Related papers: Noncommutative Linear Sigma Models
We discuss the structure of the non-anticommutative N=2 non-linear sigma-model in two dimensions, constructing differential operators which implement the deformed supersymmetry generators and using them to reproduce the classical action. We…
We study Nambu-Goldstone (NG) modes or gapless modes propagating along a skyrmion (lump) line in a relativistic and non-relativistic O(3) sigma model, the latter of which describes isotropic Heisenberg ferromagnets. We show for the…
Perturbative corrections to N=1/2 supersymmetric U(N) gauge theory at one-loop order are studied. It is shown that whereas the quantum corrections to N=1 sector of the theory are not affected by the C-deformation, the non(anti)commutativity…
We discuss the non-anticommutative (N=1/2) supersymmetric U(1) gauge theory in four dimensions, including a superpotential. We perform the one-loop renormalisation of the model, including the complete set of terms necessary for…
In this paper we deal with the issue of Lorentz symmetry breaking in quantum field theories formulated in a non-commutative space-time. We show that, unlike in some recente analysis of quantum gravity effects, supersymmetry does not protect…
A formulation of (non-anticommutative) N=1/2 supersymmetric U(N) gauge theory in noncommutative space is studied. We show that at one loop UV/IR mixing occurs. A generalization of Seiberg-Witten map to noncommutative and non-anticommutative…
We consider the GUT compatible formulation of noncommutative QED, as well as noncommutative SU(N) GUTs, for N>2, with no scalars but with fermionic matter in an arbitrary, anomaly-free representation, in the enveloping algebra approach. We…
This article studies large $N$ limits of a coupled system of $N$ interacting $\Phi^4$ equations posed over $\mathbb{T}^{d}$ for $d=2$, known as the $O(N)$ linear sigma model. Uniform in $N$ bounds on the dynamics are established, allowing…
We develop Chiral Perturbation Theory for chirally broken theories with fermions in two different representations of the gauge group. Any such theory has a non-anomalous singlet $U(1)_A$ symmetry, yielding an additional Nambu-Goldstone…
We investigate the consistency conditions for matter fields coupled to the four-dimensional (${\cal N} = 1$ supersymmetric) $\mathbb{CP}(1)$ nonlinear sigma model (the coset space $SU(2)_G/U(1)_H$). We find that consistency requires that…
We study the N=1 U(N) gauge model obtained by spontaneous breaking of N=2 supersymmetry. The Fayet-Iliopoulos term included in the N=2 action does not appear in the action on the N=1 vacuum and the superpotential is modified to break…
We study the commutative limit of the non-commutative maximally supersymmetric Yang-Mills theory in four dimensions (N=4 SYM). The commutative limits of non-commutative spaces are important in particular in the applications of…
This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…
We give an explicit proof that the noncommutative U(N) gauge theories are one-loop renormalizable
We consider the O(N) linear {\sigma} model and introduce an auxiliary field to eliminate the scalar self-interaction. Using a suitable limiting process this model can be continuously transformed into the nonlinear version of the O(N) model.…
This paper investigates the non-commutative version of the Abelian Higgs model at the one loop level. We find that the BRST invariance of the theory is maintained at this order in perturbation theory, rendering the theory one-loop…
We present numerical results for U(1) gauge theory in 2d and 4d spaces involving a non-commutative plane. Simulations are feasible thanks to a mapping of the non-commutative plane onto a twisted matrix model. In d=2 it was a long-standing…
When a continuous symmetry is spontaneously broken in nonrelativistic systems, there appear either type-I or type-II Nambu-Goldstone modes (NGMs) with linear or quadratic dispersion relation, respectively. When equation of motion or the…
We present a systematic investigation of one-loop renormalizability for nonanticommutative N=1/2, U(N) SYM theory in superspace. We first discuss classical gauge invariance of the pure gauge theory and show that in contradistinction to the…
We show how the Apparently Noninvariant Terms (ANTs), which emerge in perturbation theory of nonlinear sigma models, are consistent with the nonlinearly realized symmetry by employing the Ward-Takahashi identity (in the form of an…