in detail their role as unifying W-algebras of Casimir W-algebras.…
We introduce and study a new discrete basis of gravity constraints by making use of harmonic expansion for closed cosmological models. The full set of constraints is splitted into area-preserving spatial diffeomorphisms, forming closed…
We provide boundary conditions for three-dimensional gravity including boosted Rindler spacetimes, representing the near-horizon geometry of non-extremal black holes or flat space cosmologies. These boundary conditions force us to make some…
Let $G$ be a noncompact semisimple algebraic group with trivial center, $S < G$ a maximal split torus, $H < G$ the centralizer of $S$ in $G$ and $\Gamma < G$ an irreducible lattice. Consider the group measure space von Neumann algebra…
We consider the sl(2) current algebra at level k=-4 when the sl(2) BRST operator is nilpotent. We formulate a spectral sequence converging to the cohomology of this BRST operator. At the second term of the spectral sequence, we observe an…
We introduce higher order (polynomial) extensions of the unique (up to isomorphisms) non trivial central extension of the Heisenberg algebra. Using the boson representation of the latter, we construct the corresponding polynomial analogue…
We investigate new realisations of the $W_3$ algebra with arbitrary central charge, making use of the fact that this algebra can be linearised by the inclusion of a spin-1 current. We use the new realisations with $c=102$ and $c=100$ to…
We study two-dimensional celestial conformal field theory describing four-dimensional ${\cal N}=1$ supergravity/Yang-Mills systems and show that the underlying symmetry is a supersymmetric generalization of BMS symmetry. We construct…
The enforcement of the unimodularity condition in a gravity theory by means of a Lagrange multiplier leads, in general, to inconsistencies upon quantization. This is so, in particular, when the classic linear splitting of the metric between…
Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to asymptotically flat spacetimes in three dimensions. These field theories are naturally defined on null surfaces and hence are conformal cousins…
We consider three dimensional $N=4$ flat supergravity, with an abelian R-symmetry enhancing the gravitational phase space. We obtain the field configuration whose asymptotic symmetries at null infinity coincide with the centrally extended…
We present a mathematically rigorous canonical quantization of Yang-Mills theory in 1+1 dimensions (YM$_{1+1}$) by operator-algebraic methods. The latter are based on Hamiltonian lattice gauge theory and multi-scale analysis via inductive…
Here is discussed application of the Weyl pair to construction of universal set of quantum gates for high-dimensional quantum system. An application of Lie algebras (Hamiltonians) for construction of universal gates is revisited first. It…
We present a new formulation for the canonical approach to conformal (Weyl-squared) gravity and its extension by the Einstein-Hilbert term and a nonminimally coupled scalar field. For this purpose we use a unimodular decomposition of the…
We find a surprising connection between asymptotically flat space-times and non-relativistic conformal systems in one lower dimension. The BMS group is the group of asymptotic isometries of flat Minkowski space at null infinity. This is…
We show that the BF theory in any space-time dimension, when quantized in a certain linear covariant gauge, possesses a vector supersymmetry. The generator of the latter together with those of the BRS transformations and of the translations…
We study a Lie algebra of formal vector fields $W_n$ with its application to the perturbative deformed holomorphic symplectic structure in the A-model, and a Calabi-Yau manifold with boundaries in the B-model. A relevant concept in the…