Related papers: A regularization of field theory on non-commutativ…

We aim to connect the non commutative geometry ``quotient space'' viewpoint with the standard super Yang Mills theory approach in the spirit of Connes-Douglas-Schwartz and Douglas-Hull description of application of noncommutative geometry…

We present a general framework for Matrix theory compactified on a quotient space R^n/G, with G a discrete group of Euclidean motions in R^n. The general solution to the quotient conditions gives a gauge theory on a noncommutative space. We…

We give a simple and elegant proof of the Equivalence Theorem, stating that two field theories related by nonlinear field transformations have the same S matrix. We are thus able to identify a subclass of nonrenormalizable field theories…

Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve…

We explore the origins of non-geometric fluxes within the context of M theory described as a matrix model. Building upon compactifications of Matrix theory on non-commutative tori and twisted tori, we formulate the conditions which describe…

Deep models have advanced prediction in many domains, but their lack of interpretability remains a key barrier to the adoption in many real world applications. There exists a large body of work aiming to help humans understand these black…

Non-commutative (NC) field theories can be mapped onto twisted matrix models. This mapping enables their Monte Carlo simulation, where the large N limit of the matrix models describes the continuum limit of NC field theory. First we present…

The general prescription for constructing the continuum limit of a field theory is introduced. We then apply the prescription to construct the O(N) non-linear sigma model and the Gross-Neveu model in three dimensions using the large N…

We describe a unitary matrix model which is constructed from discrete analogs of the usual projective modules over the noncommutative torus and use it to construct a lattice version of noncommutative gauge theory. The model is a…

A new method is developed for solving the conformally invariant integrals that arise in conformal field theories with a boundary. The presence of a boundary makes previous techniques for theories without a boundary less suitable. The method…

In the previous paper (hep-th/0402010) we proposed a matrix configuration for a non-commutative S^4 (NC4S) and constructed a non-commutative (star) product for field theories on NC4S. In the present paper we will show that any matrix can be…

Random matrices in the large N expansion and the so-called double scaling limit can be used as toy models for quantum gravity: 2D quantum gravity coupled to conformal matter. This has generated a tremendous expansion of random matrix…

Theory of matrix factorizations is useful to study hypersurfaces in commutative algebra. To study noncommutative hypersurfaces, which are important objects of study in noncommutative algebraic geometry, we introduce a notion of…

Very high energy physics needs a coherent description of the four fundamental forces. Non-commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the…

We discuss aspects of recent novel approaches towards understanding the large N limit of matrix field theories with local or global non-abelian symmetry.

Field theory on a fuzzy noncommutative sphere can be considered as a particular matrix approximation of field theory on the standard commutative sphere. We investigate from this point of view the scalar $\phi^4$ theory. We demonstrate that…

Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…

We show that the large N reduction holds on group manifolds. Large N field theories defined on group manifolds are equivalent to some corresponding matrix models. For instance, gauge theories on S^3 can be regularized in a gauge invariant…

We investigate the effects of the regularization procedure used in the J-Matrix method. We show that it influences the convergence, and propose an alternative regularization approach. We explicitly perform some model calculations to…

A regularization for effective field theory with two propagating heavy particles is constructed. This regularization preserves the low-energy analytic structure, implements a low-energy power counting for the one-loop diagrams, and…