2d TQFT and baby universes

We present a one-dimensional mean field theory for topological 2D gravity. We discuss possible generalizations to other topological field theories, in particular those related to semisimple Frobenius manifolds.

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, as well as some connections, between the perturbative and non-perturbative aspects of the theory. We find rich semi-classical physics. However, when non-perturbative effects are included there is a unique closed universe state in each theory...

It is argued that quantum gravity has an interpretation as a topological field theory provided a certain constraint from the path intergral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for space - time dimensions different from 3. We then discuss possible models which may be relevant to our universe.

We propose a novel construction of a third quantised baby universe Hilbert space $\mathcal{H}_{BU}$ for the quantum gravity path integral. In contrast to the original description of $\alpha$-parameters, both the bulk and boundary microscopic parameters are fixed in our proposal. Wormholes and baby universes appear due to refined observables, of the boundary dual quantum field theories, that crucially involve the space of representations of the gauge group. Irreducible represe...

We investigate the fractal structure of $2d$ quantum gravity, both for pure gravity and for gravity coupled to multiple gaussian fields and for gravity coupled to Ising spins. The roughness of the surfaces is described in terms of baby universes and using numerical simulations we measure their distribution which is related to the string susceptibility exponent $\g_{string}$.

In the 1980's, work by Coleman and by Giddings and Strominger linked the physics of spacetime wormholes to `baby universes' and an ensemble of theories. We revisit such ideas, using features associated with a negative cosmological constant and asymptotically AdS boundaries to strengthen the results, introduce a change in perspective, and connect with recent replica wormhole discussions of the Page curve. A key new feature is an emphasis on the role of null states. We explore ...

We analyse the connections between the Wheeler DeWitt approach for two dimensional quantum gravity and holography, focusing mainly in the case of Liouville theory coupled to $c=1$ matter. Our motivation is to understand whether some form of averaging is essential for the boundary theory, if we wish to describe the bulk quantum gravity path integral of this two dimensional example. The analysis hence, is in a spirit similar to the recent studies of Jackiw-Teitelboim (JT)-gravi...

Some approaches to $2d$ gravity developed for the last years are reviewed. They are physical (Liouville) gravity, topological theories and matrix models. A special attention is paid to matrix models and their interrelations with different approaches. Almost all technical details are omitted, but examples are presented.

This paper gives a definition of an extended topological quantum field theory (TQFT) as a weak 2-functor Z: nCob_2 -> 2Vect, by analogy with the description of a TQFT as a functor Z: nCob -> Vect. We also show how to obtain such a theory from any finite group G. This theory is related to a topological gauge theory, the Dijkgraaf-Witten model. To give this definition rigorously, we first define a bicategory of cobordisms between cobordisms. We also give some explicit descripti...

We continue our study of factorizing theories of dilaton gravity, characterized by a universal bilocal interaction. All such factorizing theories can be shown to have discrete spectra, distinguished only by their local dilaton potentials. We show how such theories can be used to construct all alpha-states in the Hilbert space of baby universes of ordinary JT gravity. Large classes of these theories with different local potentials are found to be non-perturbatively equivalent ...