Related papers: The QM/NCG Correspondence
In this article I first give an abbreviated history of string theory and then describe the recently-conjectured field-string duality. This suggests a class of nonsupersymmetric gauge theories which are conformal (CGT) to leading order of…
The correspondence between conformal covariant fields in Minkowski's space-time and isometric fields in the five dimensional anti-deSitter space-time is extended to a six-dimensional bulk space and its regular sub-manifolds, so as to…
We give an introductory review of gauge/gravity duality, and associated ideas of holography, emphasising the conceptual aspects. The opening Sections gather the ingredients, viz. anti-de Sitter spacetime, conformal field theory and string…
The correspondence principle in physics between quantum mechanics and classical mechanics suggests deep relations between spectral and geometric entities of Riemannian manifolds. We survey---in a way intended to be accessible to a wide…
The AdS/CFT correspondence provides a new perspective on recurrent questions in General Relativity such as the allowed boundary conditions at infinity and the definition of gravitational conserved charges. Here we review the main insights…
Conformal field theory (CFT) has been extremely successful in describing large-scale universal effects in one-dimensional (1D) systems at quantum critical points. Unfortunately, its applicability in condensed matter physics has been limited…
Non-perturbative quantum general relativity provides a possible framework to analyze issues related to black hole thermodynamics from a fundamental perspective. A pedagogical account of the recent developments in this area is given. The…
A major unsolved problem in theoretical physics is to reconcile the classical theory of general relativity with quantum mechanics. These lectures will deal with an attempt to describe quantum gravity as a path integral over geometries known…
The fact that quantum theory is non-differentiable, while general relativity is built on the assumption of differentiability sources an incompatibility between quantum theory and gravity. Higher order geometry addresses this issue directly…
We introduce two new formulations for the notion of "quantum metric on noncommutative space". For a compact noncommutative space associated to a unital C*-algebra, our quantum metrics are elements of the spatial tensor product of the…
A version of noncommutative geometry is proposed which is based on phase-space rather than position space. The momenta encode the information contained in the algebra of forms by a map which is the noncommutative extension of the duality…
Conformal Galilei algebra contains so(1,2) subalgebra which is the conformal algebra in one dimension. In this note we generalize methods previously developed for one-dimensional many-body systems and construct a unitary map relating a…
We discuss some equivalence relations between the non-relativistic quantum mechanics for particles subjected to potentials and for particles moving freely on background geometries. In particular, we illustrate how selected geometries can be…
Divided into three parts, the first marks out enormous geometric issues with the notion of quasi-freenss of an algebra and seeks to replace this notion of formal smoothness with an approximation by means of a minimal unital commutative…
A geometric interpretation of quantum self-interacting string field theory is given. Relations between various approaches to the second quantization of an interacting string are described in terms of the geometric quantization. An algorithm…
Noncommutative geometry, in its many incarnations, appears at the crossroad of various researches in theoretical and mathematical physics: from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and…
The tools of Kerr/CFT correspondence are applied to the Kerr black hole embedded in an axial external magnetic field. Its extremal near horizon geometry remains a warped and twisted product of $AdS_2\times S^2$. The central charge of the…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
It is shown how nonlinear versions of quantum mechanics can be refolmulated in terms of a (linear) C*-algebraic theory. Then also their symmetries are described as automorphisms of the correspondong C*-algebra. The requirement of…
The AdS/CFT correspondence is a powerful tool to study the properties of conformal QCD at strong coupling in terms of a higher dimensional dual gravity theory. The power-law falloff of scattering amplitudes in the non-perturbative regime…