Related papers: Field theory amplitudes in a space with SU(2) fuzz…
Building on an analogy with ordinary scalar field theories, an epsilon expansion for rank-3 tensorial group field theories with gauge invariance condition is introduced. This allows to continuously interpolate between the dimension four…
We construct a perturbation theory for the SU(2) non-linear Sigma-model in 2+1 dimensions using a polynomial, first-order formulation, where the variables are a non-Abelian vector field L_mu (the left SU(2) current), and a non-Abelian…
These are lecture notes for an introductory course on noncommutative field and gauge theory. We begin by reviewing quantum mechanics as the prototypical noncommutative theory, as well as the geometrical language of standard gauge theory.…
We review 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…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
In this article, we explore the low energy structure of a $U(3)$ gauge theory over spaces with fuzzy sphere(s) as extra dimensions. In particular, we determine the equivariant parametrization of the gauge fields, which transform either…
We discuss scalar quantum field theories in a Lorentz-invariant three-dimensional noncommutative space-time. We first analyze the one-loop diagrams of the two-point functions, and show that the non-planar diagrams are finite and have…
An appropriate field configuration in non-polynomial closed string field theory is shown to correspond to a general off-shell field configuration in low energy effective field theory. A set of string field theoretic symmetries that act on…
Following our previous work on fractional spin symmetries (FSS) \cite{6, 7}, we consider here the construction of field theoretical models that are invariant under the $D=2(1/3,1/3)$ supersymmetric algebra.
We discuss non-commutative field theories in coordinate space. To do so we introduce pseudo-localized operators that represent interesting position dependent (gauge invariant) observables. The formalism may be applied to arbitrary field…
We discuss the second quantization of scalar field theory on the q-deformed fuzzy sphere S^2_{q,N} for q \in \R, using a path-integral approach. We find quantum field theories which are manifestly covariant under U_q(su(2)), have a smooth…
The noncommutative string theory is described by embedding open string theory in a constant second rank antisymmetric $B_{\mu\nu}$ field and the noncommutative gauge theory is defined by a deformed $\star$ product. As a check, study of…
The Hamiltonians of $SU(2)$ and $SU(3)$ gauge theories in 3+1 dimensions can be expressed in terms of gauge invariant spatial geometric variables, i.e., metrics, connections and curvature tensors which are simple local functions of the…
Experimental limits on the violation of four-dimensional Lorentz invariance imply that noncommutativity among ordinary spacetime dimensions must be small. In this talk, I review the most stringent bounds on noncommutative field theories and…
We construct N=1 supersymmetric field theory in 4+2 dimensions compatible with the theoretical framework of 2T physics and its gauge symmetries. The fields are arranged into 4+2 dimensional chiral and vector supermultiplets, and their…
Recently, string theory on some specific curved backgroud spacetime geometries has been conjectured to be equivalent to certain gauge theories (AdS/CFT correspondence). This correspondence may be used to investigate the non-perturbative…
We consider quantum field theory in four-dimensional Minkowski spacetime, with the position coordinates represented by twistors instead of the usual world-vectors. Upon imposing canonical commutation relations between twistors and dual…
Field theory and gauge theory on noncommutative spaces have been established as their own areas of research in recent years. The hope prevails that a noncommutative gauge theory will deliver testable experimental predictions and will thus…
A noncommutative and non-anticommutative quantum field theory is formulated in a superspace, in which the superspace coordinates satisfy noncommutative and non-anticommutative relations. A perturbative scalar field theory is investigated in…
We study N=2 supersymmetric U(1) gauge theory in the noncommutative harmonic superspace with nonanticommutative fermionic coordinates. We examine the gauge transformation which preserves the Wess-Zumino gauge by harmonic expansions of…