http://inspirehep.net/record/499969/files/arXiv:hep-th_9905111.pdf

Large N Field Theories, String Theory and Gravity

This article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, on both the classical and the quantum level.

Noncommutative field theory

Quantum field theory on noncommutative spaces

One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral models on a lattice Theory of scalar products Form factors Mean value of operator Q Assymptotics of correlation functions Temperature correlation functions Appendices References.

Quantum Inverse Scattering Method and Correlation Functions

A new approach to N=2 supersymmetry based on the concept of harmonic superspace is proposed and is used to give an unconstrained superfield geometric description of N=2 super Yang-Mills and supergravity theories as well as of matter N=2 hypermultiplets. The harmonic N=2 superspace has an independent coordinates, in addition to the usual ones, the isospinor harmonics ui+or- on the sphere SU(2)/U(1). The role of ui+or- is to relate the SU(2) group realised on the component fields to a U(1) group acting on the relevant superfields. Their introduction makes it possible to SU(2)-covariantise the notion of Grassmann analyticity. Crucial for the construction is the existence of an analytic subspace of the general harmonic N=2 superspace. The hypermultiplet superfields and the true prepotentials (pre-prepotentials) of N=2 super Yang-Mills and supergravity are unconstrained superfunctions over this analytic subspace. The pre-prepotentials have a clear geometric interpretation as gauge connections with respect to the internal SU(2)/U(1) directions. A radically new feature arises: the number of gauge and auxiliary degrees of freedom becomes infinite while the number of physical degrees of freedom remains finite. Other new results are the massive N=2 Yang-Mills theory and various off-shell self-interactions of hypermultiplets. The propagators for matter and Yang-Mills superfields are given.

https://iopscience.iop.org/article/10.1088/0264-9381/1/5/004/pdf

Unconstrained N=2 matter, Yang-Mills and supergravity theories in harmonic superspace

Noncommutative field theories and gravity

A Consistent noncommutative field theory: The Wess-Zumino model

We consider simple extensions of noncommutativity from flat to curved spacetime One possibility is to have a generalization of the Moyal product with a covariantly constant noncommutative tensor $\theta^{\mu\nu}$ In this case the spacetime symmetry is restricted to volume preserving diffeomorphisms which also preserve $\theta^{\mu\nu}$ Another possibility is an extension of the Kontsevich product to curved spacetime In both cases the noncommutative product is nonassociative We find the the order $\theta^2$ noncommutative correction to the Newtonian potential in the case of a covariantly constant $\theta^{\mu\nu}$ It is still of the form $1/r$ plus an angle dependent piece The coupling to matter gives rise to a propagator which is $\theta$ dependent

Victor O. Rivelles

Papers

Noncommutative field theories and gravity

A Consistent noncommutative field theory: The Wess-Zumino model

Noncommutative Gravity

Scalar field theory in the AdS/CFT correspondence revisited

N=4 Superconformal Mechanics and the Potential Structure of AdS Spaces