Related papers: A New Framework for Higher Loop Witten Diagrams

Moving detectors in relativistic quantum field theories reveal the fundamental entangled structure of the vacuum which manifests, for instance, through its thermal character when probed by a uniformly accelerated detector. In this paper, we…

In this follow up paper, we calculate higher point tree level graviton Witten diagrams in AdS$_4$ via bulk perturbation theory. We show that by rearranging the bulk to bulk graviton propagators, the calculations effectively reduce to the…

We extend the Mellin representation of conformal field theory (CFT) to allow for conformal boundaries and interfaces. We consider the simplest holographic setup dual to an interface CFT - a brane filling an $AdS_{d}$ subspace of $AdS_{d+1}$…

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…

We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective representations of their discrete symmetry groups - the…

Decision diagrams (DDs) have emerged as an efficient tool for simulating quantum circuits due to their capacity to exploit data redundancies in quantum states and quantum operations, enabling the efficient computation of probability…

Following the previous authors works (joint with I.A.Dynnikov) we develop a theory of the discrete analogs of the differential-geometrical (DG) connections in the triangulated manifolds. We study a nonstandard discretization based on the…

This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…

Infinite-dimensional differential algebraic equations (short DAEs) with input and output are studied. The concepts of operator nodes and system nodes are extended to systems which additionally may include algebraic constraints.…

To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…

We briefly recall a fundamental exterior differential system introduced by the author and then apply it to the case of three dimensions. Here we find new global tensors and intrinsic invariants of oriented Riemaniann 3-manifolds. The system…

Deep Bregman divergence measures divergence of data points using neural networks which is beyond Euclidean distance and capable of capturing divergence over distributions. In this paper, we propose deep Bregman divergences for contrastive…

We propose a new approach to the study of the correlation functions of W-algebras. The conformal blocks (chiral correlation functions), for fixed arguments, are defined to be those linear functionals on the product of the highest weight…

We analyse the Witten-Woronowicz's type deformations of the Lie superalgebra osp(2,2) and obtain a deformation parametrized by three independent parameters. For some of these algebras, finite dimensional representations are formulated in…

We explore connections between boundary representations of operator spaces and those of the associated Paulsen systems. Using the notions of finite representation and separating property which we introduced, boundary representations for…

In the Wigner framework, one abandons the assumption that the usual canonical commutation relations are necessarily valid. Instead, the compatibility of Hamilton's equations and the Heisenberg equations are the starting point, and no…

Isomorphisms of separable Hilbert spaces are analogous to isomorphisms of n-dimensional vector spaces. However, while n-dimensional spaces in applications are always realized as the Euclidean space R^n, Hilbert spaces admit various useful…

Different representations of dissipative Hamiltonian and port-Hamiltonian differential-algebraic equations (DAE) systems are presented and compared. Using global geometric and algebraic points of view, translations between the different…

In this review, we discuss recent developments concerning efficient calculations of multi-loop multi-leg scattering amplitudes. Inspired by the remarkable properties of the Loop-Tree Duality (LTD), we explain how to reconstruct an integrand…

We study three fundamental topics in the representation theory of disconnected algebraic groups whose identity component is reductive: (i) the classification of irreducible representations; (ii) the existence and properties of Weyl and dual…