Related papers: Emergent geometry and path integral optimization f…
We introduce a new optimization procedure for Euclidean path integrals which compute wave functionals in conformal field theories (CFTs). We optimize the background metric in the space on which the path integration is performed.…
The 2+1 dimensional quantum Lifshitz model can be generalised to a class of higher dimensional free field theories that exhibit Lifshitz scaling. When the dynamical critical exponent equals the number of spatial dimensions, equal time…
In this work, we formulate a path-integral optimization for two dimensional conformal field theories perturbed by relevant operators. We present several evidences how this optimization mechanism works, based on calculations in free field…
In a geometrical approach to gravity the metric and the (gravitational) connection can be independent and one deals with metric-affine theories. We construct the most general action of metric-affine effective field theories, including a…
By using the notion of fractional derivatives, we introduce a class of massless Lifshitz scalar field theory in (1+1)-dimension with an arbitrary anisotropy index $z$. The Lifshitz scale invariant ground state of the theory is constructed…
We consider the problem of finding an optimal 3D road trajectory between two points on a terrain with variable elevation. Unlike common heuristic pathfinding methods, we propose a rigorous framework based on the calculus of variations,…
We develop a field-theoretical approach to determination of the background target space fields corresponding to general $G/H$ coset conformal theories described by gauged WZW models. The basic idea is to identify the effective action of a…
The Einstein-Proca action is known to have asymptotically locally Lifshitz spacetimes as classical solutions. For dynamical exponent z=2, two-point correlation functions for fluctuations around such a geometry are derived analytically. It…
In this work we develop the path integral optimization in a class of inhomogeneous 2d CFTs constructed by putting an ordinary CFT on a space with a position dependent metric. After setting up and solving the general optimization problem, we…
In these Notes, a comprehensive description of the universal fractal geometry of conformally-invariant scaling curves or interfaces, in the plane or half-plane, is given. The present approach focuses on deriving critical exponents…
Early efforts to understand complexity in field theory have primarily employed a geometric approach based on the concept of circuit complexity in quantum information theory. In a parallel vein, it has been proposed that certain deformations…
We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The optimization is performed by minimizing certain functional, which can be interpreted as a measure of…
Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…
Both analytic and geometric forms of an optimal monotone principle for $L^p$-integral of the Green function of a simply-connected planar domain $\Omega$ with rectifiable simple curve as boundary are established through a sharp…
Many parametrization and mapping-related problems in geometry processing can be viewed as metric optimization problems, i.e., computing a metric minimizing a functional and satisfying a set of constraints, such as flatness. Penner…
We present a framework for performing efficient regression in general metric spaces. Roughly speaking, our regressor predicts the value at a new point by computing a Lipschitz extension --- the smoothest function consistent with the…
Computing optimal, collision-free trajectories for high-dimensional systems is a challenging problem. Sampling-based planners struggle with the dimensionality, whereas trajectory optimizers may get stuck in local minima due to inherent…
We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are…
The study of arXiv:2502.01174 geometrization of classical fields in the 4d--Finsler space of MES (Model of Embedded Spaces) is continued. The model postulates a proper metric set of a distributed matter element and states that the…
The gravitational path integral measure has been the subject of an increasing interest lately, and no conclusive answer yet exists for its correct form. In this paper, we adopt effective field theory techniques to shed light on this issue.…