Related papers: E6 Matrix Model
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…
Recent progress in the understanding of gravity on noncommutative spaces is discussed. A gravity theory naturally emerges from matrix models of noncommutative gauge theory. The effective metric depends on the dynamical Poisson structure,…
We study twisted M-theory in a general conifold background, and describe it in terms of a 5d non-commutative Chern-Simons-matter theory, which is equivalent to 5d non-commutative Chern-Simons theory for a supergroup. In an equivalent…
We show that the ABJM theory, which is an N=6 superconformal U(N)*U(N) Chern-Simons gauge theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model that can be derived…
We present a detailed study of a new mathematical object in $\mathrm{E}_{6(6)}\times \mathbb{R}^{+}$ generalised geometry called an `exceptional complex structure' (ECS). It is the extension of a conventional complex structure to one that…
To each second-order ordinary differential equation $\sigma $ on a smooth manifold $M$ a $G$-structure $P^\sigma $ on $J^1(\mathbb{R},M)$ is associated and the Chern connection $\nabla ^\sigma $ attached to $\sigma $ is proved to be…
A Chern-Simons matrix model was proposed by Dorey, Tong, and Turner to describe non-Abelian fractional quantum Hall effect. In this paper we study the Hilbert space of the Chern-Simons matrix model from a geometric quantization point of…
We introduce a new elliptic integrable $\sigma$-model in the form of a two-parameter deformation of the Principal Chiral Model on the group $\text{SL}_{\mathbb{R}}(N)$, generalising a construction of Cherednik for $N=2$ (up to reality…
Point particles in 3D gravity are known to behave as topological defects, while gravitational field can be expressed as the Chern-Simons theory of the appropriate local isometry group of spacetime. In the case of the Poincar\'e group,…
In this work, we propose a new and simple model that supports Chern semimetals. These new gapless topological phases share several properties with the Chern insulators like a well-defined Chern number associated to each band, topologically…
We consider a semi-classical approximation to the dynamics of a point particle in a noncommutative space. In this approximation, the noncommutativity of space coordinates is described by a Poisson bracket. For linear Poisson brackets, the…
We extend topologically massive electrodynamics, both by adding a higher derivative action to cast the entire three-term model in Chern-Simons (CS) form, and by embedding it in an AdS background. It can then be written as the sum of two CS…
We study super-Chern-Simons theory on a generic supermanifold. After a self-contained review of integration on supermanifolds, the complexes of forms (superforms, pseudo-forms and integral forms) and the extended Cartan calculus are…
We construct equivariant, string and leading order characteristic classes and Chern-Simons classes for certain infinite rank bundles associated to fibrations occurring in loop spaces, Gromov-Witten theory and gauge theory. Results include a…
The general theoretical ground for the models based on the compact angle coordinates is presented. It is observed that the proper dependence on compact coordinates has to be through the group elements and is achieved most naturally in a…
We construct two more supersymmetric E6 grand unified models with three generations within the framework of Z12 asymmetric orbifold compactification of the heterotic string theory. Such an asymmetric orbifold is missing in the…
The Hamiltonian analysis for the Chern-Simons theory and Pontryagin invariant, which depends of a connection valued in the Lie algebra of SO(3,1), is performed. By applying a pure Dirac's method we find for both theories the extended…
We begin an investigation of supersymmetric theories based on exceptional groups. The flat directions are most easily parameterized using their correspondence with gauge invariant polynomials. Symmetries and holomorphy tightly constrain the…
We study Chern-Simons theory with a complex G_C or a real G x G gauge group on a manifold with boundary - this includes Lorentzian and Euclidean (anti-) de Sitter (E/A)dS gravity for G=SU(2) or G=SL(2,R). We show that there is a canonical…
We use recent progress on Chern-Simons gauge theory in three dimensions [18] to give explicit, closed form formulas for the star product on some functions on the affine space ${\mathcal A}(\Sigma)$ of (smooth) connections on the trivialized…