Noncommutative Geometry and Matrix Theory: Compactification on Tori

Abstract

We study toroidal compactification of Matrix theory, using ideas and results of non-commutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification of these backgrounds, and argue that they correspond in supergravity to tori with constant background three-form tensor field. The paper includes an introduction for mathematicians to the IKKT formulation of Matrix theory and its relation to the BFSS Matrix theory.

harvmac, 41 pp. A slightly simpler BPS mass formula is proposed

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• Noncommutative Field Theory from String Theory: Two-loop Analysis
• Higher-Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions
• Divergences in Non-Commutative Gauge Theories with the Slavnov Term
• Non-commutativity and non-inertial effects on the Dirac oscillator in a cosmic string space-time
• Noncommutative QED and the Lifetimes of Ortho and Para Positronium
• Wilsonian Renormalization of Noncommutative Scalar Field Theory
• Free-fall in a uniform gravitational field in non-commutative quantum mechanics
• CP^n Model on Fuzzy Sphere
• Constructions of Non Commutative Instantons on $T^4$ and $K_3$
• D-branes on Group Manifolds and Deformation Quantization
• On the Three-Dimensional Pauli Equation in Noncommutative Phase-Space
• Noncommutative solitons on Kahler manifolds
• Generalized Fuzzy Torus and its Modular Properties
• Supermembrane origin of type II gauged supergravities in 9D
• Matrix Model, Noncommutative Gauge Theory and the Tachyon Potential
• Experimental test of Non-Commutative Quantum Gravity by VIP-2 Lead
• On the mass spectrum of noncommutative Schwinger model in Euclidean ${\mathbb{R}}^2$ space
• Graviton Propagators in Supergravity and Noncommutative Gauge Theory
• Graviton Propagators on Fuzzy G/H
• On Classification Of The Bubbling Geometries
• Noncommutative Dipole Field Theories And Unitarity
• Hamiltonian Formulation of Open WZW Strings
• A C*-Algebraic Model for Locally Noncommutative Spacetimes
• Noncommutative Gauge Theories from Deformation Quantization
• Unitary Quantum Field Theory on the Noncommutative Minkowski space
• Non-Linearly Extended Self-Dual Relations From The Nambu-Bracket Description Of M5-Brane In A Constant C-Field Background
• Kontsevich product and gauge invariance
• Chiral dynamics in QED and QCD in a magnetic background and nonlocal noncommutative field theories
• Tetrahedron instantons
• Brane compactifications and 4-dimensional geometry in the IKKT model
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• Correlators of Matrix Models on Homogeneous Spaces
• Twisted Bundles on Noncommutative $T^4$ and D-brane Bound States
• Note on a fermionic solution of the matrix model and noncommutative superspace
• Supercurrent Interactions in Noncommutative Yang-Mills and IIB Matrix Model
• Static spherically symmetric three-form stars
• Brane Cosmology in the Background of D-Brane with NS B Field
• Lowest Landau level theory of the bosonic Jain states
• Symplectic connections, Noncommutative Yang Mills theory and Supermembranes
• One-loop effective action and emergent gravity on quantum spaces in the IKKT matrix model
• Supersymmetry algebra and BPS states of super Yang-Mills theories on noncommutative tori
• Spontaneous breaking of translational invariance in non-commutative lambda phi^4 theory in two dimensions
• Entanglement wedge cross section for noncommutative Yang-Mills theory
• BFV-BRST analysis of equivalence between noncommutative and ordinary gauge theories
• Noncommutative Geometry as a Regulator
• Harmonic analysis approach to Gromov--Hausdorff convergence for noncommutative tori
• Worldsheet and Spacetime Properties of p-p' System with B Field and Noncommutative Geometry
• Single top quark production in $t$-channel at the LHC in Noncommutative Space-Time
• Matrix theory compactifications on twisted tori
• AdS/CFT and large-N volume independence
• Hermitian Geometry and Complex Space-Time
• Observables in a Noncommutative Unification of Quanta and Gravity. A Final Model
• Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 1. Perturbative Expansion
• The Moyal Bracket in the Coherent States framework
• Discrete Noncommutative Gauge Theory
• Canonical Quantization of Noncommutative Field Theory
• The inclusive b -> s γdecay in the noncommutative standard model
• Equations of motion, Noncommutativity and Quantization
• Non-abelian expansion of S-matrix elements and non-abelian tachyon DBI action
• Flux Stabilization of D-branes in NSNS Melvin Background
• Tilting the Noncommutative Bion
• Noncommutative K3 Surfaces
• Factorization and generalized *-products
• Tachyon Condensation in Noncommutative Gauge Theory
• Noncommutativity in weakly curved background by canonical methods
• Quantum mechanics on space with SU(2) fuzziness
• Test of Quantum Effects of Spatial Noncommutativity using Modified Electron Momentum Spectroscopy
• Noncommutative Standard Model in Top Quark Sector
• Neutral Higgs boson pair production at the LC in the Noncommutative Standard Model
• Poisson structure on a space with linear SU(2) fuzziness
• Topological Strings on Non-Commutative Resolutions
• Quantum speed limit for a relativistic electron in the noncommutative phase space
• Duality Rotations and BPS Monopoles with Space and Time Noncommutativity
• Spin(p+1,p+1) Covariant Dp-brane Bound States
• Recent Developments in Superstring Theory
• Effects of Magnetic Fields on String Pair Creation
• Searching for Effects of Spatial Noncommutativity via Chern-Simons' Processes
• BPS D0-D6 Branes in Supergravity
• Noncommutativity from spectral flow
• Noncommutative Super Yang-Mills Theories with 8 Supercharges and Brane Configurations
• Gauge theories from D7-branes over vanishing 4-cycles
• Noncommutative gauge and gravity theories and geometric Seiberg-Witten map
• Translational-invariant noncommutative gauge theory
• Non-commutativity and Supersymmetry
• Fundamental Strings as Noncommutative Solitons
• Quasi-localized states on noncommutative solitons
• Wilson Line Correlators in N=4 Non-commutative Gauge Theory on S^2 x S^2
• Index theorem in spontaneously symmetry-broken gauge theories on a fuzzy 2-sphere
• Noncommutative Superspace and Super Heisenberg Group
• Finite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions
• Superloop Space
• (1 + p)-Dimensional Open D(p - 2) Brane Theories
• Entangled state representations in noncommutative quantum mechanics
• Open Superstring and Noncommutative Geometry
• Supersymmetric Dirac-Born-Infeld theory in noncommutative space
• On the Plethora of Representations Arising in Noncommutative Quantum Mechanics and An Explicit Construction of Noncommutative 4-tori
• Instances of the Kaplansky-Lvov multilinear conjecture for polynomials of degree three
• Classical electrodynamics in a space with spin noncommutativity of coordinates
• Noncommutative SU(N) and Gauge Invariant Baryon Operator
• Extending general covariance: Moyal-type noncommutative manifolds
• Non-commutative vs. Commutative Descriptions of D-brane BIons
• Geometry from Matrices via D-branes
• On Non Commutative Calabi-Yau Hypersurfaces
• Towards Gauge theory for a class of commutative and non-associative fuzzy spaces
• Dualities in Quantum Hall System and Noncommutative Chern-Simons Theory
• Noncommutativity from the string perspective: modification of gravity at a mm without mm sized extra dimensions
• The noncommutative QED threshold energy versus the optimum collision energy
• Tales of D0 on D6 Branes: Matrix Mechanics of Identical Particles
• Higher-U(2,2)-spin fields and higher-dimensional W-gravities: quantum AdS space and radiation phenomena
• Noncommutative Maxwell-Chern-Simons theory (I): One-loop dispersion relation analysis
• On the Meaning of the String-Inspired Noncommutativity and its Implications
• Anatomy of Two-Loop Effective Action in Noncommutative Field Theories
• Dynamics of O(N) Model in a Strong Magnetic Background Field as a Modified Noncommutative Field Theory
• Charged rotating BTZ black holes in noncommutative spaces and torsion gravity
• On the Entropy of Deformed Phase Space Black Hole and the Cosmological Constant
• On the Consistency of Twisted Gauge Theory
• Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
• Noncommutative U(1) Instantons in Eight Dimensional Yang-Mills Theory
• Wave Packets in Discrete Quantum Phase Space
• Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED
• The Cutkosky rule of three dimensional noncommutative field theory in Lie algebraic noncommutative spacetime
• Admissibility Condition and Nontrivial Indices on a Noncommutative Torus
• Moyal Noncommutative Integrability and the Burgers-KdV Mapping
• Intersecting Noncommutative D-branes and Baryons in Magnetic Fields
• On the Lorentz symmetry of the noncommutative chiral bosons
• Probability of the Standard Model Appearance from a Matrix Model
• Effective actions, Wilson lines and the IR/UV mixing in noncommutative supersymmetric gauge theories
• Quantum Stabilization of Compact Space by Extra Fuzzy Space
• Thermodynamics on Fuzzy Spacetime
• Finite Theories Before and After the Discovery of a Higgs Boson at the LHC
• Noncommutativity In The Mechanics Of A Free Massless Relativistic Particle
• Possible Effects of Noncommutative Geometry on Weak CP Violation and Unitarity Triangles
• Non-commutativity parameters depend not only on the effective coordinate but on its T-dual as well
• Inferring the covariant $\Theta$-exact noncommutative coupling in the top quark pair production at linear colliders
• Intertwining noncommutativity with gravity and particle physics
• Nonassociative gauge gravity theories with R-flux star products and Batalin-Vilkovisky quantization in algebraic quantum field theory
• On Non-Commutative Correction of the Gödel-type Metric
• Boundaries in the Moyal plane
• Seiberg-Witten Geometry of Four-Dimensional $\mathcal{N}=2$ Quiver Gauge Theories
• Wilson loops in noncommutative Yang-Mills theory using gauge/gravity duality
• Non-commutativity from the double sigma model
• Consistent Anomalies in Translation-Invariant Noncommutative Gauge Theories
• Generalized Non-Commutative Inflation
• On Coordinate Transformations in Planar Noncommutative Theories
• Testing Non commutative QED gamma-gamma-gamma and gamma-gamma-gamma-gamma Couplings at LHC
• Statistical mechanics of free particles on space with Lie type noncommutativity
• NC Calabi-Yau Manifolds in Toric Varieties with NC Torus fibration
• Kronecker foliation, D1-branes and Morita equivalence of Noncommutative two-tori
• Hard Thermal Effects in Noncommutative U(N) Yang-Mills Theory
• Noncommutative Supersymmetry in Two Dimensions
• Canonical formalism and quantization of perturbative sector of higher-derivative theories
• A Note on Unitarity of Non-Relativistic Non-Commutative Theories
• Dirac-Born-Infeld action, Seiberg-Witten map, and Wilson Lines
• Wilson Loop and Dimensional Reduction in Non-Commutative Gauge Theories
• Spontaneous Lorentz Symmetry Breaking by Anti-Symmetric Tensor Field
• One-loop effective potential for scalar and vector fields on higher dimensional noncommutative flat manifolds
• Matrix Models: Fermion Doubling vs. Anomaly
• The Matrix model and the non-commutative geometry of the supermembrane
• D0-branes in an H-field Background and Noncommutative Geometry
• D-branes on Nonabelian Threefold Quotient Singularities
• Noncommutative massive Thirring model in three-dimensional spacetime
• Non-Commutativity effects in the Dirac equation in crossed electric and magnetic fields
• Green-Schwarz superstring from type IIB matrix model
• Heterotic Matrix theory with Wilson lines on the lightlike circle
• Nonabelian D-branes and Noncommutative Geometry
• Noncommutative field with constant background fields and neutral fermion
• Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement gravity versus $SU(\infty )$-QGR
• Aspects of perturbative quantum field theory on non-commutative spaces
• Recursive Relations For Processes With n Photons Of Noncommutative QED
• Nambu Quantum Mechanics on Discrete 3-Tori
• Higher derivative Chern-Simons extension in the noncommutative QED${}_3$
• Fermionic T-duality and momenta noncommutativity
• Closedness of orbits in a space with SU(2) Poisson structure
• Supermembranes and Super Matrix Models
• Dual Non-Lorentzian Backgrounds for Matrix Theories
• The Fuzzy Kaehler Coset Space with the Darboux Coordinates
• Chiral Symmetry Restoration in Holographic Noncommutative QCD
• Field Theory on a Non-commutative Plane: a Non-Perturbative Study
• A note on bosonic open strings in constant B field
• High-Temperature Effective Potential of Noncommutative Scalar Field Theory: Reduction of Degree of Freedom by Noncommutativity
• Nonlocal regularization of abelian models with spontaneous symmetry breaking
• Noncommutative Fluids
• On Non-Abelian Structure From Matrix Coordinates
• Gravitational measurements in higher dimensions
• Eight Dimensional Noncommutative Instantons and D0-D8 Bound States with B-field
• Open string with a background B-field as the first order mechanics, noncommutativity and soldering formalism
• Vector profile and gauge invariant observables of string field theory solutions for constant magnetic field background
• The Mass Gap of the Space-time and its Shape
• On Gauge Invariance of Noncommutative Chern-Simons Theories
• Landau levels in a 2D noncommutative space: matrix and quaternionic vector coherent states
• Calculating the jet quenching parameter in the plasma of NCYM theory from gauge/gravity duality
• Teleparallel Superspace in Eleven Dimensions Coupled to Supermembranes
• Finite Temperature effects on the Induced Chern-Simons term in noncommutative geometry
• Phase space quantization, noncommutativity and the gravitational field
• Supersymmetry in the Non-Commutative Plane
• Gravitational Quantum Well
• Deformed Two-Mode Quadrature Operators in Noncommutative Space
• Noncommutativity and nonassociativity of closed bosonic string on T-dual toroidal backgrounds
• Explicit N=2 supersymmetry for higher-spin massless fields in D=4 AdS superspace
• Toric Varieties with NC Toric Actions: NC Type IIA Geometry
• Structure of Noncommutative Fock space
• Abelian Toda field theories on the noncommutative plane
• Translation-Invariant Noncommutative Renormalization
• Supersymmetric interactions of a six-dimensional self-dual tensor and fixed-shape second quantized strings
• Directly from $H$-flux to the family of three nonlocal $R$-flux theories
• Non-commutativity, Zero modes and D-brane Geometry
• Particle Dynamics And Emergent Gravity
• A Note on Intersecting and Fluctuating Solitons in 4D Noncommutative Field Theory
• Extended Voros product in the coherent states framework
• Noncommutative QCD corrections to the gluonic decays of heavy quarkonia
• Noncommutative Brownian motion
• Inferring type and scale of noncommutativity from the PTOLEMY experiment
• Construction of a topological charge on fuzzy S^2 x S^2 via Ginsparg-Wilson relation
• Deformed "Commutative" Chern - Simons System
• Dynamical phase space from a SO(d,d) matrix model
• Noncommutative Open strings, D-brane and Duality
• The Phase-Space Noncommutativity Effect on the Large and Small Wavefunction Components Approach at Dirac Equation
• The form factors existing in the b->s g^* decay and the possible CP violating effects in the noncommutative standard model
• Black Holes Thermodynamics in a new kind of Noncommutative Geometry
• The Concept of a Noncommutative Riemann Surface
• Soliton on Noncommutative Orbifold $T^2/Z_k$
• Towards a background independent approach to M theory
• Energy corrections due to the noncommutative phase-space of the charged isotropic harmonic oscillator in a uniform magnetic field in 3D
• On The Interaction Of D0-Brane Bound States And RR Photons
• Noncommutative Geometry and Deformation Quantization in the Quantum Hall Fluids with Inhomogeneous Magnetic Fields
• Past and future blurring at fundamental length scale
• Noncommutative Quantization in 2D Conformal Field Theory
• MHD waves within Noncommutative Maxwell theory
• A correspondence between the free and interacting field theories
• Superstring vertex operators in type IIB matrix model
• On Low-Energy Effective Action of Noncommutative Hypermultiplet Model
• Transformation of the Dirac-Born-Infeld action under the Seiberg-Witten map
• TeV-photon paradox and space with SU(2) fuzziness
• Noncommutative Effective LQC: inclusion of potential term
• Noncommutative radial waves
• On The Complete Seiberg-Witten Map For Theories With Topological Terms
• A N=8 action for multiple M2-branes with an arbitrary number of colors
• The Stark Effect with Minimum Length
• Strong Coupling Phenomena on the Noncommutative Plane
• Reduced Models and Noncommutative Gauge Theories
• Perturbative quantization of two-dimensional space-time noncommutative QED
• Elliptic Algebra and Integrable Models for Solitons on Noncummutative Torus $\mathcal{T}$
• Laplacians on Fuzzy Riemann Surfaces
• Landau levels for graphene layers in noncommutative plane
• Noncommutative Complex Scalar Field and Casimir Effect
• Noncommutative Field Theories and Smooth Commutative Limits
• A Generalization of Slavnov-Extended Non-Commutative Gauge Theories
• Observational Constraints on Local Lorentz Invariance
• Quantum Gravity as a Multitrace Matrix Model
• Backreacted flavor in non-commutative gauge theories
• IIB Matrix Model with D1-D5 Backgrounds
• Entropy Bound with Generalized Uncertainty Principle in General Dimensions
• Ground States of Duality-twisted Sigma-Models with K3 Target Space
• Two-particle system in Coulomb potential for twist-deformed space-time
• Gauge Field Theory on the E_q(2)-covariant Plane
• Axial anomaly in the reduced model: Higher representations
• Central force problem in space with SU(2) Poisson structure
• A Stochastic Origin of Spacetime Non-Commutativity
• Orientifolds of Matrix theory and Noncommutative Geometry
• Noncommutative Black Holes
• Non-commutative Space And Chan-Paton Algebra In Open String Field Algebra
• Cwikel Estimates and Negative Eigenvalues of Schroedinger Operators on Noncommutative Tori
• $U(N)$ Yang-Mills in non-commutative space time
• Matrix Compactification On Orientifolds
• Some Issues in Noncommutative Solitons as D-branes
• Nonlinear Realization of Lorentz Symmetry
• Wilson-t'Hooft Loops in Finite-Temperature Non-commutative Dipole Field Theory from Dual Supergravity
• Commutative Geometry for Non-commutative D-branes by Tachyon Condensation
• String Field Theory and Perturbative Dynamics of Noncommutative Field Theory
• A Note on T-Duality, Open Strings in B-field Background and Canonical Transformations
• Quantum Topology Change and Large N Gauge Theories
• Compactified Quantum Fields. Is there Life Beyond the Cut-off Scale?
• Quantum corrections of (fuzzy) spacetimes from a supersymmetric reduced model with Filippov 3-algebra
• Quantized Noncommutative Geometry from Multitrace Matrix Models
• Continuity of the Spectrum of Dirac Operators of Spectral Triples for the Spectral Propinquity
• Constructive Renormalization of the $2$-dimensional Grosse-Wulkenhaar Model
• Supertubes in Matrix model and DBI action
• Angular Symmetry Breaking Induced by Electromagnetic Field
• Quantum twistors
• Lattice Superstring and Noncommutative Geometry
• Dominance of a single topological sector in gauge theory on non-commutative geometry
• Noncommutative Supersymmetric Yang-Mills Theory in Ten-Dimensions with Higher-Derivative Terms
• Noncommutative fermions and Morita equivalence
• Twisted K-theory in $g>1$ from D-branes
• Bound-state gravity from higher derivatives
• Morita Equivalence, Picard Groupoids and Noncommutative Field Theories
• Non-planar Diagrams and Non-commutative Superspace in Dijkgraaf-Vafa theory
• The Galilean Nature of V-duality for Noncommutative Open String and Yang-Mills Theories
• Generating a dynamical M2 brane from super-gravitons in a pp-wave background
• Open string derivation of winding states in thermal noncommutative field theories
• On Non Commutative G2 structure
• Mirror duality and noncommutative tori
• Magnetic Backgrounds from Generalised Complex Manifolds
• Amplitudes With Different Helicity Configurations Of Noncommutative QED
• Quantum dot with spin-orbit interaction in noncommutative phase space and analog Landau levels
• Morita Equivalence of Noncommutative Supertori
• Noncommutative Torus from Fibonacci Chains via Foliation
• Noncommutativity and Duality through the Symplectic Embedding Formalism
• Finitely-Generated Projective Modules over the Theta-deformed 4-sphere
• Twisted Conformal Field Theories and Morita equivalence
• Wave function of the Universe, Preferred reference frame effects and metric signature transition
• Non-commutative holography and scattering amplitudes in a large magnetic background
• Entanglement and separability in the noncommutative phase-space scenario
• Emergent Spacetime and Cosmic Inflation
• Quantum information aspects of noncommutative quantum mechanics
• Contravariant geometry and emergent gravity from noncommutative gauge theories
• Global Seiberg-Witten maps for U(n)-bundles on tori and T-duality
• Noncommutativities of D-branes and $\theta$-changing Degrees of Freedom in D-brane Matrix Models
• Categorical Perspective on Quantization of Poisson Algebra
• Category of Quantizations and Inverse Problem
• Axial-Anomaly in Noncommutative QED and Pauli-Villars Regularization
• Matrix model and Yukawa couplings on the noncommutative torus
• Consistent Quantization of Noncommutative D-brane in Non-constant B Field Background
• An M-theory solution generating technique and SL(2,R)
• Wilson RG of Noncommutative ${\Phi }_4^4$
• Imprints of non-commutativity on charged black holes
• Non-commutative field theory approach to two-dimensional vortex liquid system
• Non-commutative Weitzenboeck geometry, gerbe modules, and WZW branes
• Strings, Noncommutative Geometry and the Size of the Target Space
• Classification of BPS equations in higher dimensions
• Hamiltonian approach and quantization of $D=3,\mathcal{N}=1$ supersymmetric non-Abelian multiwave system
• Open-String Non-Associativity in an R-flux Background
• Softer Hard Scattering and Noncommutative Gauge-String Duality
• Some Notes Concerning the Dynamics of Noncommutative Lumps Corresponding to Nontrivial Vacua in Noncommutative Yang--Mills Models which are perturbative branches of M(atrix) Theory
• Pythagoras' Theorem on a 2D-Lattice from a "Natural" Dirac Operator and Connes' Distance Formula
• Projective Group Algebras
• Seiberg-Witten map for the 4D noncommutative BF theory
• A Note on (D(p-2),Dp) Bound State and Noncommutative Yang-Mills Theory
• String coupling and interactions in type IIB matrix model
• Two-dimensional Noncommutative atom Gas with Anandan interaction
• S-wave absorption of scalars by noncommutative D3-branes
• Universal terms for holographic entanglement entropy in noncommutative Yang--Mills theory
• A Note on Interactions of (Non-Commutative) Instantons Via AdS/CFT
• The Henon-Heiles system defined on Lie-algebraically deformed Galilei space-time
• Baryon number current in holographic noncommutative QCD
• Quantum deformation of planar amplitudes
• Fermionic T-duality and Morita Equivalence
• Light-like noncommutativity and duality from open strings/branes
• Greybody factor for D3-branes in B field
• Generalized twist deformations of Poincare and Galilei quantum groups
• Uncertainty relations for a non-canonical phase-space noncommutative algebra
• An Associative and Noncommutative Product for the Low Energy Effective Theory of a D-Brane in Curved Backgrounds and Bi-Local Fields
• Covariance of noncommutative Grassmann star product
• Strings, Dipoles and Fuzzy Spheres
• Paired quantum Hall states on noncommutative two-tori
• Noncommutative Sugawara Construction
• Eigenvalue problem for radial potentials in space with SU(2) fuzziness
• Equivalent forces in Newton equation from twist deformations and noninertial coordinate frames
• Black Hole Entropy, Topological Entropy and the Baum-Connes Conjecture in K-Theory
• Perturbed nonlinear models from Noncommutativity
• Fuzzy sphere bimodule, ABS construction to the exact soliton solutions
• Matrix Geometries Emergent from a Point
• Time-Delay at Higher Genus in High-Energy Open String Scattering
• On Projections in the Noncommutative 2-Torus Algebra
• The Slavnov-Taylor Identities for the 2+1 Dimensional Noncommutative CP${}^{N-1}$ Model
• Emergent spacetime from a Berry-inspired dynamical gauge field coupled to electromagnetism
• Tuning the separability in noncommutative space
• Generalized Dirichlet Branes and Zero-modes
• Effective Potential and Spontaneous Symmetry Breaking in the Noncommutative phi^6 Model
• Remarks on the eigenvalues distributions of D\leq 4 Yang-Mills matrix models
• Quantum Theory, Gravity and Second Order Geometry
• Closed Superstring in Noncommutative Compact Spacetime
• T-duality of a bosonic string in a weakly curved space-time
• Moyal Representation of the String Field Star Product in the Presence of a B-background
• NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion
• Axial Gauged Noncommutative U(2)/U(1) Wess-Zumino-Witten Model
• Quantization of Noncommutative Scalar Solitons at finite $\theta$
• The energy-momentum conservation law in two-particle system for twist-deformed Galilei Hopf algebras
• String with noncommutative world-sheet and stringy instantons
• Discussion on Lorentz Invariance Violation of Non-commutative Field Theory and Neutrino Oscillation
• A New Lorentz Violating Nonlocal Field Theory From String-Theory
• (p,q)-string in matrix-regularized membrane and type IIB duality
• Renormalization Group Flow for Noncommutative Fermi Liquids
• Aspects of ABJM orbifolds with discrete torsion
• (m,n)-Strings In IIB Matrix Model
• Thermal Properties of Gauge-Invariant Graphene in Noncommutative Phase-Space
• (Pre)-Inflationary Dynamics with Starobinsky Potential in Noncommutative Effective LQC
• Convergence of Spectral Triples on Fuzzy Tori to Spectral Triples on Quantum Tori
• On the Fairlie's Moyal formulation of M(atrix)- theory
• Noncommutativity Parameter As a Field on the String Worldsheet
• Symmetrization of the Berezin Star Product and Multiple Star Product Method
• Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space
• Effect of bulk Lorentz violation on anisotropic brane cosmologies
• A Twisted ${\mathcal{C}}^{\star }$-algebra formulation of Quantum Cosmology with application to the Bianchi I model
• Phenomenological studies in the matrix models
• Eight-dimensional non-geometric heterotic strings and enhanced gauge groups
• Quantization of Length in Spaces with Position-Dependent Noncommutativity
• Vacuum Pair Creation in Spin Noncommutative of Coordinates: Volkov Background and Constant Electric Field
• A note on the fuzzy sphere area spectrum, black hole luminosity, and the quantum nature of spacetime
• An Operator Approach To String Equations
• Deformed $C_{\lambda }$-Extended Heisenberg Algebra in Non-commutative Phase-Space
• Pauli energy spectrum for twist-deformed space-time
• Dbrane Phase Transitions and Monodromy in K-theory
• Dynamic and static properties of Quantum Hall and Harmonic Oscillator systems on the non-commutative plane
• From ${\mathrm{AdS}}_5$ to ${\mathrm{AdS}}_3$: TsT deformations, Magnetic fields and Holographic RG Flows
• Holographic Subregion Complexity and Fidelity Susceptibility in Noncommutative Yang--Mills Theory
• Spectral Zeta Functions in Non-Commutative Spacetimes