Related papers: Path Integral Over Conformally Self-Dual Geometrie…
The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of…
In this paper the Feynman path integral technique is applied to two-dimensional spaces of non-constant curvature: these spaces are called Darboux spaces $\DI$--$\DIV$. We start each consideration in terms of the metric and then analyze the…
We first streamline the construction of the unique six-dimensional conformal gravity action found by L\"u, Pang and Pope, that admits Einstein metrics as solutions to the field equations. We then prove that there exists a unique…
It is rather well-known that spacetime singularities are not covariant under field redefinitions. A manifestly covariant approach to singularities in classical gravity was proposed in arXiv:2008.09387. In this paper, we start to extend this…
There exist many four dimensional integrable theories. They include self-dual gauge and gravity theories, all their extended supersymmetric generalisations, as well the full (non-self-dual) N=3 super Yang-Mills equations. We review the…
We give a rigorous definition of sine dilaton gravity in terms of the worldsheet theory of the complex Liouville string arXiv:2409.17246. The latter has a known exact solution that we leverage to explore the gravitational path integral of…
We propose that large quantum fluctuations of the conformal factor drastically modify classical general relativity at cosmological distance scales, resulting in a scale invariant phase of quantum gravity in the far infrared. We derive…
Gravity-induced quantum interference is a remarkable effect that has already been confirmed experimentally, and it is a phenomenon in which quantum mechanics and gravity play simultaneously an important role. Additionally, a generalized…
We develop a two-dimensional gravity path integral formulation of the $T \bar T + \Lambda_2$ deformation of quantum field theory. This provides an exactly solvable generalization of the pure $T \bar T$ deformation that is relevant for de…
We present a coordinate-invariant approach, based on a Pauli-Villars measure, to the definition of the path integral in two-dimensional conformal field theory. We discuss some advantages of this approach compared to the operator formalism…
The Liouville action emerges as the effective action of 2-d gravity in the process of path integral quantization of the bosonic string. It yields a measure of the violation of classical symmetries of the theory at the quantum level. Certain…
We compute the counterterms necessary for the renormalization of the one-loop effective action of massive gravity from a worldline perspective. This is achieved by employing the recently proposed massive $\mathcal{N}=4$ spinning particle…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
The purpose of this article is threefold. First, we show that when one explores a conformal loop ensemble of parameter $\kappa=4$ ($\mathrm{CLE}_4$) on an independent $2$-Liouville quantum gravity ($2$-LQG) disk, the surfaces which are cut…
The search for a mathematical foundation for the path integral of Euclidean quantum gravity calls for the construction of random geometry on the spacetime manifold. Following developments in physics on the two-dimensional theory, random…
D-dimensional maximal supergravities type I with G/H coset spaces have global G-symmetry and local H symmetry, which can be gauge-fixed in symmetric or Iwasawa-type gauges. Maximal D-dimensional supergravities type II derived from higher…
We report on an instance in quantum gravity where a topological expansion resums into an effective description on a single geometry. The original theory whose gravitational path integral we study is JT quantum gravity with one asymptotic…
In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main…
A well-defined regularized path integral for Lorentzian quantum gravity in three and four dimensions is constructed, given in terms of a sum over dynamically triangulated causal space-times. Each Lorentzian geometry and its associated…
A direct anomaly calculation method for general supersymmetric models by path integral measure in superspace is established. It includes the traditional Konishi anomaly as a specific case. As another example, superconformal anomaly in…