Matrix Models in Homogeneous Spaces

Abstract

We investigate non-commutative gauge theories in homogeneous spaces G/H. We construct such theories by adding cubic terms to IIB matrix model which contain the structure constants of G. The isometry of a homogeneous space, G must be a subgroup of SO(10) in our construction. We investigate CP^2=SU(3)/U(2) case in detail which gives rise to 4 dimensional non-commutative gauge theory. We show that non-commutative gauge theory on R^4 can be realized in the large N limit by letting the action approach IIB matrix model in a definite way. We discuss possible relevances of these theories to the large N limit of IIB matrix model.

21 pages, sign errors in one loop effective action are corrected

Cited by in corpus (50)

• Emergent Gravity from Noncommutative Gauge Theory
• Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
• A Gauge-Invariant UV-IR Mixing and The Corresponding Phase Transition For U(1) Fields on the Fuzzy Sphere
• Effective Actions of Matrix Models on Homogeneous Spaces
• Intersecting branes and a standard model realization in matrix models
• Monopole Bundles over Fuzzy Complex Projective Spaces
• Dimensional Hierarchy in Quantum Hall Effects on Fuzzy Spheres
• Quantum Corrections on Fuzzy Sphere
• Dynamical aspects of the fuzzy CP${}^2$ in the large $N$ reduced model with a cubic term
• Stability of fuzzy $S^2\times S^2$ geometry in IIB matrix model
• Fiber Bundles and Matrix Models
• On the Origin of the UV-IR Mixing in Noncommutative Matrix Geometry
• On Higher Dimensional Fuzzy Spherical Branes
• Gauge Theory on Fuzzy S^2 x S^2 and Regularization on Noncommutative R^4
• Fuzzy 5-spheres and pp-wave Matrix Actions
• Perturbative versus nonperturbative dynamics of the fuzzy S^2*S^2
• Giant Gravitons and Fuzzy CP^2
• Perturbative dynamics of fuzzy spheres at large N
• 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
• 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
• Emergent Geometry from Quantized Spacetime
• N=4 Supersymmetric Yang-Mills on S^3 in Plane Wave Matrix Model at Finite Temperature
• A Novel Large-N Reduction on S^3: Demonstration in Chern-Simons Theory
• Dolan-Grady Relations and Noncommutative Quasi-Exactly Solvable Systems
• Curved-space classical solutions of a massive supermatrix model
• Fuzzy Spacetime with SU(3) Isometry in IIB Matrix Model
• On Lie-algebraic solutions of the type IIB matrix model
• Myers Effect and Tachyon Condensation
• Large N reduction on coset spaces
• Higher-Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions
• N=2 3d-Matrix Integral with Myers Term
• Graviton Propagators on Fuzzy G/H
• Graviton Propagators in Supergravity and Noncommutative Gauge Theory
• Correlators of Matrix Models on Homogeneous Spaces
• Two-Dimensional Gauge Theory and Matrix Model
• Adding a Myers Term to the IIB Matrix Model
• Wilson Line Correlators in N=4 Non-commutative Gauge Theory on S^2 x S^2
• Explicit Formulae for Noncommutative Deformations of CP^N and CH^N
• Effective Actions of IIB Matrix Model on S^3
• The Fuzzy S^4 by Quantum Deformation
• Gauge Theories in Noncommutative Homogeneous Kähler Manifolds
• D-branes Wrapped on Fuzzy del Pezzo Surfaces
• Dimensional oxidization on coset space
• Superstring vertex operators in type IIB matrix model
• The instability of intersecting fuzzy spheres
• Quantum corrections of (fuzzy) spacetimes from a supersymmetric reduced model with Filippov 3-algebra
• D-dependence of gap between critical temperatures in one-dimensional gauge theories
• Matrix equations and trilinear commutation relations