Related papers: Towards Covariant Matrix Theory
We investigate the problem of mapping, through the Morita equivalence, odd dimensional noncommutative lattice gauge theories onto suitable matrix models. We specialize our analysis to noncommutative three dimensional QED (NCQED) and scalar…
The nature of M-theory on K3 X I, where I is a line interval, is considered, with a view towards formulating a `matrix theory' representation of that situation. Various limits of this compactification of M-theory yield a number of well…
We present quantum theory of a membrane propagating in the vicinity of a time dependent orbifold singularity. The dynamics of a membrane, with the parameters space topology of a torus, winding uniformly around compact dimension of the…
In this research paper, structured bi-matrix variate, matrix quadratic equations are considered. Some lemmas related to determining the eigenvalues of unknown matrices are proved. Also, a method of determining the diagonalizabe unknown…
In this paper we present a discrete, non-perturbative formulation for type IIB string theory. Being a supersymmetric quiver matrix mechanics model in the framework of M(atrix) theory, it is a generalization of our previous proposal of…
The algebraic formulation of the quantum group gauge models in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider gauge groups taking values in the quantum groups and noncommutative gauge fields…
This is a rough transcript of talks given at the Workshop on Groups & Algebras in M Theory at Rutgers University, May 31--Jun 04, 2005. We review the basic motivation for a pre-geometric formulation of nonperturbative String/M theory, and…
We examine the structure of winding toroidal and open cylindrical membranes, especially in cases where they are stretched between boundaries. Non-zero winding or stretching means that there are linear terms in the mode expansion of the…
We compute the interaction potential between two parallel transversely boosted wrapped membranes (with fixed momentum $p_-$) in D=11 supergravity with compact light-like direction. We show that the supergravity result is in exact agreement…
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…
We attempt to derive quiver Chern-Simons-matter theories from the Bagger-Lambert theory with Nambu bracket, through an orbifold prescription which effectively induces a dimensional reduction of the internal space for 3-algebra. We consider…
We study the effective actions of various brane configurations in Matrix theory. Starting from the 0+1 dimensional quantum mechanics, we replace coordinate matrices by covariant derivatives in the large N limit, thereby obtaining effective…
We consider D1-branes in a RR flux background and show that there is a low energy - large flux double scaling limit where the D1-branes action is dominated by a Chern-Simons-Myers coupling term. As a classical solution to the matrix model,…
We present M-theory compactifications on $K_3 \times K_3$ with membranes near the $A_n$ or $D_n$ singularities of the $K_3$ spaces. By realizing each of these compactifications in two different ways as type I' models with 2- and 6-branes,…
Based on our recent work on Quantum Nambu Mechanics $\cite{af2}$, we provide an explicit quantization of the Lorenz chaotic attractor through the introduction of Non-commutative phase space coordinates as Hermitian $ N \times N $ matrices…
We describe the mathematical properties of pairwise comparisons matrices with coefficients in an arbitrary group. We provide a vocabulary adapted for the description of main algebraic properties of inconsistency maps, describe an example…
A survey of the interrelationships between matrix models and field theories on the noncommutative torus is presented. The discretization of noncommutative gauge theory by twisted reduced models is described along with a rigorous definition…
The full U-duality symmetry of toroidally compactified M-theory can only be displayed by allowing non-rectangular tori with expectation values of the gauge fields. We construct an E_d(Z) U-duality invariant mass formula incorporating…
Starting from the Schild action for membrane, we present an alternative formulation of Matrix Theory. First of all, we construct the Schild action for general bosonic p-brane which is classically equivalent to the Nambu-Goto action for…
We introduce twisted matrix factorizations for quantum complete intersections of codimension two. For such an algebra, we show that in a given dimension, almost all the indecomposable modules with bounded minimal projective resolutions…