Related papers: $\bf W_\infty$ Gravity - a Geometric Approach
We derive an action for gravity in the framework of non-commutative geometry by using the Wodzicki residue. We prove that for a Dirac operator $D$ on an $n$ dimensional compact Riemannian manifold with $n\geq 4$, $n$ even, the Wodzicki…
The interaction of matter with gravity in two dimensional spacetimes can be supplemented with a geometrical force analogous to a Lorentz force produced on a surface by a constant perpendicular magnetic field. In the special case of constant…
A geometrical study of supergravity defined on (1|1) complex superspace is presented. This approach is based on the introduction of generalized superprojective structures extending the notions of super Riemann geometry to a kind of super…
We investigate a possible unified theory of all interactions which is based only on fundamental spinor fields. The vielbein and metric arise as composite objects. The effective quantum gravitational theory can lead to a modification of…
A general method of constructing canonical gauge invariant actions is used to establish the equivalence between 2D induced gravity and a WZNW system, defined by a difference of two simple WZNW actions fo the SL(2,R) group. The…
We review some aspects of gauged WZW models. By choosing a nilpotent subgroup as gauge group, one is lead to three main applications: the construction of field theories with an extended conformal symmetry, the construction of the effective…
The w_\infty algebra is a particular generalization of the Virasoro algebra with generators of higher spin 2,3,...,\infty. It can be viewed as the algebra of a class of functions, relative to a Poisson bracket, on a suitably chosen surface.…
The possible interpretations of a new continuum model for the two-dimensional quantum gravity for $d>1$ ($d$=matter central charge), obtained by carefully treating both diffeomorphism and Weyl symmetries, are discussed. In particular we…
We study the gravitational action induced by coupling two-dimensional non-conformal, massive matter to gravity on a compact Riemann surface. We express this gravitational action in terms of finite and well-defined quantities for any value…
We describe the geomety of a set of scalar fields coupled to gravity. We consider the formalism of a differential Z_2-graded algebra of $2\times 2$ matrices whose elements are differential forms on space-time. The connection and the…
A universal symmetry algebra organizing the gravitational phase space has been recently found. It corresponds to the subset of diffeomorphisms that become physical at corners -- codimension-$2$ surfaces supporting Noether charges. It…
We relate the Teichmuller spaces obtained by Hitchin to the Teichmuller spaces of $WA_{n}$-gravity. The relationship of this space to $W$-gravity is obtained by identifying the flat $PSL(n+1,{\BR})$ connections of Hitchin to generalised…
We define an integral form of the deformed W-algebra of type gl_r, and construct its action on the K-theory groups of moduli spaces of rank r stable sheaves on a smooth projective surface S, under certain assumptions. Our construction…
By decomposing the regular representation of a particular (Heisenberg-like) Lie supergroup into irreducible subspaces, we show that not all of them can be obtained by applying geometric quantization to coadjoint orbits with an even…
The unified theory of string and two-dimensional quantum gravity is considered. The action for two-dimensional gravity is choosen in a well-known induced form and thus gravity posesses it's oun nontrivial dynamics even on the classical…
We consider N=1 two-dimensional (2d) dilatonic supergravity (SG), 2d dilatonic SG obtained by dimensional reduction from N=1 four-dimensional (4d) SG, N=2 2d dilatonic SG and string-inspired 4d dilatonic SG. For all the theories, the…
The possibility of the extension of spatial diffeomorphisms to a larger family of symmetries in a class of classical field theories is studied. The generator of the additional local symmetry contains a quadratic kinetic term and a potential…
The presence of a constant background antisymmetric tensor for open strings or D-branes forces the space-time coordinates to be noncommutative. An immediate consequence of this is that all fields get complexified. By applying this idea to…
We study $2D$ supergravity in a covariant and gauge independent way. The theory is obtained from $2D$ bosonic gravity following the square root method and the diffeomorphism superalgebra is explicitly computed. We argue that our approach…
After reviewing some aspects of gravity in two dimensions, it is shown that non-trivial embeddings of sl(2) in a semi-simple (super) Lie algebra give rise to a very large class of extensions of 2D gravity. The induced action is constructed…