Related papers: An explicit formula for Witten's 2-correlators
We verify the Invariance Conjectures of tautological equations in genus two. In particular, a uniform derivation of all known genus two equations is given.
We derive a recursive formula for certain relative Gromov-Witten invariants with maximal tangency condition via the Witten-Dijkgraaf-Verlinde-Verlinde equation. For certain relative pairs, we get explicit formulae of invariants using the…
We formulate quantum gravity in $2+\epsilon$ dimensions in such a way that the conformal mode is explicitly separated. The dynamics of the conformal mode is understood in terms of the oversubtraction due to the one loop counter term. The…
The two-dimensional theory of gravity describing a graviton-dilaton system is considered. The graviton-dilaton coupling can be fixed such that the quantum theory remains free of the conformal anomaly for any conformal dimension of the…
The reduction of the dreibein formalism of 2+1 General Relativity to the holonomies is explicitly performed. We also show explicitly how to relate these holonomies to a geometry classically, and how to generate these holonomies from any…
We generalize the geometric structures generated by Witten's ground ring. It is shown that these generalized structures involve in a natural way some geometric constructions from Self-dual gravity [1,12]. The formal twistor construction on…
We find a volume form on moduli space of double punctured Riemann surfaces whose integral satisfies the Painlev\'e I recursion relations of the genus expansion of the specific heat of 2D gravity. This allows us to express the asymptotic…
We propose a topological version of four-dimensional (Euclidean) Einstein gravity, in which anti-self-dual 2-forms and an SU(2) connection are used as fundamental fields. The theory describes the moduli space of conformally self-dual…
Recent work by physicists on gravity in two dimensions has a natural generalization to four dimensions, formulated in terms of an analogue of Segal's category [defined for the study of conformal field theory].
Abtract: The 2D model of gravity with zweibeins $e^{a}$ and the Lorentz connection one-form $\omega^{a}_{\ b}$ as independent gravitational variables is considered. The solutions of classical equations of motion which can be interpreted as…
The solutions of two-dimensional gravity following from a non-linear Lagrangian L = f(R) are classified, and their symmetry and singularity properties are described. Then a conformal transformation is applied to rewrite these solutions as…
One-matrix model in $p$-critical point on torus is considered. The generating function of correlation numbers in genus one is evaluated and used for computation correlation numbers in KdV and CFT frames. It is shown that the correlation…
We make it precise what it means to have a connection with torsion as solution of the Einstein equations. While locally the theory remains the same, the new formulation allows for topologies that would have been excluded in the standard…
A general framework for the solutions of the constraints of pure gravity is constructed. It provides with well defined mathematical criteria to classify their solutions in four classes. Complete families of solutions are obtained in some…
The 2D model of gravity with zweibeins $e^{a}$ and the Lorentz connection one-form $\omega^{a}_{\ b}$ as independent gravitational variables coupled to 2d massless Dirac matter is considered. It is shown that the classical equations of…
We investigate the space ${\cal M}$ of classical solutions to Witten's formulation of 2+1 gravity on the manifold ${\bf R} \times T^2$. ${\cal M}$ is connected, but neither Hausdorff nor a manifold. However, removing from ${\cal M}$ a set…
This paper is devoted to the Hamiltonian analysis of bimetric gravity in vierbein formulation. We identify all constraints and determine their nature. We also show an existence of additional constraint so that the scalar mode can be…
We calculate a class of two-point boundary correlators in 2D quantum gravity using its microscopic realization as loop gas on a random surface. We find a perfect agreement with the two-point boundary correlation function in Liouville…
We describe of the topology of the geometric quotients of 2n dimensional compact connected symplectic manifolds with n-1 dimensional torus actions. When the isotropy weights at each fixed point are in general position, the quotient is…
In contrast to other approaches to (2+1)-dimensional quantum gravity, the Wheeler-DeWitt equation appears to be too complicated to solve explicitly, even for simple spacetime topologies. Nevertheless, it is possible to obtain a good deal of…