2d TQFT and baby universes

Pure gravity and gauge theories in two dimensions are shown to be special cases of a much more general class of field theories each of which is characterized by a Poisson structure on a finite dimensional target space. A general scheme for the quantization of these theories is formulated. Explicit examples are studied in some detail. In particular gravity and gauge theories with equivalent actions are compared. Big gauge transformations as well as the condition of metric nond...

We clarify the relation between 2-form Einstein gravity and its topological version. The physical space of the topological version is contained in that of the Einstein gravity. Moreover a new vector field is introduced into 2-form Einstein gravity to restore the large symmetry of its topological version. The wave function of the universe is obtained for each model. (Talk given at the Workshop on General Relativity and Gravitation held at Waseda University, January 18-20, 19...

In the present thesis, we study various models of 2D dilaton gravity known as JT gravity coupled with non-trivial gauge interactions (for instance $SU(2)$ Yang-Mills, quartic interactions between $U(1)$ gauge fields and Modmax interactions etc.). In particular, we investigate the effects of the non-trivial gauge couplings on the thermal properties of black holes and wormholes in two dimensions and compute various physical observables like entropy, free energy, etc. Further, w...

We show how extended topological quantum field theories (TQFTs) can be used to obtain a kinematical setup for quantum gravity, i.e. a kinematical Hilbert space together with a representation of the observable algebra including operators of quantum geometry. In particular, we consider the holonomy-flux algebra of (2+1)-dimensional Euclidean loop quantum gravity, and construct a new representation of this algebra that incorporates a positive cosmological constant. The vacuum st...

New progress in loop gravity has lead to a simple model of `general-covariant quantum field theory'. I sum up the definition of the model in self-contained form, in terms accessible to those outside the subfield. I emphasize its formulation as a generalized topological quantum field theory with an infinite number of degrees of freedom, and its relation to lattice theory. I list the indications supporting the conjecture that the model is related to general relativity and UV fi...

We show that the surface roughness for $c<1$ matter theories coupled to $2D$ quantum gravity is described by a self-similar structure of baby universes. There exist baby universes whose neck thickness is of the order of the ultraviolet cutoff, the largest of these having a macroscopic area $\sim A^{1 \over {1-\gamma}}$, where $A$ is the total area and $\gamma$ the string susceptibility exponent.

We study quantum entanglements of baby universes which appear in non-perturbative corrections to the OSV formula for the entropy of extremal black holes in Type IIA string theory compactified on the local Calabi-Yau manifold defined as a rank 2 vector bundle over an arbitrary genus G Riemann surface. This generalizes the result for G=1 in hep-th/0504221. Non-perturbative terms can be organized into a sum over contributions from baby universes, and the total wave-function is t...

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 to those of previous related models but incorporate matter content. We also discuss the resulting quantum theory and finally present explicit formul\ae $\;$ for topological invariants.

In this thesis we study two different approaches to holography, and comment on the possible relation between them. The first approach is an analysis of the high-energy regime of quantum gravity in the eikonal approximation, where the theory reduces to a topological field theory. This is the regime where particles interact at high energies but with small momentum transfer. We do this for the cases of asymptotically dS and AdS geometries and find that in both cases the theory i...

The goal of this paper is to introduce some of the major ideas behind extended topological quantum field theories with an emphasis on explicit examples and calculations. The statement of the Cobordism Hypothesis is explained and immediately used to classify framed and oriented extended two dimensional topological quantum field theories. The passage from framed theories to oriented theories is equivalent to giving homotopy fixed points of an $SO(n)$ action on the space of fiel...