Noncommutative Gauge Symmetry Research Articles

Noncommutative gauge symmetry in the fractional quantum Hall effect

We show that a system of particles on the lowest Landau level can be coupled to a probe U(1) gauge field A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{A} $$\\end{document}μ in such a way that the theory is invariant under a noncommutative U(1) gauge symmetry. While the temporal component A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{A} $$\\end{document}0 of the probe field is coupled to the projected density operator, the spatial components A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{A} $$\\end{document}i are best interpreted as quantum displacements, which distort the interaction potential between the particles. We develop a Seiberg-Witten-type map from the noncommutative U(1) gauge symmetry to a simpler version, which we call “baby noncommutative” gauge symmetry, where the Moyal brackets are replaced by the Poisson brackets. The latter symmetry group is isomorphic to the group of volume preserving diffeomorphisms. By using this map, we resolve the apparent contradiction between the noncommutative gauge symmetry, on the one hand, and the particle-hole symmetry of the half-filled Landau level and the presence of the mixed Chern-Simons terms in the effective Lagrangian of the fractional quantum Hall states, on the other hand. We outline the general procedure which can be used to write down effective field theories which respect the noncommutative U(1) symmetry.

Non-commutative gauge symmetry from strong homotopy algebras

We explicitly construct an L ∞ algebra that defines U ⋆(1) gauge transformations on a space with an arbitrary noncommutative and even nonassociative star product. Matter fields are naturally incorporated in this scheme as L ∞ modules. Some possibilities for including P ∞ algebras are also discussed.

Topological Methods in Geometric Foundations of Teleparallel Fused Quantum Gravity

We have studied the gravitation in the context of the noncommutative manifold M₄×Z₂ where Z₂ is not the two point space but corresponds to a direction-vector attached to a space-time point. A local field theory, noncommutative Yang - Mills fields is limited to obtain the return thatsuch a symmetry group differences are. Noncommutative gauge symmetry of space - time and theinternal symmetry of the mixer is a very natural and clear perception that the gravitational forcegauge a characteristic feature of the theory. The gauge fields of the dimensionally reduced noncommutativeYang-Mills theory map onto a Weitzenbӧck spacetime and a teleparallel theory of gravity arisesas the zero curvature reduction of a Poincare gauge theory which induces an Einstein-Cartanspace-time characterized by connections with both nonvanishing torsion and curvature. This analysissuggests that noncommutative Yang-Mills theory naturally induces gravitation through a torsioned space-time. Thus as in the case of a noncommutative manifold whereZ₂ is a two-point space there appears to be aconnection between gravity and electroweak theory in this formalism this is achieved through therealization of chiral anomaly and torsion. It is noted to be that that Weitzenbӧck geometry thatEinstein's General Relativity with the teleparallel gravity equivalent, provoked by her some notablefeatures are. This show has been that the geometry torsioned space-time at which the the chiralanomaly inconsistencies in the torch made is. This show is that it naturally Weitzenbӧck geometryof the moves that the gravity of a teleparallel formula birth towards.

A no-go theorem for M5-brane theory

The BLG model for multiple M2-branes motivates an M5-brane theory with a novel gauge symmetry defined by the Nambu-Poisson structure. This Nambu-Poisson gauge symmetry for an M5-brane in large C-field background can be matched, on double dimension reduction, with the Poisson limit of the noncommutative gauge symmetry for a D4-brane in B-field background. Naively, one expects that there should exist a certain deformation of the Nambu-Poisson structure to match with the full noncommutative gauge symmetry including higher order terms. However, We prove the no-go theorem that there is no way to deform the Nambu-Poisson gauge symmetry, even without assuming the existence of a deformation of Nambu-Poisson bracket, to match with the noncommutative gauge symmetry in 4+1 dimensions to all order, regardless of how the double dimension reduction is implemented.

On the consistency of twisted gauge theory

It is argued that the twisted gauge theory is consistent provided it exhibits also the standard noncommutative gauge symmetry.

Spontaneous reduction of noncommutative gauge symmetry and model building

We propose a mechanism for the spontaneous (gauge-invariant) reduction of noncommutative ${\cal U}(n)$ gauge theories down to SU(n). This can be achieved through the condensation of composite ${\cal U}(n)$ gauge invariant fields that involves half-infinite Wilson lines in trace-U(1) noninvariant and SU(n) preserving direction. Based on this mechanism we discuss anomaly-free fully gauge invariant noncommutative Standard Model based on the minimal gauge group ${\cal U}(3)\times {\cal U}(2)\times {\cal U}(1)$, previously proposed, and show how it can be consistently reduced to the Standard Model with the usual particle spectrum. Charge quantization for quarks and leptons naturally follows from the model.

Spontaneous reduction of noncommutative gauge symmetry and model building

Spontaneous reduction of noncommutative gauge symmetry and model building

Large gauge transformations in M-theory

We cast M-brane interactions including intersecting membranes and five-branes in manifestly gauge invariant form using an arrangement of higher dimensional Dirac surfaces. We show that the noncommutative gauge symmetry present in the doubled M-theory formalism involving dual 3-form and 6-form gauge fields is preserved in a form quantised over the integers. The proper context for discussing large noncommutative gauge transformations is relative cohomology, in which the 3-form transformation parameters become exact when restricted to the five-brane worldvolume. We show how this structure yields the lattice of M-theory charges and gives rise to the conjectured 7D Hopf–Wess–Zumino term.

Non-commutative Chern–Simons for the quantum Hall system and duality

The quantum Hall system is known to have two mutually dual Chern–Simons descriptions, one associated with the hydrodynamics of the electron fluid, and another associated with the statistics. Recently, Susskind has made the claim that the hydrodynamical Chern–Simons theory should be considered to have a non-commutative gauge symmetry. The statistical Chern–Simons theory has a perturbative momentum expansion. In this paper, we study this perturbation theory and show that the effective action, although commutative at leading order, is non-commutative. This conclusion is arrived at through a careful study of the three-point function of Chern–Simons gauge fields. The non-commutative gauge symmetry of this system is thus a quantum symmetry, which we show can only be fully realized through the inclusion of all orders in perturbation theory. We discuss the duality between the two non-commutative descriptions.

Note on bosonic open strings in a constantBfield

We sketch the main steps of old covariant quantization of bosonic open strings in a constant $B$ field background. We comment on its space-time symmetries and the induced effective metric. The low-energy spectrum is evaluated and the appearance of a new non-commutative gauge symmetry is addressed.