On Matrix Model Formulations of Noncommutative Yang-Mills Theories

Abstract

We study stability of noncommutative spaces in matrix models and discuss the continuum limit which leads to noncommutative Yang-Mills theories (NCYM). It turns out that most of noncommutative spaces in bosonic models are unstable. This indicates perturbative instability of fuzzy R^D pointed out by Van Raamsdonk and Armoni et al. persists to nonperturbative level in these cases. In this sense, these bosonic NCYM are not well-defined, or at least their matrix model formulations studied in this paper do not work. We also show that noncommutative backgrounds are stable in a supersymmetric matrix model deformed by a cubic Myers term, though the deformation itself breaks supersymmetry.

24 pages, no figure, reference added, minor corrections, to be published in PRD

References in corpus (68)

• The Large N Limit of Superconformal Field Theories and Supergravity
• String Theory and Noncommutative Geometry
• M Theory As A Matrix Model: A Conjecture
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Dielectric-Branes
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Noncommutative Perturbative Dynamics
• A Large-N Reduced Model as Superstring
• Noncommutative Solitons
• Noncommutative Yang-Mills in IIB Matrix Model
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Space-Time Structures from IIB Matrix Model
• Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature
• Lattice Gauge Fields and Discrete Noncommutative Yang-Mills Theory
• Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model
• Volume independence in large Nc QCD-like gauge theories
• Finite N Matrix Models of Noncommutative Gauge Theory
• Black hole thermodynamics from simulations of lattice Yang-Mills theory
• Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model
• Emergent Gravity from Noncommutative Gauge Theory
• Dynamical Aspects of Large N Reduced Models
• Large N BPS states and emergent quantum gravity
• Non-lattice simulation for supersymmetric gauge theories in one dimension
• Chirality and Dirac Operator on Noncommutative Sphere
• Convergent Yang-Mills Matrix Theories
• Stripes from (noncommutative) stars
• Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
• Emergent Gravity and Noncommutative Branes from Yang-Mills Matrix Models
• Describing Curved Spaces by Matrices
• UV/IR Mixing via Closed Strings and Tachyonic Instabilities
• The Meaning of Infrared Singularities in Noncommutative Gauge Theories
• Towards lattice simulation of the gauge theory duals to black holes and hot strings
• Strings from IIB Matrices
• Matrix Strings in pp-wave backgrounds from deformed Super Yang-Mills Theory
• Finite Gauge Theory on Fuzzy CP^2
• String Field Theory from IIB Matrix Model
• A Non-Perturbative Study of Gauge Theory on a Non-Commutative Plane
• Phase diagram and dispersion relation of the non-commutative λϕ^{4} model in d=3
• A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
• Symmetry Breaking In Twisted Eguchi-Kawai Models
• Ginsparg-Wilson Relation, Topological Invariants and Finite Noncommutative Geometry
• Effective Actions of Matrix Models on Homogeneous Spaces
• Phase structure of twisted Eguchi-Kawai model
• Breakdown of large-N quenched reduction in SU(N) lattice gauge theories
• Dynamical aspects of the fuzzy CP${}^2$ in the large $N$ reduced model with a cubic term
• Monte Carlo Simulation of a NC Gauge Theory on The Fuzzy Sphere
• Perturbative versus nonperturbative dynamics of the fuzzy S^2*S^2
• Perturbative dynamics of fuzzy spheres at large N
• Field Equations of Massless Fields in the New Interpretation of the Matrix Model
• Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres
• Stability of Fuzzy S^2 x S^2 x S^2 in IIB Type Matrix Models
• Probing the fuzzy sphere regularisation in simulations of the 3d λϕ^4 model
• Exact fuzzy sphere thermodynamics in matrix quantum mechanics
• Absence of a fuzzy $S^4$ phase in the dimensionally reduced 5d Yang-Mills-Chern-Simons model
• Regularization of Non-commutative SYM by Orbifolds with Discrete Torsion and SL(2,Z) Duality
• Fuzzy Torus in Matrix Model
• Fuzzy Spacetime with SU(3) Isometry in IIB Matrix Model
• Localization for Yang-Mills Theory on the Fuzzy Sphere
• Yang-Mills Matrix Theory
• Graviton Propagators on Fuzzy G/H
• N=2 3d-Matrix Integral with Myers Term
• $\beta$-deformation for matrix model of M-theory
• Curved Superspaces and Local Supersymmetry in Supermatrix Model
• Adding a Myers Term to the IIB Matrix Model
• Topology Change From Quantum Instability of Gauge Theory on Fuzzy CP^2
• Towards Noncommutative Fuzzy QED
• One-loop renormalization of general noncommutative Yang-Mills field model coupled to scalar and spinor fields
• Regularization of the Covariant Derivative on Curved Space by Finite Matrices

Cited by in corpus (15)

• Exact lattice supersymmetry
• Emergent Gravity and Noncommutative Branes from Yang-Mills Matrix Models
• Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N
• Large-N reduction in QCD-like theories with massive adjoint fermions
• A proposal of a fine tuning free formulation of 4d N=4 super Yang-Mills
• Matrix Model Approach to Cosmology
• Covariant Field Equations, Gauge Fields and Conservation Laws from Yang-Mills Matrix Models
• Toward simulating Superstring/M-theory on a quantum computer
• Large-N reduced models of supersymmetric quiver, Chern-Simons gauge theories and ABJM
• Four-dimensional N=1 super Yang-Mills from matrix model
• An object oriented code for simulating supersymmetric Yang--Mills theories
• What lattice theorists can do for superstring/M-theory
• Finite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions
• Impact of Supersymmetry on Emergent Geometry in Yang-Mills Matrix Models II
• Deformed matrix models, supersymmetric lattice twists and N=1/4 supersymmetry