Related papers: Lecture Notes on Generalized Symmetries and Applic…
This brief review is intended to introduce gravitational physicists to recent developments in which general relativity is being used to describe certain aspects of condensed matter systems, e.g., superconductivity.
Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection…
Supersymmetric gauge theories have played a central role in applications of quantum field theory to mathematics. Topologically twisted supersymmetric gauge theories often admit a rigorous mathematical description: for example, the Donaldson…
We propose a method for analyzing two-dimensional symmetry protected topological (SPT) wavefunctions using a correspondence with conformal field theories (CFTs) and integrable lattice models. This method generalizes the CFT approach for the…
Spacetime and internal symmetries can be used to severely restrict the form of the equations for the fundamental laws of physics. The success of this approach in the context of general relativity and particle physics motivates the…
Motivated by recent applications to entropy theory in dynamical systems, we generalise notions introduced by Matthews and define weakly weighted and componentwisely weakly weighted (generalised) quasi-metrics. We then systematise and extend…
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
First we introduce a generalization of symmetric spaces to parabolic geometries. We provide construction of such parabolic geometries starting with classical symmetric spaces and we show that all regular parabolic geometries with smooth…
The AdS/CFT correspondence provides quantum theories of gravity in which spacetime and gravitational physics emerge from ordinary non-gravitational quantum systems with many degrees of freedom. Recent work in this context has uncovered…
C. N. Yang's ideas about local gauge symmetry and non-integrable phases have been enormously fertile sources of inspiration in fundamental physics and in the quantum theory of matter. They also arise naturally in describing the dynamics of…
In this article we introduce a generalization of the Newton transformation to the case of a system of endomorphisms. We show that it can be used in the context of extrinsic geometry of foliations and distributions yielding new integral…
A generalized version of both rectangular metric spaces and rectangular quasi-metric spaces is known as rectangular quasi b-metric spaces (RQB-MS). In the current work, we define generalized $( \theta,\phi) $-contraction mappings and study…
We generalize the dual notions of "expansion" and "collapse" so they can be applied to arbitrary metric spaces. We also expand the theory to allow for infinitely many such moves. Those tools are then employed to prove a variety of…
We present a comprehensive theoretical analysis of the General Standard Model (GSM), a recently proposed framework that unifies particle physics and cosmology within the Gravitational Quantum Field Theory (GQFT). Constructed from first…
Let $S(H)$ be the set of all self-adjoint bonded linear operators on $H$ and $\mathcal{V} \subset S(H)$ a subset that is pertinent in mathematical foundations of quantum mechanics. A symmetry is a bijective map $\phi :\mathcal{V} \to…
A Generalized Kinetic Theory was proposed in order to have the possibility to treat particles which obey a very general statistics. By adopting the same approach, we generalize here the Kinetic Theory of electrons and phonons. Equilibrium…
This text is the extended version of a talk given at the conference Geometry, Topology, QFT and Cosmology hold from May 28 to May 30, 2008 at the Observatoire de Paris. We explore the notion of solder (or soldering form) in differential…
We consider generalized gravitational entropy in various higher derivative theories of gravity dual to four dimensional CFTs using the recently proposed regularization of squashed cones. We derive the universal terms in the entanglement…
Deep learning models have proven enormously successful at using multiple layers of representation to learn relevant features of structured data. Encoding physical symmetries into these models can improve performance on difficult tasks, and…
In this lecture at a school for condensed matter physicists, I begin with basic concepts and tools for investigating phase transitions in quantum field theory. The very different roles of global and gauge symmetries in phase transitions…