Related papers: The structure of the ground ring in critical $W_3$…
We briefly review some results in the theory of quantum $W_3$ gravity in the chiral gauge. We compare them with similar results in the analogous but simpler cases of $d=2$ induced gauge theories and $d=2$ induced gravity.
We show that the new classical action for two dimensional gravity (the Jackiw-Teitelboim model) possesses a $W_3$ algebra. We quantise the resulting $W_3$ gravity in the presence of matter fields with arbitrary central charges and obtain…
I summarize some recent results obtained in collaboration with P.~Bouwknegt and K.~Pilch on the spectrum of physical states in $\cW_3$ gravity coupled to $c=2$ matter. In particular, it is shown that the algebra of operators corresponding…
A crucial property of Weyl gravity is its conformal invariance. It is shown how this gauge symmetry is exactly reflected by the two constraints in the Hamiltonian framework. Since the spatial 3-metric is one of the configuration variables,…
The boundary structure of $3+1$-dimensional gravity (in the Palatini-Cartan formalism) coupled to to gauge (Yang-Mills) and matter (scalar and spinorial) fields is described through the use of the Kijowski-Tulczijew construction. In…
We derive the supersymmetric structure present in W-gravities which has been already observed in various contexts as Yang-Mills theory, topological field theories, bosonic string and chiral W_{3}-gravity. This derivation which is made in…
The full non-linear structure of the action and transformation rules for $\W_N$-gravity coupled to matter are obtained from a non-linear truncation of those for $w_ \infty$ gravity. The geometry of the construction is discussed, and it is…
(Talk given at Strings '93, Berkeley, and at XXVII. Internationales Symposium \"uber Elementarteilchentheorie, Wendisch-Rietz, 1993) We review the superconformal properties of matter coupled to $2d$ gravity, and $W$-extensions thereof. We…
A covariant scheme for material coupling with $GL(N,R)$ gauge formulation of gravity is studied. We revisit a known idea of a Yang-Mills type construction, where quadratical power of cosmological constant have to be considered in…
We show that almost all string theories, including the bosonic string, the superstring and $W$-string theories, possess a twisted N=2 superconformal symmetry. This enables us to establish a connection between topological gravity and the…
Physical properties of the quantum gravitational vacuum state are explored by solving a lattice version of the Wheeler-DeWitt equation. The constraint of diffeomorphism invariance is strong enough to uniquely determine the structure of the…
We study the forward orbit of the critical point for polynomials of the form $f_c=z^2+c$ defined over $\mathbb{Z}_p$. Hubbard trees capture the dynamical behavior for such maps with finite critical orbit in $\mathbb{C}$. We suggest a notion…
We analyse the relationship between the components of the intrinsic torsion of an SU(3) structure on a 6-manifold and a G_2 structure on a 7-manifold. Various examples illustrate the type of SU(3) structure that can arise as a reduction of…
Based on a fundamental symmetry between space, time, mass and charge, a series of group structures of physical interest is generated, ranging from C2 to E8. The most significant result of this analysis is a version of the Dirac equation…
A covariant scheme for matter coupling with a GL(3,R) gauge formulation of gravity is studied. We revisit a known Yang-Mills type construction, where quadratical power of cosmological constant have to be considered in consistence with…
It is shown that the Sugawara-type construction for W3-algebra associated with the four magical Jordan algebras leads to the anomalous theory of W3-gravity.
Gravity is commonly thought of as one of the four force fields in nature. However, in standard formulations its mathematical structure is rather different from the Yang-Mills fields of particle physics that govern the electromagnetic, weak,…
We construct all possible Weyl invariant actions in $d=4$ for linearized spin three field in a general gravitational background. The first action is obtained as the square of the generalized Weyl tensor for a spin three gauge field in…
We investigate the phase structure of three-dimensional quantum gravity coupled to an Ising spin system by means of numerical simulations. The quantum gravity part is modelled by the summation over random simplicial manifolds, and the Ising…
We propose a step-by-step manual for the construction of alternative theories of gravity, perturbatively as well as nonperturbatively. The construction is guided by no more than two fundamental principles that we impose on the gravitational…