Related papers: Non-perturbative data for Weil-Petersson volumes a…
We present an analysis of the perturbative realization of the $TTJJ$ correlator, with two stress energy tensors and two conserved currents, using free field theory realizations, integrating out conformal sectors in the quantum corrections.…
The super Weil-Petersson metric defined over the moduli space of smooth super curves produces a natural measure over the moduli space of smooth curves. The construction of the measure uses the extra data of a spin structure on each smooth…
We present simple models which exhibit some of the remarkable features expected to hold for the as yet unknown non-perturbative formulation of string theories. Among these are: (a) the absence of a background or embedding space for the full…
We propose an optimization algorithm for computing geodesics on the universal Teichm\"uller space T(1) in the Weil-Petersson ($W P$) metric. Another realization for T(1) is the space of planar shapes, modulo translation and scale, and thus…
Weil-Petersson and Masur-Veech volumes measure the sizes of moduli spaces of Riemann surfaces equipped with hyperbolic and flat metrics, respectively. Over the past several decades, the computation of these volumes has inspired remarkable…
The large order growth of string perturbation theory in $c\le 1$ conformal field theory coupled to world sheet gravity implies the presence of $O(e^{-{1\over g_s}})$ non-perturbative effects, whose leading behavior can be calculated in the…
We derive the Weil-Petersson measure on the moduli space of hyperbolic surfaces with defects of arbitrary opening angles and use this to compute its volume. We conjecture a matrix integral computing the corresponding volumes and confirm…
Comparing structured objects such as graphs is a fundamental operation involved in many learning tasks. To this end, the Gromov-Wasserstein (GW) distance, based on Optimal Transport (OT), has proven to be successful in handling the specific…
Weil-Petersson volumes of the moduli space of curves are deeply related to the Kontsevich-Witten KdV tau function. They possess a Virasoro symmetry which comes out of recursion relations between the volumes due to Mirzakhani. Similarly, the…
We present a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…
The theory of gravitational wave turbulence describes the long-term statistical behaviour of a set of weakly nonlinear interacting waves. In this paper, we aim to study aspects of gravitational turbulence within the framework of general…
Optimal transport (OT) and Gromov-Wasserstein (GW) alignment are powerful frameworks for geometrically driven matching of probability distributions, yet their large-scale usage is hampered by high statistical and computational costs.…
The Gromov-Wasserstein (GW) transport problem is a relaxation of classic optimal transport, which seeks a transport between two measures while preserving their internal geometry. Due to meeting this theoretical underpinning, it is a…
The problem of solving perturbatively the equations describing the evolution of self-gravitating collisionless matter in an expanding universe considerably simplifies when directly formulated in terms of the gravitational and velocity…
We derive the most general mimetic scalar-tensor theory assuming a healthy "seed" action and accounting for the constraints on the speed of gravitational-wave propagation arising from the GW170817 event. By analysing linear perturbations…
This paper makes the first systematic attempt to determine using perturbation theory the positions of images by gravitational lensing due to arbitrary number of coplanar masses without any symmetry on a plane, as a function of lens and…
A simple method is presented for deriving universal formulae for the correlators, frequently denoted $W_{g,n}(\{z_i\}), i=1,..n$, of a wide range of models of physical and mathematical interest. While many alternative methods exist for…
Let $V=\bigotimes_{k=1}^{N} V_{k}$ be the $N$ spin-$j$ Hilbert space with $d=2j+1$-dimensional single particle space. We fix an orthonormal basis $\{|m_i\rangle\}$ for each $V_{k}$, with weight $m_i\in \{-j,\ldots j\}$. Let $V_{(w)}$ be the…
We present a simple and intuitive approximation for solving perturbation theory (PT) of small cosmic fluctuations. We consider only the spherically symmetric or monopole contribution to the PT integrals, which yields the exact result for…
It is proposed that a family of Jackiw-Teitelboim supergravites, recently discussed in connection with matrix models by Stanford and Witten, can be given a complete definition, to all orders in the topological expansion and beyond, in terms…