Related papers: On some (integrable) structures in low-dimensional…
In this paper, we present a construction toward a new type of TQFTs at the crossroads of low-dimensional topology, algebraic geometry, physics, and homotopy theory. It assigns TMF-modules to closed 3-manifolds and maps of TMF-modules to…
Relying on a mathematical analogy of the pure states of the two-qubit system of quantum information theory with four-component spinors we introduce the concept of the intrinsic entanglement of spinors. To explore its physical sense we study…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
We evaluate reflected entropy in certain anisotropic boundary theories dual to nonrelativistic geometries using holography. It is proposed that this quantity is proportional to the minimal area of the entanglement wedge cross section. Using…
In this paper, we analyze the question of replica symmetry in the bulk for multi-partite entanglement measures in the vacuum state of two dimensional holographic CFTs. We first define a class of multi-partite local unitary invariants,…
We show that the symmetry topological field theory (SymTFT) construction, also known as the topological holography, provides a natural and intuitive framework for the entropic order parameter characterising phases with (partially) broken…
We explain a correspondence between some invariants in the dynamics of color exchange in a 2d coloring problem, which are polynomials of winding numbers, and linking numbers in 3d. One invariant is visualized as linking of lines on a…
The objective of this work is twofold. On one hand, it is intended as a short introduction to spin networks and invariants of 3-manifolds. It covers the main areas needed to have a first understanding of the topics involved in the…
Motivated by the holographic prescriptions for computing entanglement entropy and complexity, we study the properties of volumes/areas of bulk surfaces. We obtain a simple formula for the shape dependence of holographic entanglement entropy…
We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem by using intersection…
We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d $\mathcal{N}=2$ theories where such structures a priori are not manifest. These modular structures…
Deep feature spaces have the capacity to encode complex transformations of their input data. However, understanding the relative feature-space relationship between two transformed encoded images is difficult. For instance, what is the…
We prove some classification results for tight contact structure in the 3-space, -ball and -sphere that are invariant with respect to some arbitrary involution, that is conjugated to the standard rotation around the x-axis. Unlike the…
In this work, we develop a systematic formalism to evaluate the upper bound of a large family of holographic entanglement entropy combinations when fixing $n$ subsystems and fine-tuning one other subsystem. The upper bound configurations…
We consider banana shaped regions as examples of compact regions, whose boundary has two conical singularities. Their regularised holographic entropy is calculated with all divergent as well as finite terms. The coefficient of the squared…
We present several expected properties of the holomorphic Floer theory of a holomorphic symplectic manifold. In particular, we propose a conjecture relating holomorphic Floer theory of Hitchin integrable systems and Donaldson-Thomas…
Due to their particle-like properties, three-dimensional (3D) spin textures have garnered significant interest, particularly for their potential applications in next-generation information storage devices. However, efficiently identifying…
We explain how to relate the ideas of Carroll geometry, matrix theory on instantonic objects, and infinite boost limits of M-theory. Based on these new insights, we explore the implications for possible holographic constructions involving a…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
We study a holographic theory of general spacetimes that does not rely on the existence of asymptotic regions. This theory is to be formulated in a holographic space. When a semiclassical description is applicable, the holographic space is…