Related papers: Matrix Configurations for Spherical 4-branes and N…
It has been understood that correlation functions of multi-trace operators in ${\cal N}=4$ SYM can be neatly computed using the group algebra of symmetric groups or walled Brauer algebras. On the other hand such algebras have been known to…
We show that $\frak{su}(2)$ Lie algebras of coordinate operators related to quantum spaces with $\frak{su}(2)$ noncommutativity can be conveniently represented by $SO(3)$-covariant poly-differential involutive representations. We show that…
We enhance the action of higher abelian gauge theory associated to a gerbe on an M5-brane with an action of a torus ${\mathbb T}^n (n\ge 2)$, by a noncommutative ${\mathbb T}^n$-deformation of the M5-brane. The ingredients of the…
In this work we construct an embedding of a nontrivial central extension of the contact superconformal algebra K'(4) into the Lie superalgebra of pseudodifferential symbols on the supercircle S^{1|2}. Associated with this embedding is a…
We conjecture that the Sen-Seiberg limit of the Type IIA D2-brane action in a flat spacetime background can be resummed, at all orders in \alpha', to define an associative star product on the membrane. This star product can be independently…
We develop new tools for an in-depth study of our recent proposal for Matrix Theory. We construct the anomaly-free and finite planar continuum limit of the ground state with SO(2^{13}) symmetry matching with the tadpole and tachyon free IR…
Noncommutative rational functions, i.e., elements of the universal skew field of fractions of a free algebra, can be defined through evaluations of noncommutative rational expressions on tuples of matrices. This interpretation extends their…
M(atrix) theory on an orbifold and classical two-branes therein are studied with particular emphasis to heterotic M(atrix) theory on $S_1/Z_2$ relevant to strongly coupled heterotic and dual Type IA string theories. By analyzing orbifold…
We construct a matrix representation of compact membranes analytically embedded in complex tori. Brane configurations give rise, via Bergman quantization, to U(N) gauge fields on the dual torus, with almost-anti-self-dual field strength.…
We reduce the dual version of $D=10$, $N=1$ supergravity coupled to $n$ vector fields to four dimensions, and derive the $SL(2,R)\times O(6,6+n)$ transformations which leave the equations of motion invariant. For $n=0$ $SL(2,R)$ is also a…
We construct a 2-parameter family of unitarily equivalent irreducible representations of the triply extended group $\g$ of translations of $\mathbb{R}^{4}$ associated with a family of its 4-dimensional coadjoint orbits and show how a…
Using an algebraic orbifold method, we present non-commutative aspects of $G_2$ structure of seven dimensional real manifolds. We first develop and solve the non commutativity parameter constraint equations defining $G_2$ manifold algebras.…
We present two noncommutative algebras over a field of characteristic zero that each posses a family of actions by cyclic groups of order $2n$, represented in $n \times n$ matrices, requiring generators of degree $3n$.
We study the noncommutative $\phi^4$ theory with spontaneously broken global O(2) symmetry in 4 dimensions. We demonstrate the renormalizability at one loop. This does not require any choice of ordering of the fields in the interaction…
We study noncompact and static membrane solutions in Matrix theory. Demanding axial symmetry on a membrane embedded in three spatial dimensions, we obtain a wormhole solution whose shape is the same with the catenoidal solution of…
We review an approach towards a covariant formulation of Matrix theory based on a discretization of the 11d membrane. Higher dimensional algebraic structures, such as the quantum triple Nambu bracket, naturally appear in this approach. We…
We present examples of noncommutative four-spheres that are base spaces of $SU(2)$-principal bundles with noncommutative seven-spheres as total spaces. The noncommutative coordinate algebras of the four-spheres are generated by the entries…
Using a six-orientifold, fourbranes and four fivebranes in type IIA string theory we construct $\mathcal{N}$=1 supersymmetric gauge theories in four dimensions with product group $SU(M)\times SO(N)$ or $SU(M)\times Sp(2N)$, a bifundamental…
We introduce a new duality for $\mathcal{N}=1$ supersymmetric gauged matrix models. This $0d$ duality is an order 4 symmetry, namely an equivalence between four different theories, hence we call it Quadrality. Our proposal is motivated by…
We introduce a covariant non-commutative deformation of 3+1-dimensional conformal field theory. The deformation depends on a short-distance scale \ell_p, and thus breaks scale invariance, but preserves all space-time isometries. The…