相关论文: Classical Teichmuller theory and (2+1) gravity
We study closed universes in simple models of two dimensional gravity, such as Jackiw-Teiteilboim (JT) gravity coupled to matter, and a toy topological model that captures the key features of the former. We find there is a stark contrast,…
We study, using Mean Curvature Flow methods, 3+1 dimensional cosmologies with a positive cosmological constant, matter satisfying the dominant and the strong energy conditions, and with spatial slices that can be foliated by 2-dimensional…
Recently we have proposed models of topological field theory including gravity in Mod. Phys. Lett. A 31 (2016) no.37, 1650213 and Phys. Rev. D 96 (2017) no.2, 024009, in order to solve the problem of the cosmological constant. The…
We give a natural definition of geodesics on a Riemannian supermanifold and extend the usual geodesic flow defined on the cotangent bundle of the body of the supermanifold, associated to the induced Riemannian structure on the body, to a…
Topological quantum field theories containing matter fields are constructed by twisting $N=2$ supersymmetric quantum field theories. It is shown that $N=2$ chiral (antichiral) multiplets lead to topological sigma models while $N=2$ twisted…
A theory of topological gravity is a homotopy-theoretic representation of the Segal-Tillmann topologification of a two-category with cobordisms as morphisms. This note describes a relatively accessible example of such a thing, suggested by…
This paper studies the gradient flow lines for the $L^2$ norm square of the Higgs field defined on the moduli space of semistable rank $2$ Higgs bundles twisted by a line bundle of positive degree over a compact Riemann surface $X$. The…
In the present work we consider the behavior of the geodesic flow on the unit tangent bundle of the 2-torus $T^2$ for an arbitrary Riemannian metric. A natural non-negative quantity which measures the complexity of the geodesic flow is the…
The classical theory of gravity is formulated as a gauge theory on a frame bundle with spontaneous symmetry breaking caused by the existence of Dirac fermionic fields. The pseudo-Riemannian metric (tetrad field) is the corresponding Higgs…
In the framework of the special theory of relativity, the relativistic theory of gravitation (RTG) is constructed. The energy-momentum tensor density of all the matter fields (including gravitational one) is treated as a source of the…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
Motivated by string dualities we propose topological gravity as the early phase of our universe. The topological nature of this phase naturally leads to the explanation of many of the puzzles of early universe cosmology. A concrete…
We introduce a model designed to describe charged particles as stable topological solitons of a field with values on the internal space S^3. These solitons behave like particles with relativistic properties like Lorentz contraction and…
We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow on Riemannian manifolds. First we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only…
We discuss in this Chapter a series of theoretical developments which motivate the introduction of a quantum evolution equation for which the eikonal approximation results in the geodesics of a four dimensional manifold. This geodesic…
In this paper we introduce a new geometric flow with rotational invariance and prove that, under this kind of flow, an arbitrary smooth closed contractible hypersurface in the Euclidean space Rn+1 (n, 1) converges to Sn in the C1-topology…
Starting from a topological gauge theory in two dimensions with symmetry groups $ISO(2,1)$, $SO(2,1)$ and $SO(1,2)$ we construct a model for gravity with non-trivial coupling to matter. We discuss the equations of motion which are connected…
It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact…
In this paper we give a gauge theoretic construction of the joint moduli space of stable G-Higgs bundles on closed Riemann surfaces, where the Riemann surface structure is allowed to vary in the Teichm\"uller space of the underlying smooth…
We consider gravity in 2+1 dimensions in presence of extended stationary sources with rotational symmetry. We prove by direct use of Einstein's equations that if i) the energy momentum tensor satisfies the weak energy condition, ii) the…