Related papers: Geometry and Complexity of Path Integrals in Inhom…
We present a general perturbative effective field theory (EFT) description of galaxy shape correlations, which are commonly known as intrinsic alignments. This rigorous approach extends current analytical modelling strategies in that it…
In this paper, we demonstrate that the first law of holographic pseudo-entropy, which is a non-Hermitian generalization of entanglement entropy in a two-dimensional conformal field theory (CFT), is equivalent to the perturbative Einstein…
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…
Modular invariance strongly constrains the spectrum of states of two dimensional conformal field theories. By summing over the images of the modular group, we construct candidate CFT partition functions that are modular invariant and have…
The concept of path homotopy has received widely attention in the field of path planning in recent years. In this article, a homotopy invariant based on convex dissection for a two-dimensional bounded Euclidean space is developed, which can…
We review equivariant localization techniques for the evaluation of Feynman path integrals. We develop systematic geometric methods for studying the semi-classical properties of phase space path integrals for dynamical systems, emphasizing…
The thermodynamics and the entanglement properties of two-dimensional conformal field theories ($2$d CFTs) on curved backgrounds are studied. By means of conformal mapping we study the equivalent system on flat space governed by the…
We discuss the interpretation of path integral optimization as a uniformization problem in even dimensions. This perspective allows for a systematical construction of the higher-dimensional path integral complexity in holographic conformal…
Extending the background metric optimization procedure for Euclidean path integrals of two-dimensional conformal field theories, introduced by Caputa et al. (Phys. Rev. Lett. 119, 071602 (2017)), to a $z=2$ anisotropically scale-invariant…
Significant work has gone into determining the minimal set of entropy inequalities that determine the holographic entropy cone. Holographic systems with three or more parties have been shown to obey additional inequalities that generic…
We consider the problem of optimal path planning in different homotopy classes in a given environment. Though important in robotics applications, path-planning with reasoning about homotopy classes of trajectories has typically focused on…
We demonstrate an original development of path-integral quantization in the case of a multiply connected configuration space of indistinguishable charged particles on a 2D manifold and exposed to a strong perpendicular magnetic field. The…
Integrability of equations of topological-antitopological fusion (being proposed by Cecotti and Vafa) describing ground state metric on given 2D topological field theory (TFT) model, is proved. For massive TFT models these equations are…
A kink-based path integral method, previously applied to atomic systems, is modified and used to study molecular systems. The method allows the simultaneous evolution of atomic and electronic degrees of freedom. Results for CH$_4 $, NH$_3…
We study holographic entanglement entropy in four-dimensional quantum gravity with negative cosmological constant. By using the replica trick and evaluating path integrals in the minisuperspace approximation, in conjunction with the…
We discuss a recent approach to quantum field theoretical path integration on noncommutative geometries which imply UV/IR regularising finite minimal uncertainties in positions and/or momenta. One class of such noncommutative geometries…
We consider CFT states defined by adding nonlocal multi-trace sources to the Euclidean path integral defining the vacuum state. For holographic theories, we argue that these states correspond to states in the gravitational theory with a…
Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations -- such as performing a change of the integration path -- one would like to carry out in…
We argue that given holographic CFT$_1$ in some state with a dual spacetime geometry M, and given some other holographic CFT$_2$, we can find states of CFT$_2$ whose dual geometries closely approximate arbitrarily large causal patches of M,…
The symmetries of paths in a manifold $M$ are classified with respect to a given pointwise proper action of a Lie group $G$ on $M$. Here, paths are embeddings of a compact interval into $M$. There are at least two types of symmetries:…